diff --git a/.github/gh-disabled-workflows/python-publish-test.yml b/.github/gh-disabled-workflows/python-publish-test.yml
index 17ead9c..c67e4aa 100644
--- a/.github/gh-disabled-workflows/python-publish-test.yml
+++ b/.github/gh-disabled-workflows/python-publish-test.yml
@@ -17,7 +17,7 @@ jobs:
     - name: Set up Python
       uses: actions/setup-python@v2
       with:
-        python-version: '3.8'
+        python-version: '3.12'
     - name: Install dependencies
       run: |
         python -m pip install --upgrade pip
diff --git a/.github/workflows/directory_writer.yml b/.github/workflows/directory_writer.yml
index b469e47..d164300 100644
--- a/.github/workflows/directory_writer.yml
+++ b/.github/workflows/directory_writer.yml
@@ -14,10 +14,10 @@ jobs:
     runs-on: ubuntu-latest
 
     steps:
-      - uses: actions/checkout@v2
-      - uses: actions/setup-python@v2
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v4
         with:
-          python-version: 3.8
+          python-version: 3.12
 
       - name: Write DIRECTORY.md
         run: |
@@ -27,7 +27,7 @@ jobs:
         uses: EndBug/add-and-commit@v4
         with:
           author_name: Martin Röbke
-          author_email: martin.roebke@tu-dresden.de
+          author_email: martin.roebke@web.de
           message: "Automatic Update: DIRECTORY.md"
           add: "DIRECTORY.md"
         env:
diff --git a/.github/workflows/python-app.yml b/.github/workflows/python-app.yml
index 4ed47f0..7bf067d 100644
--- a/.github/workflows/python-app.yml
+++ b/.github/workflows/python-app.yml
@@ -5,64 +5,93 @@ name: Tests
 
 on:
   push:
-    branches: [ master ]
+    branches: [master]
     paths-ignore:
-    - 'doc/**'
-    - 'gh-disabled-workflows/**'
-    - '*.md'
+      - "doc/**"
+      - "gh-disabled-workflows/**"
+      - "*.md"
   pull_request:
-    branches: [ master ]
+    branches: [master]
     paths-ignore:
-    - 'doc/**'
-    - 'gh-disabled-workflows/**'
-    - '*.md'
+      - "doc/**"
+      - "gh-disabled-workflows/**"
+      - "*.md"
+
+env:
+  graphviz-version: "12.2.1"
+  pg-version: "16"
 
 jobs:
   linux_and_coverage:
-    
     runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        python-version: ["3.8", "3.12"]
 
     steps:
-    - uses: actions/checkout@v4
-      
-    - name: Set up Python 3.8
-      uses: actions/setup-python@v2
-      with:
-        python-version: 3.8
-
-    - name: Install Workflow dependencies
-      run: |
-        python -m pip install --upgrade pip
-        pip install wheel
-        pip install flake8 flake8-import-order pytest coverage
-
-    - name: Install project dependencies
-      run: |
-        pip install .[test]
-
-    - name: Lint with flake8
-      run: |
-        # stop the build if there are Python syntax errors or undefined names
-        flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics
-        # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide
-        flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics
-
-    - name: graphviz for visualization test
-      run: |
-        sudo apt-get update && sudo apt-get install -yq graphviz
-
-    - name: Test with coverage & pytest
-      run: |
-        coverage run --source=tdvisu -m pytest .
-        coverage xml
-
-    - name: Upload coverage to Codecov
-      uses: codecov/codecov-action@v1
-      with:
-        token: ${{ secrets.CODECOV_TOKEN }}
-        file: ./coverage.xml
-        flags: unittests
-
+      - uses: actions/checkout@v4
+
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: actions/setup-python@v5
+        with:
+          python-version: ${{ matrix.python-version }}
+
+      - name: Get Graphviz
+        working-directory: ..
+        run: |
+          wget -nv "https://gitlab.com/api/v4/projects/4207231/packages/generic/graphviz-releases/${{ env.graphviz-version }}/graphviz-${{ env.graphviz-version }}.tar.gz"
+          graphviz_12_sha256="242bc18942eebda6db4039f108f387ec97856fc91ba47f21e89341c34b554df8  graphviz-${{ env.graphviz-version }}.tar.gz"
+          if [[ "$(sha256sum graphviz-${{ env.graphviz-version }}.tar.gz)" != "$graphviz_12_sha256" ]]; then
+            echo "The file is corrupted, calculated_hash: $calculated_hash"
+            exit 1
+          fi
+          # extract
+          tar -xzf graphviz-${{ env.graphviz-version }}.tar.gz
+          # dev dependencies
+          sudo apt-get install -y build-essential pkg-config libgraphviz-dev libperl-dev libsodium-dev libargon2-dev libgts-dev
+
+      - name: Install Graphviz
+        working-directory: ..
+        run: |
+          cd graphviz-${{ env.graphviz-version }}
+          ./configure --prefix=$PWD/out --with-gts
+          make --quiet
+          make install --quiet
+          echo "$PWD/out/bin" >> "$GITHUB_PATH"
+          echo "LD_LIBRARY_PATH=$PWD/out/lib" >> "$GITHUB_ENV"
+
+      - name: Install Workflow dependencies
+        run: |
+          python -m pip install --upgrade pip
+          pip install wheel
+          pip install flake8 flake8-import-order pytest coverage
+
+      - name: Install project dependencies
+        run: |
+          pip install .[test]
+
+      - name: Lint with flake8
+        run: |
+          # stop the build if there are Python syntax errors or undefined names
+          flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics
+          # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide
+          flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics
+
+      - name: Test with coverage & pytest
+        run: |
+          dot -V
+          which coverage
+          which dot
+          which pytest
+          coverage run --source=tdvisu -m pytest .
+          coverage xml
+
+      - name: Upload coverage to Codecov
+        uses: codecov/codecov-action@v5
+        with:
+          token: ${{ secrets.CODECOV_TOKEN }}
+          files: ./coverage.xml
+          flags: unittests
 
   other_os_tests:
     strategy:
@@ -73,61 +102,52 @@ jobs:
     continue-on-error: true
 
     steps:
-    - uses: actions/checkout@v4
-      
-    - name: Set up Python 3.8
-      uses: actions/setup-python@v2
-      with:
-        python-version: 3.8
-
-    - name: Install Workflow dependencies
-      run: |
-        python -m pip install --upgrade pip
-        pip install wheel
-
-    - name: Install graphviz for visualization test
-      if: ${{ runner.os == 'macOS' }}
-      uses: ts-graphviz/setup-graphviz@v2
-      with:
-        macos-skip-brew-update: 'true' # default false
-
-    - name: Setup Conda
-      if: ${{ runner.os == 'Windows' }}
-      uses: s-weigand/setup-conda@v1
-      with:
-        # Whether to activate the conda base env (Default: 'true')
-        activate-conda: true
-        # Python version which should be installed with conda (default: 'Default')
-        python-version: 3.8
-
-    - name: Install graphviz via conda
-      if: ${{ runner.os == 'Windows' }}
-      run: |
-        conda install -c anaconda graphviz
-
-    - name: add graphviz PATH
-      if: ${{ runner.os == 'Windows' }}
-      run: |
-        # should give base conda python
-        $python=Get-Command python
-        $pypath=Split-Path $python.Source -Parent
-        # Add to PATH, we know pypath is on it
-        $dot=[IO.Path]::Combine($pypath, 'Library', 'bin', 'graphviz')
-        echo $dot | Out-File -FilePath $env:GITHUB_PATH -Encoding utf8 -Append
-      shell: powershell
-
-    - name: register plugins for graphviz
-      if: ${{ runner.os == 'Windows' }}
-      run: |
-        # execute dot
-        dot -V
-        dot -c
-
-    - name: Install project dependencies
-      run: |
-        pip install .[test]
-
-    - name: Test with pytest
-      run: |
-        # Tests reside in folder 'test'
-        pytest ./test
+      - uses: actions/checkout@v4
+
+      - name: Set up Python 3.12
+        uses: actions/setup-python@v5
+        with:
+          python-version: 3.12
+
+      - name: Install workflow dependencies
+        run: |
+          python -m pip install --upgrade pip
+          pip install wheel
+
+      - name: Brew install PostgreSQL ${{ env.pg-version }}
+        if: runner.os == 'MacOS'
+        run: |
+          brew install libpq postgresql@${{ env.pg-version }}
+          # make available on PATH
+          pgpath="/opt/homebrew/opt/postgresql@${{ env.pg-version }}/bin"
+          echo $pgpath >> "$GITHUB_PATH"
+          ls "$pgpath"
+          $pgpath/pg_config --version
+
+      - name: Add PostgreSQL to PATH
+        if: runner.os == 'Windows'
+        shell: pwsh
+        run: |
+          echo "$env:PGBIN" >> "$env:GITHUB_PATH"
+          pg_config --version
+
+      - name: Setup Graphviz
+        uses: ts-graphviz/setup-graphviz@v2
+        with:
+          macos-skip-brew-update: "true" # default false
+          windows-graphviz-version: ${{ env.graphviz-version }}
+
+      - name: Register plugins for Graphviz
+        if: runner.os == 'Windows'
+        run: |
+          dot -V
+          dot -c
+
+      - name: Install project dependencies
+        run: |
+          pip install .[test]
+
+      - name: Test with pytest
+        run: |
+          # Tests reside in folder 'test'
+          pytest ./test
diff --git a/.github/workflows/python-publish.yml b/.github/workflows/python-publish.yml
index afe077d..f58e6af 100644
--- a/.github/workflows/python-publish.yml
+++ b/.github/workflows/python-publish.yml
@@ -9,23 +9,22 @@ on:
 
 jobs:
   deploy:
-
     runs-on: ubuntu-latest
 
     steps:
-    - uses: actions/checkout@v2
-    - name: Set up Python
-      uses: actions/setup-python@v2
-      with:
-        python-version: '3.8'
-    - name: Install dependencies
-      run: |
-        python -m pip install --upgrade pip
-        pip install setuptools wheel twine
-    - name: Build and publish
-      env:
-        TWINE_USERNAME: ${{ secrets.PYPI_USERNAME }}
-        TWINE_PASSWORD: ${{ secrets.PYPI_PASSWORD }}
-      run: |
-        python setup.py sdist bdist_wheel
-        twine upload dist/*
+      - uses: actions/checkout@v4
+      - name: Set up Python
+        uses: actions/setup-python@v5
+        with:
+          python-version: "3.12"
+      - name: Install dependencies
+        run: |
+          python -m pip install --upgrade pip
+          pip install 'build[virtualenv]'
+      - name: Build and publish
+        env:
+          TWINE_USERNAME: ${{ secrets.PYPI_USERNAME }}
+          TWINE_PASSWORD: ${{ secrets.PYPI_PASSWORD }}
+        run: |
+          python -m build
+          twine upload dist/*
diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5abb84a..4cdcde4 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -2,89 +2,140 @@
 
 All notable changes to this project will be documented in this file.
 
-The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/ ), and this
-project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html ).
+The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), and this
+project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
 ## [Unreleased]
+
 - No unreleased changes yet.
 
+## [1.2.0] - 2024-12-24
+
+### Added
+
+- Testsetup with python-version: `3.12` while maintaining `3.8 compatibility`
+- Specifying `psycopg[c]` for distribution: https://www.psycopg.org/psycopg3/docs/basic/install.html#local-installation
+  See [Installation](https://www.psycopg.org/psycopg3/docs/basic/install.html#installation) for the other options.
+- Several improvements and specifications to `.github\workflows\python-app.yml`
+
+### Changed
+
+See [#47]
+
+- Updated GitHub Actions [#48]
+  - Replacing installation of `setuptools` with
+    > pip install 'build[virtualenv]'
+  - Replacing old `python setup.py sdist bdist_wheel` with
+    > python -m build
+- Updated `author_email` to <martin.roebke@web.de>
+- Update and format `setup.py`
+- Updated tests for graphviz-version: `12.2.1` from usually version `2` before. Changed the output files slightly with the test settings. They look a bit cleaner, see also their https://gitlab.com/graphviz/graphviz/-/blob/main/CHANGELOG.md
+- Upgrade code for
+  - [psycopg](https://pypi.org/project/psycopg)==3.2.3 \
+    Update _wait for good connection_, replacing the `good_db_status()` method with **pg.pq.ConnStatus.OK**
+  - [pytest](https://pypi.org/project/pytest)==8.3.4
+- Updated requirements.txt
+- Updated stable-requirements.txt
+
 ## [1.1.9] - 2023-07-27
 
 ### Added
+
 - `python-benedict[xml]` to dependencies
+
 ### Changed
+
 - Updated requirements.txt
 - Updated stable-requirements.txt
 
-
 ## [1.1.8] - 2021-05-04
 
 ### Changed
+
 - Updated pyyaml from 5.3.1 to 5.4 [#33]
 - Updated py from 1.9.0 to 1.10.0 [#35]
 - Fixed python-app.yml [#34]
 
 ## [1.1.7] - 2020-09-13
+
 ### Added
+
 - Better tests around the (Dimacs) Reader
 
 ### Changed
+
 - Improved the SQL queries with explicit formats [#32]
 - Improved Readme sections for install and usage
 
 ## [1.1.6] - 2020-08-01
+
 ### Added
-- Added better property based testing with *hypothesis* [#29]
+
+- Added better property based testing with _hypothesis_ [#29]
 - Added jobs and setups to test on macos and windows [#31]
 
 ### Changed
-- *do_sort_nodes* now sorts in correct numeric order. [commit cdfcf6](https://github.com/VaeterchenFrost/tdvisu/commit/cdfcf6c332a63f05b499fe133fada4473ad7524c )
+
+- _do_sort_nodes_ now sorts in correct numeric order. [commit cdfcf6](https://github.com/VaeterchenFrost/tdvisu/commit/cdfcf6c332a63f05b499fe133fada4473ad7524c)
 - Fixed some import orders
 
 ## [1.1.5] - 2020-07-17
+
 ### Added
+
 - Added many new tests.
 - Hints for not covered code lines.
 
 ### Changed
+
 - Simplified code to parse commandline flags while removing duplications in code.
 - Entrypoint for modules visualization and construct_dpdb_visu is now in init().
 - Some improvements in utilities.solution_node
 
 ## [1.1.4] - 2020-07-14
+
 ### Added
+
 - Added the possibility to specify and create multiple graph-visualizations in one file [#25]
-- Added test case *test_vc_multiple_and_join* in [commit aa31901](https://github.com/VaeterchenFrost/tdvisu/commit/aa319016ac71f9a54023474bf820cb30929c52a8 )
-- Added test cases for [construct_dpdb_visu](https://github.com/VaeterchenFrost/tdvisu/blob/master/test/test_construct_dpdb.py )
+- Added test case _test_vc_multiple_and_join_ in [commit aa31901](https://github.com/VaeterchenFrost/tdvisu/commit/aa319016ac71f9a54023474bf820cb30929c52a8)
+- Added test cases for [construct_dpdb_visu](https://github.com/VaeterchenFrost/tdvisu/blob/master/test/test_construct_dpdb.py)
 - Add pytest-mock to tests_require
 
 ### Changed
-- Simplified and refactored TDVisu.schema.json 
-- Schema now includes possibility to specify multiple instances of generalGraph and incidenceGraph 
+
+- Simplified and refactored TDVisu.schema.json
+- Schema now includes possibility to specify multiple instances of generalGraph and incidenceGraph
 - Revisited doc/JsonAPI.md to now include all parameters available
 - Renamed test folder expected_images to expected_files
 - Updated stable-requirements.txt
 - Several minor improvements
 
 ## [1.1.3] - 2020-07-09
+
 ### Added
-- Added *TDVisu.schema.json* to validate the Json-API for TDVisu [#24]
+
+- Added _TDVisu.schema.json_ to validate the Json-API for TDVisu [#24]
 - Added 'col' to allowed formats in tw reader (default string in Mathematica)
 
 ### Changed
+
 - Fixed error where database configuration was not found in the directory
 - Fixed missing double quotation marks in JsonAPI.md
-- Moved JsonAPI.md → *doc/JsonAPI.md*
+- Moved JsonAPI.md → _doc/JsonAPI.md_
 
 ### Removed
-- Removed *generalGraph* and *incidenceGraph* from required arguments in API
+
+- Removed _generalGraph_ and _incidenceGraph_ from required arguments in API
 
 ## [1.1.2] - 2020-06-26
+
 ### Added
+
 - Tests for visualization.py using graphviz in the Github Action too
 - Tests for reader.py
 
 ### Changed
+
 - Fixed typo that prevented joining SVG in visualization
 - Fixed cases where logging.yml was not found in the working directory
 - Now using pathlib.Path for most file-related operations
@@ -92,80 +143,98 @@ project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html ).
 - Added more type hints and improved existing ones
 
 ## [1.1.1] - 2020-06-25
+
 ### Added
-- Added problem type **Sat** to tdvisu/construct_dpdb_visu.py 
+
+- Added problem type **Sat** to tdvisu/construct_dpdb_visu.py
 - Added testcases in file test/test_dijkstra.py
 
 ### Changed
-- JsonAPI.md is now updated with snake_case names and consistent with visualization_data.py 
-- Fixed default value for svg-join **v_top** to *None* from *'top'*
+
+- JsonAPI.md is now updated with snake_case names and consistent with visualization_data.py
+- Fixed default value for svg-join **v_top** to _None_ from _'top'_
 - Improved flexibility in several function parameters
 - Improved documentation and comments in several places
-- Fixed passing parameters to method *setup_tree_dec_graph*
+- Fixed passing parameters to method _setup_tree_dec_graph_
 
 ### Removed
-- Removed old dependency from  tdvisu/dijkstra.py on utilities
+
+- Removed old dependency from tdvisu/dijkstra.py on utilities
 
 ## [1.1.0] - 2020-06-07
+
 ### Added
+
 - Added file utilities.py with several static or shared things like
-    - Constants: CFG_EXT, LOGLEVEL_EPILOG, DEFAULT_LOGGING_CFG 
-    - Methods: 
-        - flatten
-        - read_yml_or_cfg combining yaml, json, cfg reader in one
-        - logging_cfg configure logging with file or DEFAULT_LOGGING_CFG 
-        - helper convert_to_adj from dijkstra.py
-        - add_edge_to (edges and adj list)
-        - gen_arg infinite Generator
-    - Styles:
-        - base_style, emphasise_node, style_hide_node, style_hide_edge
-    - Graph manipulation:
-        - bag_node
-        - solution_node
+
+  - Constants: CFG_EXT, LOGLEVEL_EPILOG, DEFAULT_LOGGING_CFG
+  - Methods:
+    - flatten
+    - read_yml_or_cfg combining yaml, json, cfg reader in one
+    - logging_cfg configure logging with file or DEFAULT_LOGGING_CFG
+    - helper convert_to_adj from dijkstra.py
+    - add_edge_to (edges and adj list)
+    - gen_arg infinite Generator
+  - Styles:
+    - base_style, emphasise_node, style_hide_node, style_hide_edge
+  - Graph manipulation:
+    - bag_node
+    - solution_node
 
 - Added file logging.yml (and .ini) with logging configuration for the module [#20]
 - Added half the tests for utilities.py
 
 ### Changed
+
 - Changed path of image SharpSatExample to the absolute URL for [PyPI].
 - Changed names of loggers to absolute name. Should be easy to adjust if needed.
 - Changed logging defaults and config in tdvisu/visualization.py and construct_dpdb_visu.py
 - Updated ArgumentParser help
-- Some fixes of code-style or variable names. 
+- Some fixes of code-style or variable names.
 
 ## [1.0.1] - 2020-06-04
+
 ### Added
+
 - Codecoverage with [Codecov]
 
 ### Changed
+
 - Changed path of image SharpSatExample to the absolute URL for [PyPI].
 
 ## [1.0.0] - 2020-06-04
+
 ### Added
+
 - Added svgjoin parameters to JsonAPI [#6]
 - Added call to svgjoin from visualization.py
 - Added workflow to display the sourcecode-files in [DIRECTORY]
 
-### Changed 
+### Changed
+
 - Moved JsonAPI and conda_packages to /doc
 - Updated arguments in svgjoin to be more flexible for multiple joins [#11]
 - Fixed scaling mechanism in svgjoin [#13]
 - Changed tests from unittest to pytest [#12]
 
 ### Removed
+
 - Changelog in JsonAPI.md
 
 ## [0.5.1] - 2020-06-01
+
 ### Added
+
 - Added publishing Action to [PyPI] [#4]
 
 ### Changed
+
 - Changed setup.py with more documentation and simpler functionality.
 - Updated Readme with a guide on how to use construct_dpdb_visu [#2]
 
 ### Removed
-- Removed publishing Action to testpypi [#4]
 
+- Removed publishing Action to testpypi [#4]
 
 ## [0.5.0-dev1] - 2020-06-01
 
@@ -177,10 +246,12 @@ project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html ).
 - Added README to tdvisu directly
 
 ### Changed
+
 - Fixed usage of `__version__` in tdvisu/construct_dpdb_visu.py
 
 ### Removed
-- Removed individual versioning 
+
+- Removed individual versioning
 
 [#1]: https://github.com/VaeterchenFrost/tdvisu/issues/1
 [#2]: https://github.com/VaeterchenFrost/tdvisu/issues/2
@@ -199,15 +270,16 @@ project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html ).
 [#33]: https://github.com/VaeterchenFrost/tdvisu/pull/33
 [#34]: https://github.com/VaeterchenFrost/tdvisu/pull/34
 [#35]: https://github.com/VaeterchenFrost/tdvisu/pull/35
-
+[#47]: https://github.com/VaeterchenFrost/tdvisu/pull/47
+[#48]: https://github.com/VaeterchenFrost/tdvisu/issues/48
 [@VaeterchenFrost]: https://github.com/VaeterchenFrost
 [PyPI]: https://pypi.org/project/tdvisu/
 [mypy]: https://github.com/python/mypy
 [DIRECTORY]: https://github.com/VaeterchenFrost/tdvisu/blob/master/DIRECTORY.md
 [Codecov]: https://codecov.io/gh/VaeterchenFrost/tdvisu
-
-[Unreleased]: https://github.com/VaeterchenFrost/tdvisu/compare/v1.1.9...master
-[1.1.8]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.1.9
+[Unreleased]: https://github.com/VaeterchenFrost/tdvisu/compare/v1.2.0...master
+[1.2.0]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.2.0
+[1.1.9]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.1.9
 [1.1.8]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.1.8
 [1.1.7]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.1.7
 [1.1.6]: https://github.com/VaeterchenFrost/tdvisu/releases/tag/v1.1.6
diff --git a/README.md b/README.md
index dbdfc21..2f724ef 100644
--- a/README.md
+++ b/README.md
@@ -1,20 +1,19 @@
 # TdVisu
+
 ![Maintenance](https://img.shields.io/badge/Maintained%3F-yes-green.svg)
 [![PyPI license](https://img.shields.io/pypi/l/tdvisu.svg)](https://pypi.python.org/pypi/tdvisu/)
-![Tests](https://github.com/VaeterchenFrost/tdvisu/workflows/Tests/badge.svg) 
+![Tests](https://github.com/VaeterchenFrost/tdvisu/workflows/Tests/badge.svg)
 [![codecov](https://codecov.io/gh/VaeterchenFrost/tdvisu/branch/master/graph/badge.svg)](https://codecov.io/gh/VaeterchenFrost/tdvisu)
 
-
 ![GitHub release (latest SemVer including pre-releases)](https://img.shields.io/github/v/release/vaeterchenfrost/tdvisu?include_prereleases)
 [![PyPI version fury.io](https://badge.fury.io/py/tdvisu.svg)](https://pypi.python.org/pypi/tdvisu/)
+![GitHub commits since latest release (by SemVer)](https://img.shields.io/github/commits-since/VaeterchenFrost/tdvisu/latest)
 [![PyPI status](https://img.shields.io/pypi/status/tdvisu.svg)](https://pypi.python.org/pypi/tdvisu/)
 [![PyPI pyversions](https://img.shields.io/pypi/pyversions/tdvisu.svg)](https://pypi.python.org/pypi/tdvisu/)
 ![PyPI - Wheel](https://img.shields.io/pypi/wheel/tdvisu)
-![GitHub repo size](https://img.shields.io/github/repo-size/VaeterchenFrost/tdvisu)
 ![GitHub code size in bytes](https://img.shields.io/github/languages/code-size/VaeterchenFrost/tdvisu)
-![GitHub commits since latest release (by SemVer)](https://img.shields.io/github/commits-since/VaeterchenFrost/tdvisu/latest)
 
-----------
+---
 
 Visualization for [dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming) on [tree decompositions](https://en.wikipedia.org/wiki/Tree_decomposition).
 
@@ -28,55 +27,69 @@ For the portable and light weight '.svg' format, all graphs for a timestep can b
 
 With the '.svg' format the images are highly customizable, and even combining several timesteps together using svg [animate](https://developer.mozilla.org/en-US/docs/Web/SVG/Element/animate) would be an option in the future.
 
-----------
+---
 
 # Using
-[Alubbock:Graphviz](https://anaconda.org/alubbock/graphviz) (or [Graphviz (>=2.38)](https://graphviz.gitlab.io/download/))
 
-[python-benedict](https://pypi.org/project/python-benedict/)
+> Note: see also the steps prepared in the CI/CD [.github/workflows/python-app.yml](https://github.com/VaeterchenFrost/tdvisu/actions/workflows/python-app.yml):
+
+[Graphviz (>=2.38)](https://graphviz.gitlab.io/download/). Be aware of changes in default layouts over different major versions of Graphviz. The project currently tests with `graphviz-version: "12.2.1"`.
 
-[for dpdb: psycopg2 (2.8.5)](https://www.psycopg.org/docs/index.html)
+[python-benedict[xml]](https://pypi.org/project/python-benedict/)
 
-----------
+PostgreSQL adapter for Python: [psycopg (3)](https://www.psycopg.org/docs/index.html)
+
+---
 
 # To register the graphviz plugins
+
 https://gitlab.com/graphviz/graphviz/-/issues/1352
+
 ```shell
 dot.exe -c
 ```
 
 # To install
 
-In a command prompt with pip (to get *pip* see: https://pip.pypa.io/en/stable/) installed:
+In a command prompt with pip (to get _pip_ see: https://pip.pypa.io/en/stable/) installed:
 Just run
+
 ```shell
 pip install -h (for more information on install options)
 pip install tdvisu
 ```
 
 To download the latest version from the default branch:
+
 ```shell
 git clone --depth 1 --single https://github.com/VaeterchenFrost/tdvisu
 ```
 
 # To isolate the dependencies
 
-With [virtualenv](https://virtualenv.pypa.io/en/latest/installation.html ) on the system installed you can isolate the environment, for example
+With [virtualenv](https://virtualenv.pypa.io/en/latest/installation.html) on the system installed you can isolate the environment, for example
+
 ```shell
-virtualenv tdvisu_dir -p 3.8
+virtualenv tdvisu_dir -p 3.12
 cd tdvisu_dir/bin/
 source activate
+# Windows: ./tdvisu_dir/Scripts/activate
 ```
+
 With [Conda](https://docs.conda.io/en/latest/) on the system installed the dependencies for this project can be automatically installed in a new environment:
 
 Go to the projects base directory.
 
-Open a *conda-command-prompt* with admin privileges and run the commands from the project folder
+Open a _conda-command-prompt_ with admin privileges and run the commands from the project folder
+
 - to create a new environment with basic dependencies:
+
 ```shell
-conda env create -f .\environment.yml
+conda env create -f ./environment.yml
 ```
+
 - to activate the environment:
+
 ```shell
 conda activate tdvisu
 ```
@@ -84,117 +97,130 @@ conda activate tdvisu
 # Install from source
 
 To clone the complete repository:
+
 ```shell
 git clone https://github.com/VaeterchenFrost/tdvisu
 ```
 
 To download only the latest version from the default branch:
+
 ```shell
 git clone --depth 1 --single https://github.com/VaeterchenFrost/tdvisu
 ```
 
 To install the project from the source folder:
+
 ```shell
 pip install -h (for more information on install options)
 pip install .
 ```
+
 to confirm that the visualization finds all dependencies:
+
 ```shell
-python .\tdvisu\visualization.py -h
+python ./tdvisu/visualization.py -h
 ```
+
 to run all tests:
+
 ```shell
-pip install .[test] 
-pytest .\test\
+pip install .[test]
+pytest ./test/
 ```
 
-----------
+---
 
 # How to use
 
 The visualization needs input in the form of the [Json API](https://github.com/VaeterchenFrost/gpusat-VISU/blob/master/JsonAPI_v1.3.md).
-The creation of this file is exemplary implemented in *construct_dpdb_visu.py* or the fork [GPUSAT](https://github.com/VaeterchenFrost/GPUSAT) and *--visufile filename* (optionally disabling preprocessing with *-p*).
+The creation of this file is exemplary implemented in _construct_dpdb_visu.py_ or the fork [GPUSAT](https://github.com/VaeterchenFrost/GPUSAT) and _--visufile filename_ (optionally disabling preprocessing with _-p_).
 
 Run the python file with the above dependencies installed:
 [visualization.py](https://github.com/VaeterchenFrost/gpusat-VISU/blob/master/satvisualization_repo/satvisu/visualization.py)
 
 **visualization.py** takes two parameters, the json-**infile** to read from, and optionally one **outputfolder**.
-With both arguments a call from IPython might look like this:
+With both arguments a run might look like this:
 
-```python
-runfile('visualization.py', 
-args='visugpusat.json examplefolder')
+```shell
+python tdvisu/visualization.py visugpusat.json examplefolder
 ```
 
 For #SAT it produces for example three different graphs suffixed with a running integer to represent timesteps:
 
-+ *TDStep* the tree decomposition with solved nodes
-+ *PrimalGraphStep* the primal graph with currently active variables highlighted
-+ *IncidenceGraphStep* the bipartite incidence graph with active clauses/variables highlighted
+- _TDStep_ the tree decomposition with solved nodes
+- _PrimalGraphStep_ the primal graph with currently active variables highlighted
+- _IncidenceGraphStep_ the bipartite incidence graph with active clauses/variables highlighted
 
 The graphs are images encoded in resolution independent **.svg files** (see https://www.lifewire.com/svg-file-4120603)
 
 <p align="center"><img src="https://raw.githubusercontent.com/VaeterchenFrost/tdvisu/master/doc/images/combined6DA4.svg?sanitize=true" width="70%"/></p>
 
 ## How to use construct_dpdb_visu.py
+
 After installing the project [dp_on_dbs](https://github.com/hmarkus/dp_on_dbs) with the there listed [requirements](https://github.com/hmarkus/dp_on_dbs#requirements), we need to
+
 - edit the [database.ini](https://github.com/VaeterchenFrost/tdvisu/blob/master/tdvisu/database.ini) with our password to [postgresql](https://www.postgresql.org/)
 - Solve a problem with `python dpdb.py [GENERAL-OPTIONS] -f <INPUT-FILE> <PROBLEM> [PROBLEM-SPECIFIC-OPTIONS]`
-  - for the problem **VertexCover** 
+  - for the problem **VertexCover**
     - with flag `--gr-file` to store the htd Input (if the input was in a different format)
   - for the problem **SharpSat**
     - with flag `--store-formula` to store the formula in the database
-- Run 
+- Run
   - **Sat** / **SharpSat**: `python construct_dpdb_visu.py [PROBLEMNUMBER]`
-  - **VertexCover**: `python construct_dpdb_visu.py [PROBLEMNUMBER] --twfile [TWFILE]` 
-   with the file in DIMACS tw-format containing the edges of the graph.
+  - **VertexCover**: `python construct_dpdb_visu.py [PROBLEMNUMBER] --twfile [TWFILE]`
+    with the file in DIMACS tw-format containing the edges of the graph.
 
-# Installation of the psycopg2 package 
+# Installation of the psycopg package 
 
-See https://www.psycopg.org/docs/install.html#build-prerequisites
+See https://www.psycopg.org/psycopg3/docs/basic/install.html
 
-For example on linux today this might need
-`sudo apt install libpq-dev` 
-before completion.
+**Note** Whatever version of `libpq` psycopg is compiled with, it will be possible to connect to PostgreSQL servers of any [supported version](https://www.psycopg.org/docs/install.html#prerequisites): just install the most recent libpq version or the most practical, without trying to match it to the version of the PostgreSQL server you will have to connect to.
 
------------------
+---
 
 # New Release
 
 ## Version
+
 - Bump `/version.py` according to the changes made
-- Change date to the release day, keep format 
+- Change date to the release day, keep format
 
 ## Requirements
+
 In case dependencies have changed, or just to update some, check
-- *requirements.txt*
-- *stable-requirements.txt* (using `pip freeze`)
-- *setup.py*
+
+- _requirements.txt_
+- _stable-requirements.txt_ (using `pip freeze`)
+- _setup.py_
 
 ## Write Changelog.md
+
 - Add tag with link (see bottom for linking examples)
-- Add changes, maybe some are already in *Unreleased*
-- Update *Unreleased* with **(No) unreleased changes**
+- Add changes, maybe some are already in _Unreleased_
+- Update _Unreleased_ with **(No) unreleased changes**
 
 ## Review code
+
 - Run tests (pytest)
 - Check codestyle (pylint)
 
 ## Push
+
 - Push changes to master
 - Wait for all automated checks! (All checks have passed...)
 
 ## Create Release
-- On the GitHub page go to: Release, **[Draft a new release](https://github.com/VaeterchenFrost/tdvisu/releases/new )** 
+
+- On the GitHub page go to: Release, **[Draft a new release](https://github.com/VaeterchenFrost/tdvisu/releases/new)**
 - Enter v'YOUR VERSION NUMBER' as the tag.
 - Add a **Release Title** (could be just the version)
 - Add some description (like in the CHANGELOG.md)
 - Click on **Publish release** on the bottom
 
-## Should automatically release to [PyPI](https://pypi.org/project/tdvisu/ )
-- For details see: [Upload Python Package](https://github.com/VaeterchenFrost/tdvisu/blob/master/.github/workflows/python-publish.yml )
+## Should automatically release to [PyPI](https://pypi.org/project/tdvisu/)
 
-**Now you are set for the new release :tada:**
+- For details see: [Upload Python Package](https://github.com/VaeterchenFrost/tdvisu/blob/master/.github/workflows/python-publish.yml)
 
-----------
+**Now you are set for the new release :tada:**
 
+---
\ No newline at end of file
diff --git a/environment.yml b/environment.yml
index 7d705e8..b22d16c 100644
--- a/environment.yml
+++ b/environment.yml
@@ -1,8 +1,6 @@
 name: tdvisu
 channels:
-  - alubbock
   - defaults
 dependencies:
   - python>=3.8
-  - graphviz
   - setuptools
diff --git a/requirements.txt b/requirements.txt
index 7e53bb8..ea8c428 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,8 +1,8 @@
 graphviz~=0.20
-hypothesis~=6.82.0
-psycopg2-binary~=2.9.6
-python-benedict~=0.32.0
-python-benedict[xml]~=0.32.0
-pytest~=7.4.0
-pytest-mock~=3.11.0
+hypothesis~=6.122
+psycopg~=3.2.3
+pytest-mock~=3.14
+pytest~=8.3
+python-benedict[xml]~=0.34.0
 PyYAML~=6.0
+xmltodict~=0.14.2
diff --git a/scripts/build_directory_md.py b/scripts/build_directory_md.py
index ea2ceed..562bd4c 100644
--- a/scripts/build_directory_md.py
+++ b/scripts/build_directory_md.py
@@ -32,22 +32,24 @@
 
 URL_BASE = "https://github.com/VaeterchenFrost/tdvisu/blob/master"
 
-AFFECTED_EXT = ('.py', '.ipynb',)
+AFFECTED_EXT = (
+    ".py",
+    ".ipynb",
+)
 
-EXCLUDED_FILENAMES = ('__init__.py',)
+EXCLUDED_FILENAMES = ("__init__.py",)
 
 
-def good_file_paths(top_dir: str = '.') -> Iterator[str]:
+def good_file_paths(top_dir: str = ".") -> Iterator[str]:
     """Return relative path to files with extension in AFFECTED_EXT."""
     for dir_path, dir_names, filenames in os.walk(top_dir):
-        dir_names[:] = [d for d in dir_names
-                        if d != 'scripts' and d[0] not in '._']
+        dir_names[:] = [d for d in dir_names if d != "scripts" and d[0] not in "._"]
         for filename in filenames:
             if filename in EXCLUDED_FILENAMES:
                 continue
             if os.path.splitext(filename)[1] in AFFECTED_EXT:
                 normalized_path = os.path.normpath(dir_path)
-                if normalized_path != '.':
+                if normalized_path != ".":
                     yield os.path.join(normalized_path, filename)
                 else:
                     yield filename
@@ -68,19 +70,20 @@ def print_path(old_path: str, new_path: str) -> str:
     return new_path
 
 
-def print_directory_md(top_dir: str = '.') -> None:
+def print_directory_md(top_dir: str = ".") -> None:
     """Print the markdown for files with selected extensions recursing top_dir."""
-    old_path = ''
+    old_path = ""
     for filepath in sorted(good_file_paths(top_dir)):
         filepath, filename = os.path.split(filepath)
         if filepath != old_path:
             old_path = print_path(old_path, filepath)
         indent = (filepath.count(os.sep) + 1) if filepath else 0
-        url = '/'.join((URL_BASE, *[quote(part)
-                                    for part in (filepath, filename) if part]))
-        filename = os.path.splitext(filename.replace('_', ' ').title())[0]
+        url = "/".join(
+            (URL_BASE, *[quote(part) for part in (filepath, filename) if part])
+        )
+        filename = os.path.splitext(filename.replace("_", " ").title())[0]
         print(f"{md_prefix(indent)} [{filename}]({url})")
 
 
 if __name__ == "__main__":
-    print_directory_md('.')
+    print_directory_md(".")
diff --git a/setup.py b/setup.py
index fc50a90..69a2311 100644
--- a/setup.py
+++ b/setup.py
@@ -28,7 +28,7 @@ def read_files(files, delim: str = "\n") -> str:
     data = []
     try:
         for file in files:
-            with open(file, encoding='utf-8') as handle:
+            with open(file, encoding="utf-8") as handle:
                 data.append(handle.read())
     except IOError:
         pass
@@ -37,35 +37,43 @@ def read_files(files, delim: str = "\n") -> str:
 
 description = "Visualizing Dynamic Programming on Tree Decompositions."
 
-long_description = read_files(['README.md', 'CHANGELOG.md'])
+long_description = read_files(["README.md", "CHANGELOG.md"])
 
 classifiers = [
-    'Development Status :: 4 - Beta',
-    'Environment :: Console',
-    'Intended Audience :: Science/Research',
-    'Intended Audience :: Education',
-    'Intended Audience :: Developers',
-    'Operating System :: OS Independent',
-    'License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+)',
-    'Programming Language :: Python :: 3',
-    'Programming Language :: Python :: 3.8',
-    'Topic :: Scientific/Engineering :: Visualization',
-    'Topic :: Multimedia :: Graphics :: Presentation']
+    "Development Status :: 4 - Beta",
+    "Environment :: Console",
+    "Intended Audience :: Science/Research",
+    "Intended Audience :: Education",
+    "Intended Audience :: Developers",
+    "Operating System :: OS Independent",
+    "License :: OSI Approved :: GNU General Public License v3 or later (GPLv3+)",
+    "Programming Language :: Python :: 3",
+    "Programming Language :: Python :: 3.12",
+    "Topic :: Scientific/Engineering :: Visualization",
+    "Topic :: Multimedia :: Graphics :: Presentation",
+]
 
-tests_require = ['hypothesis', 'pytest', 'pytest-mock']
+tests_require = ["hypothesis", "pytest", "pytest-mock"]
 
-setup(name="tdvisu",
-      version=version,
-      description=description,
-      long_description=long_description,
-      long_description_content_type='text/markdown',
-      url="https://github.com/VaeterchenFrost/tdvisu",
-      author="Martin Röbke",
-      author_email="martin.roebke@mailbox.tu-dresden.de",
-      license='GPLv3',
-      packages=['tdvisu'],
-      platforms='any',
-      install_requires=['graphviz', 'psycopg2-binary', 'python-benedict', 'python-benedict[xml]', 'PyYAML'],
-      extras_require={'test': tests_require},
-      classifiers=classifiers,
-      keywords='graph visualization dynamic-programming msol-solver')
+setup(
+    name="tdvisu",
+    version=version,
+    description=description,
+    long_description=long_description,
+    long_description_content_type="text/markdown",
+    url="https://github.com/VaeterchenFrost/tdvisu",
+    author="Martin Röbke",
+    author_email="martin.roebke@web.de",
+    license="GPLv3",
+    packages=["tdvisu"],
+    platforms="any",
+    install_requires=[
+        "graphviz",
+        "psycopg[c]",
+        "python-benedict[xml]",
+        "PyYAML",
+    ],
+    extras_require={"test": tests_require},
+    classifiers=classifiers,
+    keywords="graph visualization dynamic-programming msol-solver",
+)
diff --git a/stable-requirements.txt b/stable-requirements.txt
index 3cc7f9f..83a9837 100644
--- a/stable-requirements.txt
+++ b/stable-requirements.txt
@@ -1,22 +1,24 @@
-attrs==23.1.0
-certifi==2024.7.4
-charset-normalizer==3.2.0
+attrs==24.3.0
+certifi==2024.12.14
+charset-normalizer==3.4.0
 colorama==0.4.6
-graphviz==0.20.1
-hypothesis==6.82.0
-idna==3.7
+graphviz==0.20.3
+hypothesis==6.122.3
+idna==3.10
 iniconfig==2.0.0
-packaging==23.1
-pluggy==1.2.0
-psycopg2==2.9.6
-pytest==7.4.0
-pytest-mock==3.11.1
-python-benedict==0.32.0
-python-fsutil==0.10.0
-python-slugify==8.0.1
-PyYAML==6.0.1
-requests==2.32.2
+packaging==24.2
+pluggy==1.5.0
+psycopg==3.2.3
+pytest==8.3.4
+pytest-mock==3.14.0
+python-benedict==0.34.0
+python-fsutil==0.14.1
+python-slugify==8.0.4
+PyYAML==6.0.2
+requests==2.32.3
 sortedcontainers==2.4.0
 text-unidecode==1.3
-urllib3==2.2.2
-xmltodict==0.13.0
+typing_extensions==4.12.2
+tzdata==2024.2
+urllib3==2.2.3
+xmltodict==0.14.2
diff --git a/tdvisu/construct_dpdb_visu.py b/tdvisu/construct_dpdb_visu.py
index f395f62..11422f6 100644
--- a/tdvisu/construct_dpdb_visu.py
+++ b/tdvisu/construct_dpdb_visu.py
@@ -34,8 +34,8 @@
 from time import sleep
 from typing import List, Optional, Tuple
 
-import psycopg2 as pg
-from psycopg2 import sql
+import psycopg as pg
+from psycopg import sql
 
 from tdvisu.dijkstra import bidirectional_dijkstra as find_path
 from tdvisu.reader import TwReader
@@ -52,35 +52,6 @@
     "application_name": "dpdb-admin"
 }
 
-PSYCOPG2_8_5_TASTATUS = {
-    pg.extensions.TRANSACTION_STATUS_IDLE:
-        ('TRANSACTION_STATUS_IDLE ',
-         '(The session is idle and there is no current transaction.)'),
-
-        pg.extensions.TRANSACTION_STATUS_ACTIVE:
-        ('TRANSACTION_STATUS_ACTIVE ',
-         '(A command is currently in progress.)'),
-
-        pg.extensions.TRANSACTION_STATUS_INTRANS:
-        ('TRANSACTION_STATUS_INTRANS ',
-         '(The session is idle in a valid transaction block.)'),
-
-        pg.extensions.TRANSACTION_STATUS_INERROR:
-        ('TRANSACTION_STATUS_INERROR ',
-         '(The session is idle in a failed transaction block.)'),
-
-        pg.extensions.TRANSACTION_STATUS_UNKNOWN:
-        ('TRANSACTION_STATUS_UNKNOWN ',
-         '(Reported if the connection with the server is bad.)')
-}
-
-
-def good_db_status() -> tuple:
-    """Any good db status to proceed."""
-    return (pg.extensions.TRANSACTION_STATUS_IDLE,
-            pg.extensions.TRANSACTION_STATUS_INTRANS)
-
-
 def read_cfg(cfg_file, section: str, prefer_cfg: bool = False) -> dict:
     """Read the config file and return the result of one section."""
     try:
@@ -247,9 +218,8 @@ def read_timeline(self, edgearray) -> list:
 class DpdbSharpSatVisu(IDpdbVisuConstruct):
     """Implementation of the JSON-construction for the SharpSat problem."""
 
-    def __init__(self, db: pg.extensions.connection,
-                 problem: int, intermed_nodes: bool):
-        """db : psycopg2.connection
+    def __init__(self, db: pg.Connection, problem: int, intermed_nodes: bool):
+        """db : psycopg.connection
             database to read from.
         problem : int
             index of the problem.
@@ -263,13 +233,14 @@ def __init__(self, db: pg.extensions.connection,
         self.num_vars = None
 
         # wait for good connection
-        status = db.get_transaction_status()
         sleeptimer = 0.5
-        while status not in good_db_status():
-            logging.warning("Waiting %fs for DB connection in status %s",
-                            sleeptimer, PSYCOPG2_8_5_TASTATUS[status])
+        while (status:=db.info.status) != pg.pq.ConnStatus.OK:
+            logging.warning(
+                "Waiting %.2fs for DB connection in status %s",
+                sleeptimer,
+                status._name_,
+            )
             sleep(sleeptimer)
-            status = db.get_transaction_status()
 
         self.connection = db
 
@@ -524,14 +495,14 @@ def construct(self) -> dict:
                 'treeDecJson': tree_dec_json}
 
 
-def connect() -> pg.extensions.connection:
+def connect():
     """Connect to the PostgreSQL database server using the params from config."""
 
     conn = None
     try:
         # read connection parameters
-        params = db_config(filename='Archive/database.json')
-        db_name = params['database']
+        params = db_config(filename="database.ini")
+        db_name = params["database"]
         LOGGER.info("Connecting to the PostgreSQL database '%s'...", db_name)
         conn = pg.connect(**params)
         with conn.cursor() as cur:  # create a cursor
diff --git a/tdvisu/dijkstra.py b/tdvisu/dijkstra.py
index 338a7f7..8f30497 100644
--- a/tdvisu/dijkstra.py
+++ b/tdvisu/dijkstra.py
@@ -48,7 +48,7 @@
 from itertools import count
 
 
-def bidirectional_dijkstra(edges, source, target, weight='weight'):
+def bidirectional_dijkstra(edges, source, target, weight="weight"):
     r"""Dijkstra's algorithm for shortest paths using bidirectional search.
 
     Parameters
@@ -127,7 +127,7 @@ def bidirectional_dijkstra(edges, source, target, weight='weight'):
     push = heappush
     pop = heappop
     # Init:  [Forward, Backward]
-    dists = [{}, {}]   # dictionary of final distances
+    dists = [{}, {}]  # dictionary of final distances
     paths = [{source: [source]}, {target: [target]}]  # dictionary of paths
     fringe = [[], []]  # heap of (distance, node) for choosing node to expand
     seen = [{source: 0}, {target: 0}]  # dict of distances to seen nodes
@@ -164,8 +164,7 @@ def bidirectional_dijkstra(edges, source, target, weight='weight'):
                 vw_length = dists[direction][v] + weight(w, v, d)
             if w in dists[direction]:
                 if vw_length < dists[direction][w]:
-                    raise ValueError(
-                        "Contradictory paths found: negative weights?")
+                    raise ValueError("Contradictory paths found: negative weights?")
             elif w not in seen[direction] or vw_length < seen[direction][w]:
                 # relaxing
                 seen[direction][w] = vw_length
@@ -229,12 +228,14 @@ def _weight_function(weight, multigraph: bool = False):
     return lambda u, v, data: data.get(weight, 1)
 
 
-if __name__ == "__main__":   # pragma: no cover
+if __name__ == "__main__":  # pragma: no cover
     # Show one example and print to console
-    EDGES = {2: {1: {}, 3: {}, 4: {}},
-             1: {2: {}},
-             3: {2: {}},
-             4: {2: {}, 5: {}},
-             5: {4: {}}}
+    EDGES = {
+        2: {1: {}, 3: {}, 4: {}},
+        1: {2: {}},
+        3: {2: {}},
+        4: {2: {}, 5: {}},
+        5: {4: {}},
+    }
     RESULT = bidirectional_dijkstra(EDGES, 3, 5)
     print(RESULT)
diff --git a/tdvisu/logging.yml b/tdvisu/logging.yml
index 3c23a55..b486892 100644
--- a/tdvisu/logging.yml
+++ b/tdvisu/logging.yml
@@ -1,33 +1,29 @@
-version: 1
+---
 formatters:
-  simple:
-    format: "%(asctime)s %(levelname)s %(message)s"
-    datefmt: "%H:%M:%S"
   full:
-    format: "%(asctime)s,%(msecs)d %(levelname)s[%(filename)s:%(lineno)d] %(message)s"
-    datefmt: "%Y-%m-%d %H:%M:%S"
+    datefmt: '%Y-%m-%d %H:%M:%S'
+    format: '%(asctime)s,%(msecs)d %(levelname)s[%(filename)s:%(lineno)d] %(message)s'
+  simple:
+    datefmt: '%H:%M:%S'
+    format: '%(asctime)s %(levelname)s %(message)s'
 handlers:
   console:
     class: logging.StreamHandler
-    level: WARNING
     formatter: full
+    level: WARNING
     stream: ext://sys.stdout
 loggers:
-  visualization.py:
-    level: NOTSET
-    
-  svgjoin.py:
+  construct_dpdb_visu.py:
     level: NOTSET
-    
   reader.py:
     level: NOTSET
-    
-  construct_dpdb_visu.py:
+  svgjoin.py:
     level: NOTSET
-    
   utilities.py:
     level: NOTSET
-
+  visualization.py:
+    level: NOTSET
 root:
-  level: WARNING
   handlers: [console]
+  level: WARNING
+version: 1
\ No newline at end of file
diff --git a/tdvisu/reader.py b/tdvisu/reader.py
index bee21ee..c377624 100644
--- a/tdvisu/reader.py
+++ b/tdvisu/reader.py
@@ -46,11 +46,12 @@ def main()
 
 from tdvisu.utilities import add_edge_to
 
-logger = logging.getLogger('reader.py')
+logger = logging.getLogger("reader.py")
 
 
-class Reader():
+class Reader:
     """Base class for string-readers."""
+
     @classmethod
     def from_filename(cls, fname) -> Reader:
         with open(fname, "r") as file:
@@ -150,7 +151,7 @@ def store_problem_vars(self):
 
     def body(self, lines) -> None:
         """Store the content from the given lines in the edges and adjacency_dict."""
-        if self.format not in ('col', 'tw'):
+        if self.format not in ("col", "tw"):
             logger.error("Not a tw file!")
             sys.exit(1)
 
@@ -163,7 +164,8 @@ def body(self, lines) -> None:
                 logger.warning(
                     "Expected exactly 2 vertices at line %d, but %d found",
                     lineno,
-                    len(line))
+                    len(line),
+                )
             vertex1 = int(line[0])
             vertex2 = int(line[1])
 
@@ -171,5 +173,7 @@ def body(self, lines) -> None:
 
         if len(self.edges) != self.num_edges:
             logger.warning(
-                "Number of edges mismatch preamble (%d vs %d)", len(
-                    self.edges), self.num_edges)
+                "Number of edges mismatch preamble (%d vs %d)",
+                len(self.edges),
+                self.num_edges,
+            )
diff --git a/tdvisu/svgjoin.py b/tdvisu/svgjoin.py
index 660246e..ea06ab8 100644
--- a/tdvisu/svgjoin.py
+++ b/tdvisu/svgjoin.py
@@ -30,7 +30,7 @@
 
 from tdvisu.utilities import gen_arg
 
-LOGGER = logging.getLogger('svg_join.py')
+LOGGER = logging.getLogger("svg_join.py")
 
 
 # indices
@@ -41,19 +41,20 @@
 def test_viewbox(viewbox: List[float]):
     """Should be of form [0, 0, +x, +y]"""
     assert len(viewbox) == 4, "viewbox should have exactly 4 values"
-    assert viewbox[:2] == [0., 0.], "[min-x,min-y] should be zero."
+    assert viewbox[:2] == [0.0, 0.0], "[min-x,min-y] should be zero."
     assert viewbox[WIDTH] > 0, "should have positive width"
     assert viewbox[HEIGHT] > 0, "should have positive height"
 
 
 def append_svg(
-        first_dict: dict,
-        snd_dict: dict,
-        centerpad: float = 0.,
-        v_bottom: float = None,
-        v_top: float = None,
-        scale2: float = 1,
-        ndigits: int = 3) -> dict:
+    first_dict: dict,
+    snd_dict: dict,
+    centerpad: float = 0.0,
+    v_bottom: float = None,
+    v_top: float = None,
+    scale2: float = 1,
+    ndigits: int = 3,
+) -> dict:
     """Modifies the first of two xml-svg dictionary containing a viewbox to
     append the second svg to the right of the first image.
 
@@ -89,8 +90,8 @@ def append_svg(
 
     """
 
-    first_svg = first_dict['svg']
-    second_svg = snd_dict['svg']
+    first_svg = first_dict["svg"]
+    second_svg = snd_dict["svg"]
 
     # The value of the viewBox attribute is a list of four numbers:
     #     min-x, min-y, width and height.
@@ -100,53 +101,54 @@ def append_svg(
     # See also
     # https://developer.mozilla.org/en-US/docs/Web/SVG/Attribute/viewBox
 
-    pattern = re.compile(r'\s*,\s*|\s+')
-    viewbox1: List[float] = list(
-        map(float, re.split(pattern, first_svg['@viewBox'])))
-    viewbox2: List[float] = list(
-        map(float, re.split(pattern, second_svg['@viewBox'])))
+    pattern = re.compile(r"\s*,\s*|\s+")
+    viewbox1: List[float] = list(map(float, re.split(pattern, first_svg["@viewBox"])))
+    viewbox2: List[float] = list(map(float, re.split(pattern, second_svg["@viewBox"])))
 
     test_viewbox(viewbox1)  # viewbox1 validation
     test_viewbox(viewbox2)  # viewbox2 validation
 
     trafo_result = f_transform(
-        viewbox1[HEIGHT], viewbox2[HEIGHT], v_bottom, v_top, scale2)
-    vertical_snd = trafo_result['vertical_snd']
-    combine_height = trafo_result['combine_height']
-    scale2 = trafo_result['scale2']
+        viewbox1[HEIGHT], viewbox2[HEIGHT], v_bottom, v_top, scale2
+    )
+    vertical_snd = trafo_result["vertical_snd"]
+    combine_height = trafo_result["combine_height"]
+    scale2 = trafo_result["scale2"]
 
     LOGGER.info(
         "Transformed with vertical_snd=%s combine_height=%s scale2=%s",
-        *(vertical_snd, combine_height, scale2))
+        *(vertical_snd, combine_height, scale2),
+    )
 
     viewbox1[HEIGHT] = round(combine_height - 0.5)
     h_displacement = float(viewbox1[WIDTH]) + centerpad
-    viewbox1[WIDTH] = round(max(float(viewbox1[WIDTH]),
-                                h_displacement + scale2 * viewbox2[WIDTH]) - 0.5)
+    viewbox1[WIDTH] = round(
+        max(float(viewbox1[WIDTH]), h_displacement + scale2 * viewbox2[WIDTH]) - 0.5
+    )
 
     # new viewbox
-    first_svg['@viewBox'] = ' '.join(map(str, viewbox1))  # new viewbox
+    first_svg["@viewBox"] = " ".join(map(str, viewbox1))  # new viewbox
     # update width and height
-    first_svg['@width'] = f"{viewbox1[WIDTH]}pt"
-    first_svg['@height'] = f"{viewbox1[HEIGHT]}pt"
+    first_svg["@width"] = f"{viewbox1[WIDTH]}pt"
+    first_svg["@height"] = f"{viewbox1[HEIGHT]}pt"
     # move second image group next to first
     v_transform = round(max(0, vertical_snd), ndigits)
     transform = f"translate({h_displacement} {v_transform}) scale({scale2}) "
     # now scales with scale2
-    transform += second_svg['g'].get('@transform', '')
-    second_svg['g']['@transform'] = transform
+    transform += second_svg["g"].get("@transform", "")
+    second_svg["g"]["@transform"] = transform
 
     if vertical_snd < 0:
         # move first image, add after other transform
-        transform = first_svg['g'].get('@transform', '')
+        transform = first_svg["g"].get("@transform", "")
         transform += f" translate(0 {round(-vertical_snd,ndigits)})"
-        first_svg['g']['@transform'] = transform
+        first_svg["g"]["@transform"] = transform
 
     # add group to list of 'g'
-    if isinstance(first_svg['g'], list):
-        first_svg['g'].append(second_svg['g'])
+    if isinstance(first_svg["g"], list):
+        first_svg["g"].append(second_svg["g"])
     else:
-        first_svg['g'] = [first_svg['g'], second_svg['g']]
+        first_svg["g"] = [first_svg["g"], second_svg["g"]]
 
     return first_dict
 
@@ -165,10 +167,13 @@ def append_svg(
 """
 
 
-def f_transform(h_one_, h_two_,
-                v_bottom: Union[float, str, None] = None,
-                v_top: Union[float, str, None] = None,
-                scale2: float = 1) -> Dict[str, float]:
+def f_transform(
+    h_one_,
+    h_two_,
+    v_bottom: Union[float, str, None] = None,
+    v_top: Union[float, str, None] = None,
+    scale2: float = 1,
+) -> Dict[str, float]:
     """Calculate vertical position and scaling of second image.
 
     The input for v_bottom, v_top is in units from\n
@@ -197,14 +202,20 @@ def f_transform(h_one_, h_two_,
         'vertical_snd','combine_height','scale2'
 
     """
-    v_displacement = 0.
+    v_displacement = 0.0
     # cast to float
     h_one = float(h_one_)
     h_two = float(h_two_)
     LOGGER.debug("Calculating with h_one=%f h_two=%f", h_one, h_two)
     # normalize values
-    conversion = {'bottom': 1, 'center': 0.5, 'top': 0, 'inf': 0,
-                  -float('inf'): 1, float('inf'): 0}
+    conversion = {
+        "bottom": 1,
+        "center": 0.5,
+        "top": 0,
+        "inf": 0,
+        -float("inf"): 1,
+        float("inf"): 0,
+    }
     v_bottom = conversion.get(v_bottom, v_bottom)
     if isinstance(v_bottom, str):
         raise ValueError(f"Encountered {v_bottom=} not in {conversion=}")
@@ -227,7 +238,9 @@ def f_transform(h_one_, h_two_,
             # moving the centerline according to value and scaling
             LOGGER.info(
                 "The values of 'v_top', 'v_bottom' are both interpreted "
-                "as %f - interpreting as centerline!", v_top)
+                "as %f - interpreting as centerline!",
+                v_top,
+            )
             half = size2 / h_one / 2
             v_top = v_top - half
             v_bottom = v_bottom + half
@@ -245,22 +258,25 @@ def f_transform(h_one_, h_two_,
     # bottom - top
     combine_height = (max(1, v_bottom) - min(0, v_top)) * h_one
 
-    return {'vertical_snd': v_displacement,
-            'combine_height': combine_height,
-            'scale2': scale2}
+    return {
+        "vertical_snd": v_displacement,
+        "combine_height": combine_height,
+        "scale2": scale2,
+    }
 
 
 def svg_join(
-        base_names: list,
-        folder: str = '',
-        num_images: int = 1,
-        outname: str = 'combined',
-        suffix: str = '%d.svg',
-        preserve_aspectratio: str = 'xMinYMin',
-        padding: Union[int, Iterable[int]] = 0,
-        scale2: Union[float, Iterable[float]] = 1,
-        v_top: Union[None, float, str, Iterable[Union[None, float, str]]] = None,
-        v_bottom: Union[None, float, str, Iterable[Union[None, float, str]]] = None):
+    base_names: list,
+    folder: str = "",
+    num_images: int = 1,
+    outname: str = "combined",
+    suffix: str = "%d.svg",
+    preserve_aspectratio: str = "xMinYMin",
+    padding: Union[int, Iterable[int]] = 0,
+    scale2: Union[float, Iterable[float]] = 1,
+    v_top: Union[None, float, str, Iterable[Union[None, float, str]]] = None,
+    v_bottom: Union[None, float, str, Iterable[Union[None, float, str]]] = None,
+):
     """
     Joines different svg-images from tdvisu placed in 'folder' for every timestep
     in the horizontal order specified in 'in_names'.
@@ -309,7 +325,7 @@ def svg_join(
         LOGGER.warning("svg_join called with one file - nothing to join!")
         return
     # use path library for normalizing the path
-    folder = Path(folder if folder else '')
+    folder = Path(folder if folder else "")
 
     resultname = str(folder / outname) + suffix
     names = [str(folder / name) + suffix for name in base_names]
@@ -326,20 +342,30 @@ def svg_join(
         with open(names[1] % step) as file:
             im_2 = benedict.from_xml(file.read())
 
-        result = append_svg(im_1, im_2, centerpad=next(gen_padding),
-                            v_bottom=next(gen_v_bottom),
-                            v_top=next(gen_v_top), scale2=next(gen_scale2))
+        result = append_svg(
+            im_1,
+            im_2,
+            centerpad=next(gen_padding),
+            v_bottom=next(gen_v_bottom),
+            v_top=next(gen_v_top),
+            scale2=next(gen_scale2),
+        )
 
         # rest:
         for name in names[2:]:
             with open(name % step) as file:
                 image = benedict.from_xml(file.read())
-            result = append_svg(result, image, centerpad=next(gen_padding),
-                                v_bottom=next(gen_v_bottom),
-                                v_top=next(gen_v_top), scale2=next(gen_scale2))
-
-        result['svg']['@preserveAspectRatio'] = preserve_aspectratio
-        with open(resultname % step, 'w') as file:
+            result = append_svg(
+                result,
+                image,
+                centerpad=next(gen_padding),
+                v_bottom=next(gen_v_bottom),
+                v_top=next(gen_v_top),
+                scale2=next(gen_scale2),
+            )
+
+        result["svg"]["@preserveAspectRatio"] = preserve_aspectratio
+        with open(resultname % step, "w") as file:
             result.to_xml(output=file, pretty=True)
 
         if step < 10:
@@ -349,9 +375,11 @@ def svg_join(
 
 if __name__ == "__main__":  # pragma: no cover
     logging.basicConfig(level=logging.DEBUG)
-    svg_join(['TDStep', 'graph'],
-             'Archive/WheelGraph7',
-             outname="default_06sc15_rise",
-             v_bottom=[1, .85, .7, .55, .4],
-             scale2=1.5,
-             num_images=5)
+    svg_join(
+        ["TDStep", "graph"],
+        "Archive/WheelGraph7",
+        outname="default_06sc15_rise",
+        v_bottom=[1, 0.85, 0.7, 0.55, 0.4],
+        scale2=1.5,
+        num_images=5,
+    )
diff --git a/tdvisu/utilities.py b/tdvisu/utilities.py
index 03c2218..ba9b6e3 100644
--- a/tdvisu/utilities.py
+++ b/tdvisu/utilities.py
@@ -25,21 +25,22 @@
 import logging
 import logging.config
 from collections.abc import Iterable as iter_type
-from configparser import ConfigParser, Error as CfgError, ParsingError
+from configparser import ConfigParser
+from configparser import Error as CfgError
+from configparser import ParsingError
 from itertools import chain
 from pathlib import Path
-from typing import (Any, Generator, Iterable, Iterator,
-                    List, Tuple, TypeVar, Union)
-
-from tdvisu.version import __date__, __version__
+from typing import Any, Generator, Iterable, Iterator, List, Tuple, TypeVar, Union
 
 import yaml
 
-LOGGER = logging.getLogger('utilities.py')
+from tdvisu.version import __date__, __version__
 
-CFG_EXT = ('.ini', '.cfg', '.conf', '.config')
+LOGGER = logging.getLogger("utilities.py")
+
+CFG_EXT = (".ini", ".cfg", ".conf", ".config")
 LOGLEVEL_EPILOG = """
-Logging levels for python 3.8.2:
+Logging levels for Python:
     CRITICAL: 50
     ERROR:    40
     WARNING:  30
@@ -48,43 +49,43 @@
     NOTSET:    0 (will traverse the logging hierarchy until a value is found)
     """
 DEFAULT_LOGGING_CFG = {
-    'version': 1,
-    'formatters': {
-        'simple': {
-            'format': '%(asctime)s %(levelname)s %(message)s',
-            'datefmt': '%H:%M:%S'}},
-    'handlers': {
-        'console': {
-            'class': 'logging.StreamHandler',
-            'level': 'WARNING',
-            'formatter': 'simple',
-            'stream': 'ext://sys.stdout'}},
-    'loggers': {
-        'visualization.py': {
-            'level': 'NOTSET',
-            'handlers': ['console'],
-            'propagate': False},
-        'svgjoin.py': {
-            'level': 'NOTSET',
-            'handlers': ['console'],
-            'propagate': False},
-        'reader.py': {
-            'level': 'NOTSET',
-            'handlers': ['console'],
-            'propagate': False},
-        'construct_dpdb_visu.py': {
-            'level': 'NOTSET',
-            'handlers': ['console'],
-            'propagate': False}},
-    'root': {
-        'level': 'WARNING',
-        'handlers': ['console']}}
-
-_T = TypeVar('_T')
+    "version": 1,
+    "formatters": {
+        "simple": {
+            "format": "%(asctime)s %(levelname)s %(message)s",
+            "datefmt": "%H:%M:%S",
+        }
+    },
+    "handlers": {
+        "console": {
+            "class": "logging.StreamHandler",
+            "level": "WARNING",
+            "formatter": "simple",
+            "stream": "ext://sys.stdout",
+        }
+    },
+    "loggers": {
+        "visualization.py": {
+            "level": "NOTSET",
+            "handlers": ["console"],
+            "propagate": False,
+        },
+        "svgjoin.py": {"level": "NOTSET", "handlers": ["console"], "propagate": False},
+        "reader.py": {"level": "NOTSET", "handlers": ["console"], "propagate": False},
+        "construct_dpdb_visu.py": {
+            "level": "NOTSET",
+            "handlers": ["console"],
+            "propagate": False,
+        },
+    },
+    "root": {"level": "WARNING", "handlers": ["console"]},
+}
+
+_T = TypeVar("_T")
 
 
 def flatten(iterable: Iterable[Iterable[_T]]) -> Iterator[_T]:
-    """ Flatten at first level.
+    """Flatten at first level.
 
     Turn ex=[[1,2],[3,4]] into
     [1, 2, 3, 4]
@@ -94,8 +95,9 @@ def flatten(iterable: Iterable[Iterable[_T]]) -> Iterator[_T]:
     return chain.from_iterable(iterable)
 
 
-def read_yml_or_cfg(file: Union[str, Path], prefer_cfg: bool = False,
-                    cfg_ext=CFG_EXT) -> Any:
+def read_yml_or_cfg(
+    file: Union[str, Path], prefer_cfg: bool = False, cfg_ext=CFG_EXT
+) -> Any:
     """
     Read the file and return its content as a python object.
 
@@ -115,8 +117,10 @@ def read_yml_or_cfg(file: Union[str, Path], prefer_cfg: bool = False,
         But maybe just a list or a single object.
 
     """
-    err_str = ("utilities.read_yml_or_cfg encountered '{}' while "
-               "reading config from '{}' and prefer_cfg={}")
+    err_str = (
+        "utilities.read_yml_or_cfg encountered '{}' while "
+        "reading config from '{}' and prefer_cfg={}"
+    )
 
     file = Path(file)
     if not file.exists():
@@ -153,8 +157,9 @@ def read_yml_or_cfg(file: Union[str, Path], prefer_cfg: bool = False,
     return dict()
 
 
-def logging_cfg(filename: str, prefer_cfg: bool = False,
-                loglevel: Union[None, int, str] = None) -> None:
+def logging_cfg(
+    filename: str, prefer_cfg: bool = False, loglevel: Union[None, int, str] = None
+) -> None:
     """Configure logging for this module"""
     logging.basicConfig()
     read_err = "could not read configuration from '%s'"
@@ -168,7 +173,7 @@ def logging_cfg(filename: str, prefer_cfg: bool = False,
         except ValueError:
             loglevel = loglevel.upper()
 
-    if prefer_cfg or file.suffix.lower() in CFG_EXT:        # .config
+    if prefer_cfg or file.suffix.lower() in CFG_EXT:  # .config
         try:
             logging.config.fileConfig(file, defaults=DEFAULT_LOGGING_CFG)
             if loglevel is not None:
@@ -181,7 +186,7 @@ def logging_cfg(filename: str, prefer_cfg: bool = False,
             LOGGER.error(read_err, file.resolve(), exc_info=True)
         except ValueError:
             LOGGER.error(config_err, file.resolve(), exc_info=True)
-    try:                                                    # dict
+    try:  # dict
         file_content = read_yml_or_cfg(file, prefer_cfg=prefer_cfg)
         logging.config.dictConfig(file_content)
         if loglevel is not None:
@@ -196,8 +201,7 @@ def logging_cfg(filename: str, prefer_cfg: bool = False,
         LOGGER.error(config_err, file.resolve(), exc_info=True)
 
 
-def convert_to_adj(
-        edgelist: Iterable[Tuple[int, int]], directed: bool = False) -> dict:
+def convert_to_adj(edgelist: Iterable[Tuple[int, int]], directed: bool = False) -> dict:
     """
     Helper function to convert the edgelist into the adj-format from NetworkX.
 
@@ -218,7 +222,7 @@ def convert_to_adj(
         https://networkx.github.io/documentation/networkx-2.1/_modules/networkx/classes/graph.html
     """
     adj = dict()
-    for (source, target) in edgelist:
+    for source, target in edgelist:
         if source not in adj:
             adj[source] = {}
         adj[source][target] = {}
@@ -230,11 +234,7 @@ def convert_to_adj(
     return adj
 
 
-def add_edge_to(
-        edges: set,
-        adjacency_dict: dict,
-        vertex1: Any,
-        vertex2: Any) -> None:
+def add_edge_to(edges: set, adjacency_dict: dict, vertex1: Any, vertex2: Any) -> None:
     """
     Adding (undirected) edge from 'vertex1' to 'vertex2'
     to the edges and adjacency-list.
@@ -293,17 +293,14 @@ def gen_arg(arg_or_iter: Any) -> Generator:
         yield item
 
 
-def base_style(
-        graph,
-        node: str,
-        color: str = 'white',
-        penwidth: float = 1.0) -> None:
+def base_style(graph, node: str, color: str = "white", penwidth: float = 1.0) -> None:
     """Style the node with default fillcolor and penwidth."""
     graph.node(node, fillcolor=color, penwidth=str(penwidth))
 
 
-def emphasise_node(graph, node: str, color: str = 'yellow',
-                   penwidth: float = 2.5) -> None:
+def emphasise_node(
+    graph, node: str, color: str = "yellow", penwidth: float = 2.5
+) -> None:
     """Emphasise node with a different fillcolor (default:'yellow')
     and penwidth (default:2.5).
     """
@@ -315,22 +312,23 @@ def emphasise_node(graph, node: str, color: str = 'yellow',
 
 def style_hide_node(graph, node: str) -> None:
     """Make the node invisible during drawing."""
-    graph.node(node, style='invis')
+    graph.node(node, style="invis")
 
 
 def style_hide_edge(graph, source: str, target: str) -> None:
     """Make the edge source->target invisible during drawing."""
-    graph.edge(source, target, style='invis')
+    graph.edge(source, target, style="invis")
 
 
 def bag_node(
-        head,
-        tail,
-        anchor: str = 'anchor',
-        headcolor: str = 'white',
-        tableborder: int = 0,
-        cellborder: int = 0,
-        cellspacing: int = 0) -> str:
+    head,
+    tail,
+    anchor: str = "anchor",
+    headcolor: str = "white",
+    tableborder: int = 0,
+    cellborder: int = 0,
+    cellspacing: int = 0,
+) -> str:
     """HTML format with 'head' as the first label, then appending
     further labels.
 
@@ -356,13 +354,14 @@ def bag_node(
 
 
 def solution_node(
-        solution_table: Iterable[List[str]],
-        toplabel: str = '',
-        bottomlabel: str = '',
-        transpose: bool = False,
-        linesmax: int = 1000,
-        columnsmax: int = 50,
-        fillstr: str = '...') -> str:
+    solution_table: Iterable[List[str]],
+    toplabel: str = "",
+    bottomlabel: str = "",
+    transpose: bool = False,
+    linesmax: int = 1000,
+    columnsmax: int = 50,
+    fillstr: str = "...",
+) -> str:
     """Fill the node from the 2D-matrix 'solution_table' COLUMNBASED!.
     Optionally add a line above and/or below the table for labels.
     The size of the result can be limited by using linesmax and columnsmax.
@@ -398,62 +397,64 @@ def solution_node(
     | botlabel |
     |----------|
     """
-    result = ''
+    result = ""
     if toplabel:
-        result += toplabel + '|'
+        result += toplabel + "|"
 
     if len(solution_table) == 0:
-        result += 'empty'
+        result += "empty"
     else:
         if transpose:
             solution_table = list(zip(*solution_table))
 
         # limit lines backwards from length of column
-        vslice = (min(-1, linesmax - len(solution_table[0]))
-                  if linesmax > 0 else -1)
+        vslice = min(-1, linesmax - len(solution_table[0])) if linesmax > 0 else -1
         # limit columns forwards minus one
-        hslice = (min(len(solution_table), columnsmax)
-                  if columnsmax > 0 else len(solution_table)) - 1
+        hslice = (
+            min(len(solution_table), columnsmax)
+            if columnsmax > 0
+            else len(solution_table)
+        ) - 1
 
-        result += '{'                                       # insert table
+        result += "{"  # insert table
         for column in solution_table[:hslice]:
-            result += '{'                                   # start column
+            result += "{"  # start column
             for row in column[:vslice]:
-                result += str(row) + '|'
-            if vslice < -1:     # add one indicator of shortening
-                result += fillstr + '|'
+                result += str(row) + "|"
+            if vslice < -1:  # add one indicator of shortening
+                result += fillstr + "|"
             for row in column[-1:]:
                 result += str(row)
-            result += '}|'      # sep. between columns
+            result += "}|"  # sep. between columns
         # adding one column-skipping indicator
         if hslice < len(solution_table) - 1:
-            result += '{'                                   # start column
+            result += "{"  # start column
             for row in column[:vslice]:
-                result += fillstr + '|'
-            if vslice < -1:     # add one indicator of shortening
-                result += fillstr + '|'
+                result += fillstr + "|"
+            if vslice < -1:  # add one indicator of shortening
+                result += fillstr + "|"
             for row in column[-1:]:
                 result += fillstr
-            result += '}|'      # sep. between columns
+            result += "}|"  # sep. between columns
         # last column (usually a summary of the previous cols)
         for column in solution_table[-1:]:
-            result += '{'                                   # start column
+            result += "{"  # start column
             for row in column[:vslice]:
-                result += str(row) + '|'
-            if vslice < -1:     # add one indicator of shortening
-                result += fillstr + '|'
+                result += str(row) + "|"
+            if vslice < -1:  # add one indicator of shortening
+                result += fillstr + "|"
             for row in column[-1:]:
                 result += str(row)
-            result += '}'      # sep. between columns
-        result += '}'                                       # close table
+            result += "}"  # sep. between columns
+        result += "}"  # close table
 
     if bottomlabel:
-        result += '|' + bottomlabel
+        result += "|" + bottomlabel
 
-    return '{' + result + '}'
+    return "{" + result + "}"
 
 
-def get_parser(extra_desc: str = '') -> argparse.ArgumentParser:
+def get_parser(extra_desc: str = "") -> argparse.ArgumentParser:
     """
     Prepare an argument parser for TDVisu scripts.
 
@@ -475,11 +476,16 @@ def get_parser(extra_desc: str = '') -> argparse.ArgumentParser:
         This is free software, and you are welcome to redistribute it
         under certain conditions; see COPYING for more information.
         """
-        + "\n" + extra_desc,
+        + "\n"
+        + extra_desc,
         epilog=LOGLEVEL_EPILOG,
-        formatter_class=argparse.RawDescriptionHelpFormatter)
-
-    parser.add_argument('--version', action='version',
-                        version='%(prog)s ' + __version__ + ', ' + __date__)
-    parser.add_argument('--loglevel', help="set the minimal loglevel for root")
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+    )
+
+    parser.add_argument(
+        "--version",
+        action="version",
+        version="%(prog)s " + __version__ + ", " + __date__,
+    )
+    parser.add_argument("--loglevel", help="set the minimal loglevel for root")
     return parser
diff --git a/tdvisu/version.py b/tdvisu/version.py
index f32f803..aa0ef0a 100644
--- a/tdvisu/version.py
+++ b/tdvisu/version.py
@@ -4,7 +4,7 @@
 """
 
 # Base version.
-__version__ = '1.1.9'
+__version__ = "1.2.0"
 
 # Year-Month-Day of last version change
-__date__ = '2023-07-27'
+__date__ = "2024-12-24"
diff --git a/tdvisu/visualization.py b/tdvisu/visualization.py
index e2409a1..c0f3e1f 100644
--- a/tdvisu/visualization.py
+++ b/tdvisu/visualization.py
@@ -39,15 +39,27 @@
 from graphviz import Digraph, Graph
 
 from tdvisu.svgjoin import svg_join
-from tdvisu.utilities import (bag_node, base_style, emphasise_node, flatten,
-                              get_parser, logging_cfg, solution_node,
-                              style_hide_edge, style_hide_node)
-from tdvisu.visualization_data import (GeneralGraphData, IncidenceGraphData,
-                                       SvgJoinData, VisualizationData)
-
-LOGGER = logging.getLogger('visualization.py')
-
-StrOrIo = NewType('StrOrIo', Union[str, io.TextIOWrapper])
+from tdvisu.utilities import (
+    bag_node,
+    base_style,
+    emphasise_node,
+    flatten,
+    get_parser,
+    logging_cfg,
+    solution_node,
+    style_hide_edge,
+    style_hide_node,
+)
+from tdvisu.visualization_data import (
+    GeneralGraphData,
+    IncidenceGraphData,
+    SvgJoinData,
+    VisualizationData,
+)
+
+LOGGER = logging.getLogger("visualization.py")
+
+StrOrIo = NewType("StrOrIo", Union[str, io.TextIOWrapper])
 
 
 def read_json(json_data: StrOrIo) -> dict:
@@ -97,9 +109,9 @@ def inspect_json(self, infile: StrOrIo) -> VisualizationData:
         LOGGER.debug("Found keys: %s", visudata.keys())
 
         try:
-            _incid = visudata.get('incidenceGraph', None)
-            _general_graph = visudata.get('generalGraph', None)
-            _svg_join = visudata.get('svgjoin', None)
+            _incid = visudata.get("incidenceGraph", None)
+            _general_graph = visudata.get("generalGraph", None)
+            _svg_join = visudata.get("svgjoin", None)
 
             incid_data: List[IncidenceGraphData] = list()
             if _incid:
@@ -108,10 +120,9 @@ def inspect_json(self, infile: StrOrIo) -> VisualizationData:
                 # unwrap as list:
                 for data in _incid:
                     # add object to incid_data
-                    data['edges'] = [[x['id'], x['list']]
-                                     for x in data['edges']]
+                    data["edges"] = [[x["id"], x["list"]] for x in data["edges"]]
                     incid_data += [IncidenceGraphData(**data)]
-            visudata.pop('incidenceGraph', None)
+            visudata.pop("incidenceGraph", None)
 
             general_graph_data: List[GeneralGraphData] = list()
             if _general_graph:
@@ -119,36 +130,39 @@ def inspect_json(self, infile: StrOrIo) -> VisualizationData:
                     _general_graph = [_general_graph]
                 for data in _general_graph:
                     general_graph_data += [GeneralGraphData(**data)]
-            visudata.pop('generalGraph', None)
+            visudata.pop("generalGraph", None)
 
             svg_join_data: Optional[SvgJoinData] = None
             if _svg_join:
                 svg_join_data = SvgJoinData(**_svg_join)
-            if 'svgjoin' in visudata:
-                visudata.pop('svgjoin')
-
-            self.timeline = visudata['tdTimeline']
-            visudata.pop('tdTimeline')
-            self.tree_dec = visudata['treeDecJson']
-            self.bagpre = self.tree_dec['bagpre']
-            self.joinpre = self.tree_dec.get('joinpre', 'Join %d~%d')
-            self.solpre = self.tree_dec.get('solpre', 'sol%d')
-            self.soljoinpre = self.tree_dec.get('soljoinpre', 'solJoin%d~%d')
-            visudata.pop('treeDecJson')
+            if "svgjoin" in visudata:
+                visudata.pop("svgjoin")
+
+            self.timeline = visudata["tdTimeline"]
+            visudata.pop("tdTimeline")
+            self.tree_dec = visudata["treeDecJson"]
+            self.bagpre = self.tree_dec["bagpre"]
+            self.joinpre = self.tree_dec.get("joinpre", "Join %d~%d")
+            self.solpre = self.tree_dec.get("solpre", "sol%d")
+            self.soljoinpre = self.tree_dec.get("soljoinpre", "solJoin%d~%d")
+            visudata.pop("treeDecJson")
         except KeyError as err:
             raise KeyError(f"Key {err} not found in the input Json.")
-        return VisualizationData(incidence_graphs=incid_data,
-                                 general_graphs=general_graph_data,
-                                 svg_join=svg_join_data,
-                                 **visudata)
+        return VisualizationData(
+            incidence_graphs=incid_data,
+            general_graphs=general_graph_data,
+            svg_join=svg_join_data,
+            **visudata,
+        )
 
     def setup_tree_dec_graph(
-            self,
-            rankdir: str = 'BT',
-            shape: str = 'box',
-            fillcolor: str = 'white',
-            style: str = 'rounded,filled',
-            margin: str = '0.11,0.01') -> None:
+        self,
+        rankdir: str = "BT",
+        shape: str = "box",
+        fillcolor: str = "white",
+        style: str = "rounded,filled",
+        margin: str = "0.11,0.01",
+    ) -> None:
         """Create self.tree_dec_digraph
         strict means not a multigraph - equal edges get merged.
 
@@ -156,74 +170,89 @@ def setup_tree_dec_graph(
             - normally Bottom-Top or Top-Bottom.
         """
         self.tree_dec_digraph = Digraph(
-            'Tree-Decomposition', strict=True,
-            graph_attr={'rankdir': rankdir},
+            "Tree-Decomposition",
+            strict=True,
+            graph_attr={"rankdir": rankdir},
             node_attr={
-                'shape': shape,
-                'fillcolor': fillcolor,
-                'style': style,
-                'margin': margin})
+                "shape": shape,
+                "fillcolor": fillcolor,
+                "style": style,
+                "margin": margin,
+            },
+        )
 
     def basic_tdg(self) -> None:
         """Create basic bag structure in tree_dec_digraph."""
-        for item in self.tree_dec['labeldict']:
-            bagname = self.bagpre % str(item['id'])
-            self.tree_dec_digraph.node(bagname,
-                                       bag_node(bagname, item['labels']))
-
-        self.tree_dec_digraph.edges([(self.bagpre % str(first), self.bagpre % str(
-            second)) for (first, second) in self.tree_dec['edgearray']])
-
-    def forward_iterate_tdg(
-            self,
-            joinpre: str,
-            solpre: str,
-            soljoinpre: str) -> None:
+        for item in self.tree_dec["labeldict"]:
+            bagname = self.bagpre % str(item["id"])
+            self.tree_dec_digraph.node(bagname, bag_node(bagname, item["labels"]))
+
+        self.tree_dec_digraph.edges(
+            [
+                (self.bagpre % str(first), self.bagpre % str(second))
+                for (first, second) in self.tree_dec["edgearray"]
+            ]
+        )
+
+    def forward_iterate_tdg(self, joinpre: str, solpre: str, soljoinpre: str) -> None:
         """Create the final positions of all nodes with solutions."""
-        tdg = self.tree_dec_digraph                 # shorten name
+        tdg = self.tree_dec_digraph  # shorten name
 
-        for i, node in enumerate(self.timeline):    # Create the positions
+        for i, node in enumerate(self.timeline):  # Create the positions
             if len(node) > 1:
                 # solution to be displayed
                 id_inv_bags = node[0]
                 if isinstance(id_inv_bags, int):
                     last_sol = solpre % id_inv_bags
-                    tdg.node(last_sol, solution_node(
-                        *(node[1])), shape='record')
+                    tdg.node(last_sol, solution_node(*(node[1])), shape="record")
 
                     tdg.edge(self.bagpre % id_inv_bags, last_sol)
 
-                else:                               # joined node with 2 bags
-                    suc = self.timeline[i + 1][0]   # get the joined bags
+                else:  # joined node with 2 bags
+                    suc = self.timeline[i + 1][0]  # get the joined bags
 
-                    LOGGER.debug('joining %s to %s ', node[0], suc)
+                    LOGGER.debug("joining %s to %s ", node[0], suc)
 
                     id_inv_bags = tuple(id_inv_bags)
                     last_sol = soljoinpre % id_inv_bags
-                    tdg.node(last_sol, solution_node(
-                        *(node[1])), shape='record')
+                    tdg.node(last_sol, solution_node(*(node[1])), shape="record")
 
                     tdg.edge(joinpre % id_inv_bags, last_sol)
                     # edges
                     for child in id_inv_bags:  # basically "remove" current
                         # TODO check where 2 args are possibly occuring
                         tdg.edge(
-                            self.bagpre % child
-                            if isinstance(child, int) else joinpre % child,
-                            self.bagpre % suc
-                            if isinstance(suc, int) else joinpre % suc,
-                            style='invis',
-                            constraint='false')
-                        tdg.edge(self.bagpre % child if isinstance(child, int)
-                                 else joinpre % child,
-                                 joinpre % id_inv_bags)
-                    tdg.edge(joinpre % id_inv_bags, self.bagpre % suc
-                             if isinstance(suc, int) else joinpre % suc)
-
-    def backwards_iterate_tdg(self, joinpre: str, solpre: str, soljoinpre: str,
-                              view: bool = False) -> None:
+                            (
+                                self.bagpre % child
+                                if isinstance(child, int)
+                                else joinpre % child
+                            ),
+                            (
+                                self.bagpre % suc
+                                if isinstance(suc, int)
+                                else joinpre % suc
+                            ),
+                            style="invis",
+                            constraint="false",
+                        )
+                        tdg.edge(
+                            (
+                                self.bagpre % child
+                                if isinstance(child, int)
+                                else joinpre % child
+                            ),
+                            joinpre % id_inv_bags,
+                        )
+                    tdg.edge(
+                        joinpre % id_inv_bags,
+                        self.bagpre % suc if isinstance(suc, int) else joinpre % suc,
+                    )
+
+    def backwards_iterate_tdg(
+        self, joinpre: str, solpre: str, soljoinpre: str, view: bool = False
+    ) -> None:
         """Cut the single steps back and update emphasis acordingly."""
-        tdg = self.tree_dec_digraph     # shorten name
+        tdg = self.tree_dec_digraph  # shorten name
         last_sol = ""
         _filename = self.outfolder / self.data.td_file
         for i, node in enumerate(reversed(self.timeline)):
@@ -234,11 +263,10 @@ def backwards_iterate_tdg(self, joinpre: str, solpre: str, soljoinpre: str,
                 # Delete previous emphasis
                 prevhead = self.timeline[len(self.timeline) - i][0]
                 bag = (
-                    self.bagpre %
-                    prevhead if isinstance(
-                        prevhead,
-                        int) else joinpre %
-                    tuple(prevhead))
+                    self.bagpre % prevhead
+                    if isinstance(prevhead, int)
+                    else joinpre % tuple(prevhead)
+                )
                 base_style(tdg, bag)
                 if last_sol:
                     style_hide_node(tdg, last_sol)
@@ -256,36 +284,39 @@ def backwards_iterate_tdg(self, joinpre: str, solpre: str, soljoinpre: str,
                     last_sol = soljoinpre % id_inv_bags
                     emphasise_node(tdg, last_sol)
 
-            emphasise_node(tdg,
-                           self.bagpre %
-                           id_inv_bags if isinstance(
-                               id_inv_bags,
-                               int) else joinpre %
-                           id_inv_bags)
+            emphasise_node(
+                tdg,
+                (
+                    self.bagpre % id_inv_bags
+                    if isinstance(id_inv_bags, int)
+                    else joinpre % id_inv_bags
+                ),
+            )
 
             tdg.render(
-                view=view, format='svg',
-                filename=str(_filename) + str(len(self.timeline) - i)
+                view=view,
+                format="svg",
+                filename=str(_filename) + str(len(self.timeline) - i),
             )
 
     def tree_dec_timeline(self, view: bool = False) -> None:
         """Main-method for handling all construction of the timeline."""
 
         self.setup_tree_dec_graph(
-            rankdir=self.data.orientation,
-            fillcolor=self.data.bagcolor)
+            rankdir=self.data.orientation, fillcolor=self.data.bagcolor
+        )
         self.basic_tdg()
 
         # Iterate labeldict
         self.forward_iterate_tdg(
-            joinpre=self.joinpre,
-            solpre=self.solpre,
-            soljoinpre=self.soljoinpre)
+            joinpre=self.joinpre, solpre=self.solpre, soljoinpre=self.soljoinpre
+        )
         self.backwards_iterate_tdg(
             view=view,
             joinpre=self.joinpre,
             solpre=self.solpre,
-            soljoinpre=self.soljoinpre)
+            soljoinpre=self.soljoinpre,
+        )
 
         # Prepare supporting graph timeline
 
@@ -296,8 +327,13 @@ def tree_dec_timeline(self, view: bool = False) -> None:
             elif isinstance(step[0], int):
                 _timeline.append(
                     next(
-                        (item.get('items') for item in self.tree_dec['labeldict']
-                         if item['id'] == step[0])))
+                        (
+                            item.get("items")
+                            for item in self.tree_dec["labeldict"]
+                            if item["id"] == step[0]
+                        )
+                    )
+                )
             else:
                 # Join operation - no clauses involved in computation
                 _timeline.append(None)
@@ -305,15 +341,15 @@ def tree_dec_timeline(self, view: bool = False) -> None:
         if self.data.incidence_graphs:
             for incidence_data in self.data.incidence_graphs:
                 self.prepare_incidence(incidence_data, _timeline, view)
-                LOGGER.info("Created incidence-graph for file='%s'",
-                            incidence_data.inc_file)
+                LOGGER.info(
+                    "Created incidence-graph for file='%s'", incidence_data.inc_file
+                )
         if self.data.general_graphs:
             for graph_data in self.data.general_graphs:
-                self.general_graph(timeline=_timeline, view=view,
-                                   **asdict(graph_data))
+                self.general_graph(timeline=_timeline, view=view, **asdict(graph_data))
                 LOGGER.info(
-                    "Created general-graph for file='%s'",
-                    graph_data.file_basename)
+                    "Created general-graph for file='%s'", graph_data.file_basename
+                )
         if self.data.svg_join:
             self.call_svgjoin()
 
@@ -321,18 +357,21 @@ def prepare_incidence(self, incid, _timeline, view):
         """Prepare incidence construction."""
         if incid.infer_primal or incid.infer_dual:
             # prepare incid edges with abs:
-            abs_clauses = [[cl[0], list(map(abs, cl[1]))]
-                           for cl in incid.edges]
+            abs_clauses = [[cl[0], list(map(abs, cl[1]))] for cl in incid.edges]
         if incid.infer_primal:
             # vertex for each variable + edge if the variables
             # occur in the same clause:
-            primal_edges = set(flatten(             # remove duplicates
-                [itertools.combinations(cl[1], 2)
-                 for cl in abs_clauses]))
+            primal_edges = set(
+                flatten(  # remove duplicates
+                    [itertools.combinations(cl[1], 2) for cl in abs_clauses]
+                )
+            )
             # check if any node is really isolated:
-            isolated = [cl[1][0] for cl in abs_clauses
-                        if len(cl[1]) == 1 and
-                        not any(cl[1][0] in sl for sl in primal_edges)]
+            isolated = [
+                cl[1][0]
+                for cl in abs_clauses
+                if len(cl[1]) == 1 and not any(cl[1][0] in sl for sl in primal_edges)
+            ]
 
             self.general_graph(
                 timeline=_timeline,
@@ -340,18 +379,22 @@ def prepare_incidence(self, incid, _timeline, view):
                 extra_nodes=set(isolated),
                 graph_name=incid.primal_file,
                 file_basename=incid.primal_file,
-                var_name=incid.var_name_two)
+                var_name=incid.var_name_two,
+            )
             LOGGER.info("Created infered primal-graph")
 
         if incid.infer_dual:
             # Edge, if clauses share the same variable
-            dual_edges = [(cl[0], other[0])
-                          for i, cl in enumerate(abs_clauses)
-                          for other in abs_clauses[i + 1:]  # no multiples
-                          if any(var in cl[1] for var in other[1])]
+            dual_edges = [
+                (cl[0], other[0])
+                for i, cl in enumerate(abs_clauses)
+                for other in abs_clauses[i + 1 :]  # no multiples
+                if any(var in cl[1] for var in other[1])
+            ]
             # check if any clause is isolated:
-            isolated = [cl[0] for cl in abs_clauses
-                        if not any(cl[0] in sl for sl in dual_edges)]
+            isolated = [
+                cl[0] for cl in abs_clauses if not any(cl[0] in sl for sl in dual_edges)
+            ]
 
             self.general_graph(
                 timeline=_timeline,
@@ -359,41 +402,45 @@ def prepare_incidence(self, incid, _timeline, view):
                 extra_nodes=set(isolated),
                 graph_name=incid.dual_file,
                 file_basename=incid.dual_file,
-                var_name=incid.var_name_one)
+                var_name=incid.var_name_one,
+            )
             LOGGER.info("Created infered dual-graph")
 
         self.incidence(
             edges=incid.edges,
             timeline=_timeline,
             inc_file=incid.inc_file,
-            num_vars=self.tree_dec['num_vars'],
-            colors=self.data.colors, view=view,
+            num_vars=self.tree_dec["num_vars"],
+            colors=self.data.colors,
+            view=view,
             fontsize=incid.fontsize,
             penwidth=incid.penwidth,
             basefill=self.data.bagcolor,
             var_name_one=incid.var_name_one,
             var_name_two=incid.var_name_two,
-            column_distance=incid.column_distance)
+            column_distance=incid.column_distance,
+        )
 
     def general_graph(
-            self,
-            timeline: Iterable[Optional[List[int]]],
-            edges: Iterable[Iterable[int]],
-            extra_nodes: Iterable[int] = tuple(),
-            view: bool = False,
-            fontsize: int = 20,
-            fontcolor: str = 'black',
-            penwidth: float = 2.2,
-            first_color: str = 'yellow',
-            first_style: str = 'filled',
-            second_color: str = 'green',
-            second_style: str = 'dotted,filled',
-            third_color: str = 'red',
-            graph_name: str = 'graph',
-            file_basename: str = 'graph',
-            do_sort_nodes: bool = True,
-            do_adj_nodes: bool = True,
-            var_name: str = '') -> None:
+        self,
+        timeline: Iterable[Optional[List[int]]],
+        edges: Iterable[Iterable[int]],
+        extra_nodes: Iterable[int] = tuple(),
+        view: bool = False,
+        fontsize: int = 20,
+        fontcolor: str = "black",
+        penwidth: float = 2.2,
+        first_color: str = "yellow",
+        first_style: str = "filled",
+        second_color: str = "green",
+        second_style: str = "dotted,filled",
+        third_color: str = "red",
+        graph_name: str = "graph",
+        file_basename: str = "graph",
+        do_sort_nodes: bool = True,
+        do_adj_nodes: bool = True,
+        var_name: str = "",
+    ) -> None:
         """
         Creates one graph emphasized for the given timeline.
 
@@ -423,113 +470,117 @@ def general_graph(
         """
         _filename = self.outfolder / file_basename
         LOGGER.info("Generating general-graph for '%s'", file_basename)
-        vartag_n: str = var_name + '%d'
+        vartag_n: str = var_name + "%d"
         # sfdp http://yifanhu.net/SOFTWARE/SFDP/index.html
-        default_engine = 'sfdp'
+        default_engine = "sfdp"
 
         graph = Graph(
             graph_name,
             strict=True,
             engine=default_engine,
             graph_attr={
-                'fontsize': str(fontsize),
-                'overlap': 'false',
-                'outputorder': 'edgesfirst',
-                'K': '2'},
+                "fontsize": str(fontsize),
+                "overlap": "false",
+                "outputorder": "edgesfirst",
+                "K": "2",
+            },
             node_attr={
-                'fontcolor': str(fontcolor),
-                'penwidth': str(penwidth),
-                'style': 'filled',
-                'fillcolor': 'white'})
+                "fontcolor": str(fontcolor),
+                "penwidth": str(penwidth),
+                "style": "filled",
+                "fillcolor": "white",
+            },
+        )
 
         if do_sort_nodes:
             bodybaselen = len(graph.body)
             # 1: layout with circo
-            graph.engine = 'circo'
+            graph.engine = "circo"
             # 2: nodes in edges+extra_nodes make a circle
-            nodes = sorted([vartag_n % n for n in set(
-                itertools.chain(flatten(edges), extra_nodes))],
-                key=lambda x: (len(x), x))
+            nodes = sorted(
+                [
+                    vartag_n % n
+                    for n in set(itertools.chain(flatten(edges), extra_nodes))
+                ],
+                key=lambda x: (len(x), x),
+            )
             for i, node in enumerate(nodes):
                 graph.edge(str(nodes[i - 1]), str(node))
             # 3: reads in bytes!
-            code_lines = graph.pipe('plain').splitlines()
+            code_lines = graph.pipe("plain").splitlines()
             # 4: save the (sorted) positions
-            assert code_lines[0].startswith(b'graph')
-            node_positions = [line.split()[1:4] for line in code_lines[1:]
-                              if line.startswith(b'node')]
+            assert code_lines[0].startswith(b"graph")
+            node_positions = [
+                line.split()[1:4] for line in code_lines[1:] if line.startswith(b"node")
+            ]
             # 5: cut layout
             graph.body = graph.body[:bodybaselen]
             for line in node_positions:
-                graph.node(line[0].decode(),
-                           pos='%f,%f!' % (float(line[1]), float(line[2])))
+                graph.node(
+                    line[0].decode(), pos="%f,%f!" % (float(line[1]), float(line[2]))
+                )
             # 6: Engine uses previous positions
-            graph.engine = 'neato'
+            graph.engine = "neato"
 
-        for (src, tar) in edges:
+        for src, tar in edges:
             graph.edge(vartag_n % src, vartag_n % tar)
         for nodeid in extra_nodes:
             graph.node(vartag_n % nodeid)
 
         bodybaselen = len(graph.body)
 
-        for i, variables in enumerate(timeline, start=1):    # all timesteps
+        for i, variables in enumerate(timeline, start=1):  # all timesteps
             # reset highlighting
             graph.body = graph.body[:bodybaselen]
 
             if variables is None:
-                graph.render(
-                    view=view,
-                    format='svg',
-                    filename=str(_filename) + str(i))
+                graph.render(view=view, format="svg", filename=str(_filename) + str(i))
                 continue
 
             for var in variables:
-                graph.node(
-                    vartag_n % var,
-                    fillcolor=first_color,
-                    style=first_style)
+                graph.node(vartag_n % var, fillcolor=first_color, style=first_style)
 
             # highlight edges between variables
-            for (s, t) in edges:
+            for s, t in edges:
                 if s in variables and t in variables:
                     graph.edge(
                         vartag_n % s,
                         vartag_n % t,
                         color=third_color,
-                        penwidth=str(penwidth))
+                        penwidth=str(penwidth),
+                    )
 
             if do_adj_nodes:
                 # set.difference accepts list as argument, "-" does not.
                 edges = [set(edge) for edge in edges]
                 adjacent = {
-                    edge.difference(variables).pop() for edge in edges if len(
-                        edge.difference(variables)) == 1}
+                    edge.difference(variables).pop()
+                    for edge in edges
+                    if len(edge.difference(variables)) == 1
+                }
 
                 for var in adjacent:
-                    graph.node(vartag_n % var,
-                               color=second_color,
-                               style=second_style)
+                    graph.node(vartag_n % var, color=second_color, style=second_style)
 
-            graph.render(view=view, format='svg',
-                         filename=str(_filename) + str(i))
+            graph.render(view=view, format="svg", filename=str(_filename) + str(i))
 
     def incidence(
-            self,
-            timeline: Iterable[Optional[List[int]]],
-            num_vars: int,
-            colors: List,
-            edges: List,
-            inc_file: str = 'IncidenceGraphStep',
-            view: bool = False,
-            fontsize: Union[str, int] = 16,
-            penwidth: float = 2.2,
-            basefill: str = 'white',
-            sndshape: str = 'diamond',
-            neg_tail: str = 'odot',
-            var_name_one: str = '',
-            var_name_two: str = '',
-            column_distance: float = 0.5) -> None:
+        self,
+        timeline: Iterable[Optional[List[int]]],
+        num_vars: int,
+        colors: List,
+        edges: List,
+        inc_file: str = "IncidenceGraphStep",
+        view: bool = False,
+        fontsize: Union[str, int] = 16,
+        penwidth: float = 2.2,
+        basefill: str = "white",
+        sndshape: str = "diamond",
+        neg_tail: str = "odot",
+        var_name_one: str = "",
+        var_name_two: str = "",
+        column_distance: float = 0.5,
+    ) -> None:
         """
         Creates the incidence graph emphasized for the given timeline.
 
@@ -566,125 +617,135 @@ def incidence(
         """
         _filename = self.outfolder / inc_file
 
-        clausetag_n = var_name_one + '%d'
-        vartag_n = var_name_two + '%d'
+        clausetag_n = var_name_one + "%d"
+        vartag_n = var_name_two + "%d"
 
         g_incid = Graph(
             inc_file,
             strict=True,
             graph_attr={
-                'splines': 'false',
-                'ranksep': '0.2',
-                'nodesep': str(float(column_distance)),
-                'fontsize': str(
-                    int(fontsize)),
-                'compound': 'true'},
+                "splines": "false",
+                "ranksep": "0.2",
+                "nodesep": str(float(column_distance)),
+                "fontsize": str(int(fontsize)),
+                "compound": "true",
+            },
             edge_attr={
-                'penwidth': str(float(penwidth)),
-                'dir': 'back',
-                'arrowtail': 'none'})
-        with g_incid.subgraph(name='cluster_clause',
-                              edge_attr={'style': 'invis'},
-                              node_attr={'style': 'rounded,filled',
-                                         'fillcolor': basefill}) as clauses:
-            clauses.attr(label='clauses')
-            clauses.edges([(clausetag_n % (i + 1), clausetag_n % (i + 2))
-                           for i in range(len(edges) - 1)])
-
-        g_incid.attr('node', shape=sndshape,
-                     penwidth=str(float(penwidth)),
-                     style='dotted')
-        with g_incid.subgraph(name='cluster_ivar',
-                              edge_attr={'style': 'invis'}) as ivars:
-            ivars.attr(label='variables')
-            ivars.edges([(vartag_n % (i + 1), vartag_n % (i + 2))
-                         for i in range(num_vars - 1)])
+                "penwidth": str(float(penwidth)),
+                "dir": "back",
+                "arrowtail": "none",
+            },
+        )
+        with g_incid.subgraph(
+            name="cluster_clause",
+            edge_attr={"style": "invis"},
+            node_attr={"style": "rounded,filled", "fillcolor": basefill},
+        ) as clauses:
+            clauses.attr(label="clauses")
+            clauses.edges(
+                [
+                    (clausetag_n % (i + 1), clausetag_n % (i + 2))
+                    for i in range(len(edges) - 1)
+                ]
+            )
+
+        g_incid.attr(
+            "node", shape=sndshape, penwidth=str(float(penwidth)), style="dotted"
+        )
+        with g_incid.subgraph(
+            name="cluster_ivar", edge_attr={"style": "invis"}
+        ) as ivars:
+            ivars.attr(label="variables")
+            ivars.edges(
+                [(vartag_n % (i + 1), vartag_n % (i + 2)) for i in range(num_vars - 1)]
+            )
             for i in range(num_vars):
-                g_incid.node(vartag_n %
-                             (i + 1), vartag_n %
-                             (i + 1), color=colors[(i + 1) %
-                                                   len(colors)])
+                g_incid.node(
+                    vartag_n % (i + 1),
+                    vartag_n % (i + 1),
+                    color=colors[(i + 1) % len(colors)],
+                )
 
-        g_incid.attr('edge', constraint='false')
+        g_incid.attr("edge", constraint="false")
 
         for clause in edges:
             for var in clause[1]:
                 if var >= 0:
-                    g_incid.edge(clausetag_n % clause[0],
-                                 vartag_n % var,
-                                 color=colors[var % len(colors)])
+                    g_incid.edge(
+                        clausetag_n % clause[0],
+                        vartag_n % var,
+                        color=colors[var % len(colors)],
+                    )
                 else:
-                    g_incid.edge(clausetag_n % clause[0],
-                                 vartag_n % -var,
-                                 color=colors[-var % len(colors)],
-                                 arrowtail=neg_tail)
+                    g_incid.edge(
+                        clausetag_n % clause[0],
+                        vartag_n % -var,
+                        color=colors[-var % len(colors)],
+                        arrowtail=neg_tail,
+                    )
 
         # make edgelist variable-based (varX, clauseY), ...
         #  var_cl_iter [(1, 1), (4, 1), ...
-        var_cl_iter = tuple(flatten([[(x, y[0]) for x in y[1]]
-                                     for y in edges]))
+        var_cl_iter = tuple(flatten([[(x, y[0]) for x in y[1]] for y in edges]))
 
         bodybaselen = len(g_incid.body)
-        for i, variables in enumerate(timeline, start=1):    # all timesteps
+        for i, variables in enumerate(timeline, start=1):  # all timesteps
 
             # reset highlighting
             g_incid.body = g_incid.body[:bodybaselen]
             if variables is None:
-                g_incid.render(view=view, format='svg',
-                               filename=str(_filename) + str(i))
+                g_incid.render(
+                    view=view, format="svg", filename=str(_filename) + str(i)
+                )
                 continue
 
             emp_clause = {
-                var_cl[1] for var_cl in var_cl_iter if abs(
-                    var_cl[0]) in variables}
+                var_cl[1] for var_cl in var_cl_iter if abs(var_cl[0]) in variables
+            }
 
-            emp_var = {abs(var_cl[0])
-                       for var_cl in var_cl_iter if var_cl[1] in emp_clause}
+            emp_var = {
+                abs(var_cl[0]) for var_cl in var_cl_iter if var_cl[1] in emp_clause
+            }
 
             for var in emp_var:
                 _vartag = vartag_n % abs(var)
-                _style = 'solid,filled' if var in variables else 'dotted,filled'
-                g_incid.node(
-                    _vartag,
-                    _vartag,
-                    style=_style,
-                    fillcolor='yellow')
+                _style = "solid,filled" if var in variables else "dotted,filled"
+                g_incid.node(_vartag, _vartag, style=_style, fillcolor="yellow")
 
             for clause in emp_clause:
                 g_incid.node(
-                    clausetag_n % clause,
-                    clausetag_n % clause,
-                    fillcolor='yellow')
+                    clausetag_n % clause, clausetag_n % clause, fillcolor="yellow"
+                )
 
             for edge in var_cl_iter:
                 (var, clause) = edge
 
-                _style = 'solid' if clause in emp_clause else 'dotted'
+                _style = "solid" if clause in emp_clause else "dotted"
                 _vartag = vartag_n % abs(var)
 
                 if var >= 0:
-                    g_incid.edge(clausetag_n % clause,
-                                 _vartag,
-                                 color=colors[var % len(colors)],
-                                 style=_style)
-                else:                                       # negated variable
-                    g_incid.edge(clausetag_n % clause,
-                                 _vartag,
-                                 color=colors[-var % len(colors)],
-                                 arrowtail='odot',
-                                 style=_style)
-
-            g_incid.render(
-                view=view,
-                format='svg',
-                filename=str(_filename) + str(i))
+                    g_incid.edge(
+                        clausetag_n % clause,
+                        _vartag,
+                        color=colors[var % len(colors)],
+                        style=_style,
+                    )
+                else:  # negated variable
+                    g_incid.edge(
+                        clausetag_n % clause,
+                        _vartag,
+                        color=colors[-var % len(colors)],
+                        arrowtail="odot",
+                        style=_style,
+                    )
+
+            g_incid.render(view=view, format="svg", filename=str(_filename) + str(i))
 
     def call_svgjoin(self) -> None:
         """Analyzes content in data.svg_join for the call to svg_join."""
         sj_data = self.data.svg_join
         if not sj_data.base_names:
-            LOGGER.warning(
-                "svg_join data in JsonAPI contains no file-names to join.")
+            LOGGER.warning("svg_join data in JsonAPI contains no file-names to join.")
             return
         if isinstance(sj_data.base_names, str):
             sj_data.base_names = [sj_data.base_names]
@@ -712,31 +773,30 @@ def main(args: List[str]) -> None:
     -------
     None
     """
-    parser = get_parser(
-        "Visualizing Dynamic Programming on Tree-Decompositions.")
+    parser = get_parser("Visualizing Dynamic Programming on Tree-Decompositions.")
     # possible to use stdin for the file.
-    parser.add_argument('infile', nargs='?',
-                        type=argparse.FileType('r', encoding='UTF-8'),
-                        default=sys.stdin,
-                        help="Input file for the visualization "
-                        "must conform with the 'JsonAPI.md'")
-    parser.add_argument('outfolder',
-                        help="Folder to output the visualization results")
+    parser.add_argument(
+        "infile",
+        nargs="?",
+        type=argparse.FileType("r", encoding="UTF-8"),
+        default=sys.stdin,
+        help="Input file for the visualization " "must conform with the 'JsonAPI.md'",
+    )
+    parser.add_argument("outfolder", help="Folder to output the visualization results")
 
     # get cmd-arguments
     options = parser.parse_args(args)
 
-    logging_cfg(filename='logging.yml', loglevel=options.loglevel)
+    logging_cfg(filename="logging.yml", loglevel=options.loglevel)
     LOGGER.info("Called with '%s'", options)
 
     infile = options.infile
     outfolder = options.outfolder
     if not outfolder:
-        outfolder = 'outfolder'
+        outfolder = "outfolder"
     outfolder = Path(outfolder).resolve()
 
-    LOGGER.info("Will read from '%s' and write to folder '%s'",
-                infile.name, outfolder)
+    LOGGER.info("Will read from '%s' and write to folder '%s'", infile.name, outfolder)
     visu = Visualization(infile=infile, outfolder=outfolder)
     visu.tree_dec_timeline()
 
diff --git a/tdvisu/visualization_data.py b/tdvisu/visualization_data.py
index 439debe..8f2c9ee 100644
--- a/tdvisu/visualization_data.py
+++ b/tdvisu/visualization_data.py
@@ -28,11 +28,12 @@
 @dataclass
 class SvgJoinData:
     """Class for holding different parameters to join the results."""
+
     base_names: Union[str, Iterable[str]]
     folder: Optional[str] = None
-    outname: str = 'combined'
-    suffix: str = '%d.svg'
-    preserve_aspectratio: str = 'xMinYMin'
+    outname: str = "combined"
+    suffix: str = "%d.svg"
+    preserve_aspectratio: str = "xMinYMin"
     num_images: int = 1
     padding: Union[int, Iterable[int]] = 0
     scale2: Union[float, Iterable[float]] = 1.0
@@ -43,38 +44,40 @@ class SvgJoinData:
 @dataclass
 class IncidenceGraphData:
     """Class holding different parameters for the incidence graph."""
+
     edges: list
-    subgraph_name_one: str = 'clauses'
-    subgraph_name_two: str = 'variables'
-    var_name_one: str = ''
-    var_name_two: str = ''
+    subgraph_name_one: str = "clauses"
+    subgraph_name_two: str = "variables"
+    var_name_one: str = ""
+    var_name_two: str = ""
     infer_primal: bool = False
     infer_dual: bool = False
-    primal_file: str = 'PrimalGraphStep'
-    inc_file: str = 'IncidenceGraphStep'
-    dual_file: str = 'DualGraphStep'
+    primal_file: str = "PrimalGraphStep"
+    inc_file: str = "IncidenceGraphStep"
+    dual_file: str = "DualGraphStep"
     fontsize: int = 16
     penwidth: float = 2.2
-    second_shape: str = 'diamond'
+    second_shape: str = "diamond"
     column_distance: float = 0.5
 
 
 @dataclass
 class GeneralGraphData:
     """Class holding different parameters for the general graph."""
+
     edges: list
     extra_nodes: Optional[list] = None
-    graph_name: str = 'graph'
-    file_basename: str = 'graph'
-    var_name: str = ''
+    graph_name: str = "graph"
+    file_basename: str = "graph"
+    var_name: str = ""
     do_sort_nodes: bool = False
     do_adj_nodes: bool = False
     fontsize: int = 20
-    first_color: str = 'yellow'
-    first_style: str = 'filled'
-    second_color: str = 'green'
-    second_style: str = 'dotted,filled'
-    third_color: str = 'red'
+    first_color: str = "yellow"
+    first_style: str = "filled"
+    second_color: str = "green"
+    second_style: str = "dotted,filled"
+    third_color: str = "red"
 
     def __post_init__(self):
         if self.extra_nodes is None:
@@ -84,46 +87,51 @@ def __post_init__(self):
 @dataclass
 class VisualizationData:
     """Class holding different parameters for Visualization."""
+
     incidence_graphs: Optional[List[IncidenceGraphData]] = None
     general_graphs: Optional[List[GeneralGraphData]] = None
     svg_join: Optional[SvgJoinData] = None
-    td_file: str = 'TDStep'
+    td_file: str = "TDStep"
     colors: Optional[list] = None
-    orientation: str = 'BT'
+    orientation: str = "BT"
     linesmax: int = 100
     columnsmax: int = 20
-    bagcolor: str = 'white'
+    bagcolor: str = "white"
     fontsize: int = 20
     penwidth: float = 2.2
-    fontcolor: str = 'black'
+    fontcolor: str = "black"
     emphasis: Optional[dict] = None
 
     def __post_init__(self):
         if self.colors is None:
             self.colors = [
-                '#0073a1',
-                '#b14923',
-                '#244320',
-                '#b1740f',
-                '#a682ff',
-                '#004066',
-                '#0d1321',
-                '#da1167',
-                '#604909',
-                '#0073a1',
-                '#b14923',
-                '#244320',
-                '#b1740f',
-                '#a682ff']
+                "#0073a1",
+                "#b14923",
+                "#244320",
+                "#b1740f",
+                "#a682ff",
+                "#004066",
+                "#0d1321",
+                "#da1167",
+                "#604909",
+                "#0073a1",
+                "#b14923",
+                "#244320",
+                "#b1740f",
+                "#a682ff",
+            ]
         if self.emphasis is None:
             self.emphasis = dict()
         # merge input over defaults:
-        self.emphasis = {**{"firstcolor": 'yellow',
-                            "secondcolor": 'green',
-                            "firststyle": 'filled',
-                            "secondstyle": 'dotted,filled'
-                            },
-                         **self.emphasis}
+        self.emphasis = {
+            **{
+                "firstcolor": "yellow",
+                "secondcolor": "green",
+                "firststyle": "filled",
+                "secondstyle": "dotted,filled",
+            },
+            **self.emphasis,
+        }
 
 
 if __name__ == "__main__":  # pragma: no cover
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep1 b/test/expected_files/test_sat_and_join/PrimalGraphStep1
index 059bc8e..0180a69 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep1
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep1
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep2 b/test/expected_files/test_sat_and_join/PrimalGraphStep2
index 0effa1e..437d49b 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep2
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep2
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep3 b/test/expected_files/test_sat_and_join/PrimalGraphStep3
index dbc4132..8c369fd 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep3
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep3
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep4 b/test/expected_files/test_sat_and_join/PrimalGraphStep4
index 110797e..3ba1703 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep4
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep4
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep5 b/test/expected_files/test_sat_and_join/PrimalGraphStep5
index c296a41..6bc3ba7 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep5
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep5
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_sat_and_join/PrimalGraphStep6 b/test/expected_files/test_sat_and_join/PrimalGraphStep6
index 9a442ff..bcbd712 100644
--- a/test/expected_files/test_sat_and_join/PrimalGraphStep6
+++ b/test/expected_files/test_sat_and_join/PrimalGraphStep6
@@ -1,14 +1,14 @@
 strict graph PrimalGraphStep {
 	graph [K=2 fontsize=20 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	v_8 [pos="2.454100,0.606720!"]
-	v_1 [pos="1.592900,0.250000!"]
-	v_2 [pos="0.731720,0.606720!"]
-	v_3 [pos="0.375000,1.467900!"]
-	v_4 [pos="0.731720,2.329100!"]
-	v_5 [pos="1.592900,2.685800!"]
-	v_6 [pos="2.454100,2.329100!"]
-	v_7 [pos="2.810800,1.467900!"]
+	v_8 [pos="5.225600,1.082200!"]
+	v_1 [pos="3.216400,0.250000!"]
+	v_2 [pos="1.207200,1.082200!"]
+	v_3 [pos="0.375000,3.091400!"]
+	v_4 [pos="1.207200,5.100600!"]
+	v_5 [pos="3.216400,5.932800!"]
+	v_6 [pos="5.225600,5.100600!"]
+	v_7 [pos="6.057800,3.091400!"]
 	v_3 -- v_8
 	v_1 -- v_5
 	v_4 -- v_6
diff --git a/test/expected_files/test_vc_multiple_and_join/TDStep1.svg b/test/expected_files/test_vc_multiple_and_join/TDStep1.svg
index a9bad39..f572ba3 100644
--- a/test/expected_files/test_vc_multiple_and_join/TDStep1.svg
+++ b/test/expected_files/test_vc_multiple_and_join/TDStep1.svg
@@ -1,73 +1,73 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.41.20170921.1950 (20170921.1950)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: Tree&#45;Decomposition Pages: 1 -->
-<svg width="467pt" height="624pt"
- viewBox="0.00 0.00 467.00 624.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="460pt" height="652pt"
+ viewBox="0.00 0.00 459.86 652.38" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 <title>Tree&#45;Decomposition</title>
-<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"/>
 <!-- bag 1 -->
 <g id="node1" class="node">
 <title>bag 1</title>
-<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"/>
-<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"/>
-<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"/>
+<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"/>
+<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 </g>
 <!-- sol1 -->
 <!-- bag 1&#45;&gt;sol1 -->
 <!-- bag 2 -->
 <g id="node2" class="node">
 <title>bag 2</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"/>
-<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"/>
-<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"/>
+<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"/>
+<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 </g>
 <!-- bag 2&#45;&gt;bag 1 -->
 <g id="edge1" class="edge">
 <title>bag 2&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"/>
-<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"/>
+<path fill="none" stroke="black" d="M143.13,-209.36C153.29,-238.13 168.06,-279.99 179.14,-311.4"/>
+<polygon fill="black" stroke="black" points="175.76,-312.35 182.39,-320.61 182.37,-310.02 175.76,-312.35"/>
 </g>
 <!-- sol2 -->
 <!-- bag 2&#45;&gt;sol2 -->
 <!-- bag 3 -->
 <g id="node3" class="node">
 <title>bag 3</title>
-<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"/>
-<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"/>
-<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"/>
+<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"/>
+<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 </g>
 <!-- bag 3&#45;&gt;bag 1 -->
 <g id="edge2" class="edge">
 <title>bag 3&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"/>
-<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"/>
+<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"/>
+<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"/>
 </g>
 <!-- sol3 -->
 <!-- bag 3&#45;&gt;sol3 -->
 <!-- bag 4 -->
 <g id="node4" class="node">
 <title>bag 4</title>
-<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"/>
-<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"/>
-<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"/>
+<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"/>
+<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 </g>
 <!-- bag 4&#45;&gt;bag 3 -->
 <g id="edge3" class="edge">
 <title>bag 4&#45;&gt;bag 3</title>
-<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"/>
-<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"/>
+<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"/>
+<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"/>
 </g>
 <!-- sol4 -->
 <!-- bag 4&#45;&gt;sol4 -->
diff --git a/test/expected_files/test_vc_multiple_and_join/TDStep2.svg b/test/expected_files/test_vc_multiple_and_join/TDStep2.svg
index 9951c19..5d8bea3 100644
--- a/test/expected_files/test_vc_multiple_and_join/TDStep2.svg
+++ b/test/expected_files/test_vc_multiple_and_join/TDStep2.svg
@@ -1,133 +1,133 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.41.20170921.1950 (20170921.1950)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: Tree&#45;Decomposition Pages: 1 -->
-<svg width="467pt" height="624pt"
- viewBox="0.00 0.00 467.00 624.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="460pt" height="652pt"
+ viewBox="0.00 0.00 459.86 652.38" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 <title>Tree&#45;Decomposition</title>
-<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"/>
 <!-- bag 1 -->
 <g id="node1" class="node">
 <title>bag 1</title>
-<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"/>
-<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"/>
-<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"/>
+<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"/>
+<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 </g>
 <!-- sol1 -->
 <!-- bag 1&#45;&gt;sol1 -->
 <!-- bag 2 -->
 <g id="node2" class="node">
 <title>bag 2</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"/>
-<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"/>
-<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"/>
+<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"/>
+<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 </g>
 <!-- bag 2&#45;&gt;bag 1 -->
 <g id="edge1" class="edge">
 <title>bag 2&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"/>
-<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"/>
+<path fill="none" stroke="black" d="M143.13,-209.36C153.29,-238.13 168.06,-279.99 179.14,-311.4"/>
+<polygon fill="black" stroke="black" points="175.76,-312.35 182.39,-320.61 182.37,-310.02 175.76,-312.35"/>
 </g>
 <!-- sol2 -->
 <g id="node5" class="node">
 <title>sol2</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"/>
-<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-391.5 128,-391.5 "/>
-<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-374.5 30,-374.5 "/>
-<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-357.5 30,-357.5 "/>
-<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-340.5 30,-340.5 "/>
-<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-323.5 30,-323.5 "/>
-<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-306.5 30,-306.5 "/>
-<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-289.5 30,-391.5 "/>
-<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-374.5 60,-374.5 "/>
-<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-357.5 60,-357.5 "/>
-<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-340.5 60,-340.5 "/>
-<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-323.5 60,-323.5 "/>
-<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-306.5 60,-306.5 "/>
-<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-289.5 60,-391.5 "/>
-<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-374.5 90,-374.5 "/>
-<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-357.5 90,-357.5 "/>
-<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-340.5 90,-340.5 "/>
-<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-323.5 90,-323.5 "/>
-<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-306.5 90,-306.5 "/>
-<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-289.5 90,-391.5 "/>
-<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-374.5 128,-374.5 "/>
-<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-357.5 128,-357.5 "/>
-<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-340.5 128,-340.5 "/>
-<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-323.5 128,-323.5 "/>
-<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-306.5 128,-306.5 "/>
-<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-289.5 128,-289.5 "/>
-<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"/>
+<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-409.54 124.86,-409.54"/>
+<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-391.6 29.34,-391.6"/>
+<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-373.66 29.34,-373.66"/>
+<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-355.72 29.34,-355.72"/>
+<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-337.78 29.34,-337.78"/>
+<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-319.84 29.34,-319.84"/>
+<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-301.9 29.34,-409.54"/>
+<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-391.6 58.68,-391.6"/>
+<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-373.66 58.68,-373.66"/>
+<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-355.72 58.68,-355.72"/>
+<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-337.78 58.68,-337.78"/>
+<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-319.84 58.68,-319.84"/>
+<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-301.9 58.68,-409.54"/>
+<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-391.6 88.02,-391.6"/>
+<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-373.66 88.02,-373.66"/>
+<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-355.72 88.02,-355.72"/>
+<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-337.78 88.02,-337.78"/>
+<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-319.84 88.02,-319.84"/>
+<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-301.9 88.02,-409.54"/>
+<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-391.6 124.86,-391.6"/>
+<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-373.66 124.86,-373.66"/>
+<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-355.72 124.86,-355.72"/>
+<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-337.78 124.86,-337.78"/>
+<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-319.84 124.86,-319.84"/>
+<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-301.9 124.86,-301.9"/>
+<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 2&#45;&gt;sol2 -->
 <g id="edge4" class="edge">
 <title>bag 2&#45;&gt;sol2</title>
-<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"/>
-<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"/>
+<path fill="none" stroke="black" d="M118.61,-209.36C111.68,-227.29 102.79,-250.3 94.13,-272.7"/>
+<polygon fill="black" stroke="black" points="90.93,-271.28 90.59,-281.86 97.46,-273.8 90.93,-271.28"/>
 </g>
 <!-- bag 3 -->
 <g id="node3" class="node">
 <title>bag 3</title>
-<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"/>
-<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"/>
-<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"/>
+<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"/>
+<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 </g>
 <!-- bag 3&#45;&gt;bag 1 -->
 <g id="edge2" class="edge">
 <title>bag 3&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"/>
-<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"/>
+<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"/>
+<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"/>
 </g>
 <!-- sol3 -->
 <!-- bag 3&#45;&gt;sol3 -->
 <!-- bag 4 -->
 <g id="node4" class="node">
 <title>bag 4</title>
-<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"/>
-<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"/>
-<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"/>
+<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"/>
+<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 </g>
 <!-- bag 4&#45;&gt;bag 3 -->
 <g id="edge3" class="edge">
 <title>bag 4&#45;&gt;bag 3</title>
-<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"/>
-<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"/>
+<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"/>
+<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"/>
 </g>
 <!-- sol4 -->
 <!-- bag 4&#45;&gt;sol4 -->
diff --git a/test/expected_files/test_vc_multiple_and_join/TDStep3.svg b/test/expected_files/test_vc_multiple_and_join/TDStep3.svg
index 3785276..7321e21 100644
--- a/test/expected_files/test_vc_multiple_and_join/TDStep3.svg
+++ b/test/expected_files/test_vc_multiple_and_join/TDStep3.svg
@@ -1,195 +1,195 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.41.20170921.1950 (20170921.1950)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: Tree&#45;Decomposition Pages: 1 -->
-<svg width="467pt" height="624pt"
- viewBox="0.00 0.00 467.00 624.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="460pt" height="652pt"
+ viewBox="0.00 0.00 459.86 652.38" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 <title>Tree&#45;Decomposition</title>
-<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"/>
 <!-- bag 1 -->
 <g id="node1" class="node">
 <title>bag 1</title>
-<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"/>
-<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"/>
-<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"/>
+<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"/>
+<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 </g>
 <!-- sol1 -->
 <!-- bag 1&#45;&gt;sol1 -->
 <!-- bag 2 -->
 <g id="node2" class="node">
 <title>bag 2</title>
-<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"/>
-<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"/>
-<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"/>
+<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"/>
+<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 </g>
 <!-- bag 2&#45;&gt;bag 1 -->
 <g id="edge1" class="edge">
 <title>bag 2&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"/>
-<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"/>
+<path fill="none" stroke="black" d="M142.99,-208.94C153.12,-237.67 167.94,-279.65 179.07,-311.2"/>
+<polygon fill="black" stroke="black" points="175.71,-312.19 182.34,-320.46 182.31,-309.86 175.71,-312.19"/>
 </g>
 <!-- sol2 -->
 <g id="node5" class="node">
 <title>sol2</title>
-<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"/>
-<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "/>
-<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "/>
-<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "/>
-<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "/>
-<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "/>
-<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "/>
-<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "/>
-<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "/>
-<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "/>
-<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "/>
-<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "/>
-<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "/>
-<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "/>
-<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "/>
-<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "/>
-<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "/>
-<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "/>
-<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "/>
-<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "/>
-<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "/>
-<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "/>
-<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "/>
-<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "/>
-<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "/>
-<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "/>
-<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"/>
+<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"/>
+<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"/>
+<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"/>
+<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"/>
+<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"/>
+<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"/>
+<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"/>
+<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"/>
+<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"/>
+<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"/>
+<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"/>
+<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"/>
+<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"/>
+<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"/>
+<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"/>
+<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"/>
+<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"/>
+<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"/>
+<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"/>
+<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"/>
+<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"/>
+<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"/>
+<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"/>
+<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"/>
+<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"/>
+<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 2&#45;&gt;sol2 -->
 <g id="edge4" class="edge">
 <title>bag 2&#45;&gt;sol2</title>
-<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"/>
-<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"/>
+<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"/>
+<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"/>
 </g>
 <!-- bag 3 -->
 <g id="node3" class="node">
 <title>bag 3</title>
-<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"/>
-<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"/>
-<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"/>
+<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"/>
+<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 </g>
 <!-- bag 3&#45;&gt;bag 1 -->
 <g id="edge2" class="edge">
 <title>bag 3&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"/>
-<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"/>
+<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"/>
+<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"/>
 </g>
 <!-- sol3 -->
 <!-- bag 3&#45;&gt;sol3 -->
 <!-- bag 4 -->
 <g id="node4" class="node">
 <title>bag 4</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"/>
-<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"/>
-<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"/>
+<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"/>
+<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 </g>
 <!-- bag 4&#45;&gt;bag 3 -->
 <g id="edge3" class="edge">
 <title>bag 4&#45;&gt;bag 3</title>
-<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"/>
-<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"/>
+<path fill="none" stroke="black" d="M307.62,-67.94C298.66,-86.91 287.35,-110.86 277.73,-131.22"/>
+<polygon fill="black" stroke="black" points="274.63,-129.58 273.53,-140.12 280.96,-132.57 274.63,-129.58"/>
 </g>
 <!-- sol4 -->
 <g id="node6" class="node">
 <title>sol4</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"/>
-<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-218.5 459,-218.5 "/>
-<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-201.5 361,-201.5 "/>
-<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-184.5 361,-184.5 "/>
-<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-167.5 361,-167.5 "/>
-<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-150.5 361,-150.5 "/>
-<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-133.5 361,-133.5 "/>
-<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-116.5 361,-218.5 "/>
-<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-201.5 391,-201.5 "/>
-<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-184.5 391,-184.5 "/>
-<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-167.5 391,-167.5 "/>
-<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-150.5 391,-150.5 "/>
-<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-133.5 391,-133.5 "/>
-<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-116.5 391,-218.5 "/>
-<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-201.5 421,-201.5 "/>
-<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-184.5 421,-184.5 "/>
-<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-167.5 421,-167.5 "/>
-<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-150.5 421,-150.5 "/>
-<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-133.5 421,-133.5 "/>
-<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-116.5 421,-218.5 "/>
-<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-201.5 459,-201.5 "/>
-<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-184.5 459,-184.5 "/>
-<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-167.5 459,-167.5 "/>
-<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-150.5 459,-150.5 "/>
-<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-133.5 459,-133.5 "/>
-<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-116.5 459,-116.5 "/>
-<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"/>
+<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-229.02 451.86,-229.02"/>
+<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-211.08 356.34,-211.08"/>
+<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-193.14 356.34,-193.14"/>
+<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-175.2 356.34,-175.2"/>
+<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-157.26 356.34,-157.26"/>
+<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-139.32 356.34,-139.32"/>
+<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-121.38 356.34,-229.02"/>
+<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-211.08 385.68,-211.08"/>
+<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-193.14 385.68,-193.14"/>
+<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-175.2 385.68,-175.2"/>
+<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-157.26 385.68,-157.26"/>
+<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-139.32 385.68,-139.32"/>
+<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-121.38 385.68,-229.02"/>
+<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-211.08 415.02,-211.08"/>
+<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-193.14 415.02,-193.14"/>
+<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-175.2 415.02,-175.2"/>
+<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-157.26 415.02,-157.26"/>
+<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-139.32 415.02,-139.32"/>
+<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-121.38 415.02,-229.02"/>
+<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-211.08 451.86,-211.08"/>
+<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-193.14 451.86,-193.14"/>
+<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-175.2 451.86,-175.2"/>
+<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-157.26 451.86,-157.26"/>
+<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-139.32 451.86,-139.32"/>
+<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-121.38 451.86,-121.38"/>
+<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 4&#45;&gt;sol4 -->
 <g id="edge5" class="edge">
 <title>bag 4&#45;&gt;sol4</title>
-<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"/>
-<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"/>
+<path fill="none" stroke="black" d="M339.24,-67.94C342.8,-75.48 346.74,-83.81 350.79,-92.39"/>
+<polygon fill="black" stroke="black" points="347.5,-93.62 354.94,-101.17 353.83,-90.63 347.5,-93.62"/>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/TDStep4.svg b/test/expected_files/test_vc_multiple_and_join/TDStep4.svg
index 756dec9..2c2f6de 100644
--- a/test/expected_files/test_vc_multiple_and_join/TDStep4.svg
+++ b/test/expected_files/test_vc_multiple_and_join/TDStep4.svg
@@ -1,255 +1,255 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.41.20170921.1950 (20170921.1950)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: Tree&#45;Decomposition Pages: 1 -->
-<svg width="467pt" height="624pt"
- viewBox="0.00 0.00 467.00 624.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="460pt" height="652pt"
+ viewBox="0.00 0.00 459.86 652.38" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 <title>Tree&#45;Decomposition</title>
-<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"/>
 <!-- bag 1 -->
 <g id="node1" class="node">
 <title>bag 1</title>
-<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"/>
-<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"/>
-<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"/>
+<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"/>
+<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 </g>
 <!-- sol1 -->
 <!-- bag 1&#45;&gt;sol1 -->
 <!-- bag 2 -->
 <g id="node2" class="node">
 <title>bag 2</title>
-<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"/>
-<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"/>
-<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"/>
+<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"/>
+<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 </g>
 <!-- bag 2&#45;&gt;bag 1 -->
 <g id="edge1" class="edge">
 <title>bag 2&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"/>
-<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"/>
+<path fill="none" stroke="black" d="M142.99,-208.94C153.12,-237.67 167.94,-279.65 179.07,-311.2"/>
+<polygon fill="black" stroke="black" points="175.71,-312.19 182.34,-320.46 182.31,-309.86 175.71,-312.19"/>
 </g>
 <!-- sol2 -->
 <g id="node5" class="node">
 <title>sol2</title>
-<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"/>
-<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "/>
-<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "/>
-<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "/>
-<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "/>
-<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "/>
-<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "/>
-<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "/>
-<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "/>
-<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "/>
-<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "/>
-<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "/>
-<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "/>
-<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "/>
-<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "/>
-<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "/>
-<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "/>
-<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "/>
-<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "/>
-<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "/>
-<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "/>
-<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "/>
-<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "/>
-<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "/>
-<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "/>
-<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "/>
-<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"/>
+<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"/>
+<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"/>
+<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"/>
+<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"/>
+<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"/>
+<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"/>
+<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"/>
+<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"/>
+<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"/>
+<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"/>
+<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"/>
+<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"/>
+<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"/>
+<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"/>
+<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"/>
+<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"/>
+<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"/>
+<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"/>
+<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"/>
+<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"/>
+<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"/>
+<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"/>
+<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"/>
+<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"/>
+<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"/>
+<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 2&#45;&gt;sol2 -->
 <g id="edge4" class="edge">
 <title>bag 2&#45;&gt;sol2</title>
-<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"/>
-<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"/>
+<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"/>
+<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"/>
 </g>
 <!-- bag 3 -->
 <g id="node3" class="node">
 <title>bag 3</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"/>
-<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"/>
-<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"/>
+<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"/>
+<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 </g>
 <!-- bag 3&#45;&gt;bag 1 -->
 <g id="edge2" class="edge">
 <title>bag 3&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"/>
-<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"/>
+<path fill="none" stroke="black" d="M245.73,-209.36C235.57,-238.13 220.8,-279.99 209.72,-311.4"/>
+<polygon fill="black" stroke="black" points="206.49,-310.02 206.47,-320.61 213.1,-312.35 206.49,-310.02"/>
 </g>
 <!-- sol3 -->
 <g id="node7" class="node">
 <title>sol3</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M280,-272.5C280,-272.5 384,-272.5 384,-272.5 390,-272.5 396,-278.5 396,-284.5 396,-284.5 396,-396.5 396,-396.5 396,-402.5 390,-408.5 384,-408.5 384,-408.5 280,-408.5 280,-408.5 274,-408.5 268,-402.5 268,-396.5 268,-396.5 268,-284.5 268,-284.5 268,-278.5 274,-272.5 280,-272.5"/>
-<text text-anchor="middle" x="332" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-391.5 396,-391.5 "/>
-<text text-anchor="middle" x="283" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-374.5 298,-374.5 "/>
-<text text-anchor="middle" x="283" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-357.5 298,-357.5 "/>
-<text text-anchor="middle" x="283" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-340.5 298,-340.5 "/>
-<text text-anchor="middle" x="283" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-323.5 298,-323.5 "/>
-<text text-anchor="middle" x="283" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-306.5 298,-306.5 "/>
-<text text-anchor="middle" x="283" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-289.5 298,-391.5 "/>
-<text text-anchor="middle" x="313" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-374.5 328,-374.5 "/>
-<text text-anchor="middle" x="313" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-357.5 328,-357.5 "/>
-<text text-anchor="middle" x="313" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-340.5 328,-340.5 "/>
-<text text-anchor="middle" x="313" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-323.5 328,-323.5 "/>
-<text text-anchor="middle" x="313" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-306.5 328,-306.5 "/>
-<text text-anchor="middle" x="313" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-289.5 328,-391.5 "/>
-<text text-anchor="middle" x="343" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-374.5 358,-374.5 "/>
-<text text-anchor="middle" x="343" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-357.5 358,-357.5 "/>
-<text text-anchor="middle" x="343" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-340.5 358,-340.5 "/>
-<text text-anchor="middle" x="343" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-323.5 358,-323.5 "/>
-<text text-anchor="middle" x="343" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-306.5 358,-306.5 "/>
-<text text-anchor="middle" x="343" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-289.5 358,-391.5 "/>
-<text text-anchor="middle" x="377" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-374.5 396,-374.5 "/>
-<text text-anchor="middle" x="377" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-357.5 396,-357.5 "/>
-<text text-anchor="middle" x="377" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-340.5 396,-340.5 "/>
-<text text-anchor="middle" x="377" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-323.5 396,-323.5 "/>
-<text text-anchor="middle" x="377" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-306.5 396,-306.5 "/>
-<text text-anchor="middle" x="377" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-289.5 396,-289.5 "/>
-<text text-anchor="middle" x="332" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 3</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M276,-283.96C276,-283.96 376.86,-283.96 376.86,-283.96 382.86,-283.96 388.86,-289.96 388.86,-295.96 388.86,-295.96 388.86,-415.48 388.86,-415.48 388.86,-421.48 382.86,-427.48 376.86,-427.48 376.86,-427.48 276,-427.48 276,-427.48 270,-427.48 264,-421.48 264,-415.48 264,-415.48 264,-295.96 264,-295.96 264,-289.96 270,-283.96 276,-283.96"/>
+<text text-anchor="middle" x="326.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-409.54 388.86,-409.54"/>
+<text text-anchor="middle" x="278.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-391.6 293.34,-391.6"/>
+<text text-anchor="middle" x="278.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-373.66 293.34,-373.66"/>
+<text text-anchor="middle" x="278.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-355.72 293.34,-355.72"/>
+<text text-anchor="middle" x="278.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-337.78 293.34,-337.78"/>
+<text text-anchor="middle" x="278.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-319.84 293.34,-319.84"/>
+<text text-anchor="middle" x="278.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-301.9 293.34,-409.54"/>
+<text text-anchor="middle" x="308.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-391.6 322.68,-391.6"/>
+<text text-anchor="middle" x="308.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-373.66 322.68,-373.66"/>
+<text text-anchor="middle" x="308.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-355.72 322.68,-355.72"/>
+<text text-anchor="middle" x="308.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-337.78 322.68,-337.78"/>
+<text text-anchor="middle" x="308.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-319.84 322.68,-319.84"/>
+<text text-anchor="middle" x="308.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-301.9 322.68,-409.54"/>
+<text text-anchor="middle" x="337.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-391.6 352.02,-391.6"/>
+<text text-anchor="middle" x="337.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-373.66 352.02,-373.66"/>
+<text text-anchor="middle" x="337.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-355.72 352.02,-355.72"/>
+<text text-anchor="middle" x="337.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-337.78 352.02,-337.78"/>
+<text text-anchor="middle" x="337.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-319.84 352.02,-319.84"/>
+<text text-anchor="middle" x="337.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-301.9 352.02,-409.54"/>
+<text text-anchor="middle" x="370.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-391.6 388.86,-391.6"/>
+<text text-anchor="middle" x="370.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-373.66 388.86,-373.66"/>
+<text text-anchor="middle" x="370.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-355.72 388.86,-355.72"/>
+<text text-anchor="middle" x="370.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-337.78 388.86,-337.78"/>
+<text text-anchor="middle" x="370.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-319.84 388.86,-319.84"/>
+<text text-anchor="middle" x="370.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-301.9 388.86,-301.9"/>
+<text text-anchor="middle" x="326.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 3</text>
 </g>
 <!-- bag 3&#45;&gt;sol3 -->
 <g id="edge6" class="edge">
 <title>bag 3&#45;&gt;sol3</title>
-<path fill="none" stroke="black" d="M273.69,-199.07C281.13,-216.97 290.87,-240.44 300.26,-263.06"/>
-<polygon fill="black" stroke="black" points="297.05,-264.44 304.11,-272.34 303.51,-261.76 297.05,-264.44"/>
+<path fill="none" stroke="black" d="M270.25,-209.36C277.18,-227.29 286.07,-250.3 294.73,-272.7"/>
+<polygon fill="black" stroke="black" points="291.4,-273.8 298.27,-281.86 297.93,-271.28 291.4,-273.8"/>
 </g>
 <!-- bag 4 -->
 <g id="node4" class="node">
 <title>bag 4</title>
-<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"/>
-<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"/>
-<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"/>
+<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"/>
+<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 </g>
 <!-- bag 4&#45;&gt;bag 3 -->
 <g id="edge3" class="edge">
 <title>bag 4&#45;&gt;bag 3</title>
-<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"/>
-<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"/>
+<path fill="none" stroke="black" d="M307.96,-67.23C299,-86.19 287.62,-110.28 277.93,-130.8"/>
+<polygon fill="black" stroke="black" points="274.79,-129.26 273.68,-139.79 281.12,-132.24 274.79,-129.26"/>
 </g>
 <!-- sol4 -->
 <g id="node6" class="node">
 <title>sol4</title>
-<path fill="white" stroke="black" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"/>
-<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-<polyline fill="none" stroke="black" points="331,-218.5 459,-218.5 "/>
-<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="331,-201.5 361,-201.5 "/>
-<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-184.5 361,-184.5 "/>
-<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-167.5 361,-167.5 "/>
-<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-150.5 361,-150.5 "/>
-<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-133.5 361,-133.5 "/>
-<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-116.5 361,-218.5 "/>
-<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-<polyline fill="none" stroke="black" points="361,-201.5 391,-201.5 "/>
-<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="361,-184.5 391,-184.5 "/>
-<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-167.5 391,-167.5 "/>
-<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-150.5 391,-150.5 "/>
-<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="361,-133.5 391,-133.5 "/>
-<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-116.5 391,-218.5 "/>
-<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" points="391,-201.5 421,-201.5 "/>
-<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="391,-184.5 421,-184.5 "/>
-<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-167.5 421,-167.5 "/>
-<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="391,-150.5 421,-150.5 "/>
-<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-133.5 421,-133.5 "/>
-<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="421,-116.5 421,-218.5 "/>
-<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="421,-201.5 459,-201.5 "/>
-<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-184.5 459,-184.5 "/>
-<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-167.5 459,-167.5 "/>
-<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" points="421,-150.5 459,-150.5 "/>
-<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-133.5 459,-133.5 "/>
-<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="331,-116.5 459,-116.5 "/>
-<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="white" stroke="black" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"/>
+<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+<polyline fill="none" stroke="black" points="327,-229.02 451.86,-229.02"/>
+<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="327,-211.08 356.34,-211.08"/>
+<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-193.14 356.34,-193.14"/>
+<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-175.2 356.34,-175.2"/>
+<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-157.26 356.34,-157.26"/>
+<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-139.32 356.34,-139.32"/>
+<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-121.38 356.34,-229.02"/>
+<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+<polyline fill="none" stroke="black" points="356.34,-211.08 385.68,-211.08"/>
+<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="356.34,-193.14 385.68,-193.14"/>
+<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-175.2 385.68,-175.2"/>
+<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-157.26 385.68,-157.26"/>
+<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="356.34,-139.32 385.68,-139.32"/>
+<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-121.38 385.68,-229.02"/>
+<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" points="385.68,-211.08 415.02,-211.08"/>
+<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="385.68,-193.14 415.02,-193.14"/>
+<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-175.2 415.02,-175.2"/>
+<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="385.68,-157.26 415.02,-157.26"/>
+<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-139.32 415.02,-139.32"/>
+<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="415.02,-121.38 415.02,-229.02"/>
+<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="415.02,-211.08 451.86,-211.08"/>
+<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-193.14 451.86,-193.14"/>
+<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-175.2 451.86,-175.2"/>
+<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" points="415.02,-157.26 451.86,-157.26"/>
+<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-139.32 451.86,-139.32"/>
+<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="327,-121.38 451.86,-121.38"/>
+<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 4&#45;&gt;sol4 -->
 <g id="edge5" class="edge">
 <title>bag 4&#45;&gt;sol4</title>
-<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"/>
-<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"/>
+<path fill="none" stroke="black" d="M338.9,-67.23C342.61,-75.08 346.74,-83.82 350.99,-92.82"/>
+<polygon fill="black" stroke="black" points="347.74,-94.14 355.18,-101.68 354.07,-91.15 347.74,-94.14"/>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/TDStep5.svg b/test/expected_files/test_vc_multiple_and_join/TDStep5.svg
index 9e477db..e7ccc47 100644
--- a/test/expected_files/test_vc_multiple_and_join/TDStep5.svg
+++ b/test/expected_files/test_vc_multiple_and_join/TDStep5.svg
@@ -1,347 +1,347 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.41.20170921.1950 (20170921.1950)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: Tree&#45;Decomposition Pages: 1 -->
-<svg width="467pt" height="624pt"
- viewBox="0.00 0.00 467.00 624.00" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="460pt" height="652pt"
+ viewBox="0.00 0.00 459.86 652.38" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 <title>Tree&#45;Decomposition</title>
-<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"/>
 <!-- bag 1 -->
 <g id="node1" class="node">
 <title>bag 1</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"/>
-<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"/>
-<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"/>
+<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"/>
+<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 </g>
 <!-- sol1 -->
 <g id="node8" class="node">
 <title>sol1</title>
-<path fill="yellow" stroke="black" stroke-width="2.5" d="M131,-445.5C131,-445.5 265,-445.5 265,-445.5 271,-445.5 277,-451.5 277,-457.5 277,-457.5 277,-603.5 277,-603.5 277,-609.5 271,-615.5 265,-615.5 265,-615.5 131,-615.5 131,-615.5 125,-615.5 119,-609.5 119,-603.5 119,-603.5 119,-457.5 119,-457.5 119,-451.5 125,-445.5 131,-445.5"/>
-<text text-anchor="middle" x="198" y="-603.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-598.5 277,-598.5 "/>
-<text text-anchor="middle" x="134" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-581.5 149,-581.5 "/>
-<text text-anchor="middle" x="134" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-564.5 149,-564.5 "/>
-<text text-anchor="middle" x="134" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-547.5 149,-547.5 "/>
-<text text-anchor="middle" x="134" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-530.5 149,-530.5 "/>
-<text text-anchor="middle" x="134" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-513.5 149,-513.5 "/>
-<text text-anchor="middle" x="134" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-496.5 149,-496.5 "/>
-<text text-anchor="middle" x="134" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-479.5 149,-479.5 "/>
-<text text-anchor="middle" x="134" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-462.5 149,-598.5 "/>
-<text text-anchor="middle" x="164" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-581.5 179,-581.5 "/>
-<text text-anchor="middle" x="164" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-564.5 179,-564.5 "/>
-<text text-anchor="middle" x="164" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-547.5 179,-547.5 "/>
-<text text-anchor="middle" x="164" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-530.5 179,-530.5 "/>
-<text text-anchor="middle" x="164" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-513.5 179,-513.5 "/>
-<text text-anchor="middle" x="164" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-496.5 179,-496.5 "/>
-<text text-anchor="middle" x="164" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-479.5 179,-479.5 "/>
-<text text-anchor="middle" x="164" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-462.5 179,-598.5 "/>
-<text text-anchor="middle" x="194" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-581.5 209,-581.5 "/>
-<text text-anchor="middle" x="194" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-564.5 209,-564.5 "/>
-<text text-anchor="middle" x="194" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-547.5 209,-547.5 "/>
-<text text-anchor="middle" x="194" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-530.5 209,-530.5 "/>
-<text text-anchor="middle" x="194" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-513.5 209,-513.5 "/>
-<text text-anchor="middle" x="194" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-496.5 209,-496.5 "/>
-<text text-anchor="middle" x="194" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-479.5 209,-479.5 "/>
-<text text-anchor="middle" x="194" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-462.5 209,-598.5 "/>
-<text text-anchor="middle" x="224" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-581.5 239,-581.5 "/>
-<text text-anchor="middle" x="224" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-564.5 239,-564.5 "/>
-<text text-anchor="middle" x="224" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-547.5 239,-547.5 "/>
-<text text-anchor="middle" x="224" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-530.5 239,-530.5 "/>
-<text text-anchor="middle" x="224" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-513.5 239,-513.5 "/>
-<text text-anchor="middle" x="224" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-496.5 239,-496.5 "/>
-<text text-anchor="middle" x="224" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-479.5 239,-479.5 "/>
-<text text-anchor="middle" x="224" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-462.5 239,-598.5 "/>
-<text text-anchor="middle" x="258" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-581.5 277,-581.5 "/>
-<text text-anchor="middle" x="258" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-564.5 277,-564.5 "/>
-<text text-anchor="middle" x="258" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-547.5 277,-547.5 "/>
-<text text-anchor="middle" x="258" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-530.5 277,-530.5 "/>
-<text text-anchor="middle" x="258" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">6</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-513.5 277,-513.5 "/>
-<text text-anchor="middle" x="258" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-496.5 277,-496.5 "/>
-<text text-anchor="middle" x="258" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-479.5 277,-479.5 "/>
-<text text-anchor="middle" x="258" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-462.5 277,-462.5 "/>
-<text text-anchor="middle" x="198" y="-450.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 4</text>
+<path fill="yellow" stroke="black" stroke-width="2.5" d="M129.33,-464.48C129.33,-464.48 259.53,-464.48 259.53,-464.48 265.53,-464.48 271.53,-470.48 271.53,-476.48 271.53,-476.48 271.53,-631.88 271.53,-631.88 271.53,-637.88 265.53,-643.88 259.53,-643.88 259.53,-643.88 129.33,-643.88 129.33,-643.88 123.33,-643.88 117.33,-637.88 117.33,-631.88 117.33,-631.88 117.33,-476.48 117.33,-476.48 117.33,-470.48 123.33,-464.48 129.33,-464.48"/>
+<text text-anchor="middle" x="194.43" y="-629.86" font-family="Times New Roman,serif" font-size="14.00">sol bag 1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-625.94 271.53,-625.94"/>
+<text text-anchor="middle" x="132" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-608 146.67,-608"/>
+<text text-anchor="middle" x="132" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-590.06 146.67,-590.06"/>
+<text text-anchor="middle" x="132" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-572.12 146.67,-572.12"/>
+<text text-anchor="middle" x="132" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-554.18 146.67,-554.18"/>
+<text text-anchor="middle" x="132" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-536.24 146.67,-536.24"/>
+<text text-anchor="middle" x="132" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-518.3 146.67,-518.3"/>
+<text text-anchor="middle" x="132" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-500.36 146.67,-500.36"/>
+<text text-anchor="middle" x="132" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-482.42 146.67,-625.94"/>
+<text text-anchor="middle" x="161.34" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-608 176.01,-608"/>
+<text text-anchor="middle" x="161.34" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-590.06 176.01,-590.06"/>
+<text text-anchor="middle" x="161.34" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-572.12 176.01,-572.12"/>
+<text text-anchor="middle" x="161.34" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-554.18 176.01,-554.18"/>
+<text text-anchor="middle" x="161.34" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-536.24 176.01,-536.24"/>
+<text text-anchor="middle" x="161.34" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-518.3 176.01,-518.3"/>
+<text text-anchor="middle" x="161.34" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-500.36 176.01,-500.36"/>
+<text text-anchor="middle" x="161.34" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-482.42 176.01,-625.94"/>
+<text text-anchor="middle" x="190.68" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-608 205.35,-608"/>
+<text text-anchor="middle" x="190.68" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-590.06 205.35,-590.06"/>
+<text text-anchor="middle" x="190.68" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-572.12 205.35,-572.12"/>
+<text text-anchor="middle" x="190.68" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-554.18 205.35,-554.18"/>
+<text text-anchor="middle" x="190.68" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-536.24 205.35,-536.24"/>
+<text text-anchor="middle" x="190.68" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-518.3 205.35,-518.3"/>
+<text text-anchor="middle" x="190.68" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-500.36 205.35,-500.36"/>
+<text text-anchor="middle" x="190.68" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-482.42 205.35,-625.94"/>
+<text text-anchor="middle" x="220.02" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-608 234.69,-608"/>
+<text text-anchor="middle" x="220.02" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-590.06 234.69,-590.06"/>
+<text text-anchor="middle" x="220.02" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-572.12 234.69,-572.12"/>
+<text text-anchor="middle" x="220.02" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-554.18 234.69,-554.18"/>
+<text text-anchor="middle" x="220.02" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-536.24 234.69,-536.24"/>
+<text text-anchor="middle" x="220.02" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-518.3 234.69,-518.3"/>
+<text text-anchor="middle" x="220.02" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-500.36 234.69,-500.36"/>
+<text text-anchor="middle" x="220.02" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-482.42 234.69,-625.94"/>
+<text text-anchor="middle" x="253.11" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-608 271.53,-608"/>
+<text text-anchor="middle" x="253.11" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-590.06 271.53,-590.06"/>
+<text text-anchor="middle" x="253.11" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-572.12 271.53,-572.12"/>
+<text text-anchor="middle" x="253.11" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-554.18 271.53,-554.18"/>
+<text text-anchor="middle" x="253.11" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-536.24 271.53,-536.24"/>
+<text text-anchor="middle" x="253.11" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-518.3 271.53,-518.3"/>
+<text text-anchor="middle" x="253.11" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-500.36 271.53,-500.36"/>
+<text text-anchor="middle" x="253.11" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-482.42 271.53,-482.42"/>
+<text text-anchor="middle" x="194.43" y="-468.4" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 4</text>
 </g>
 <!-- bag 1&#45;&gt;sol1 -->
 <g id="edge7" class="edge">
 <title>bag 1&#45;&gt;sol1</title>
-<path fill="none" stroke="black" d="M198,-372.12C198,-389.53 198,-412.35 198,-435.2"/>
-<polygon fill="black" stroke="black" points="194.5,-435.33 198,-445.33 201.5,-435.33 194.5,-435.33"/>
+<path fill="none" stroke="black" d="M194.43,-390.05C194.43,-407.47 194.43,-429.81 194.43,-452.34"/>
+<polygon fill="black" stroke="black" points="190.93,-452.24 194.43,-462.24 197.93,-452.24 190.93,-452.24"/>
 </g>
 <!-- bag 2 -->
 <g id="node2" class="node">
 <title>bag 2</title>
-<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"/>
-<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"/>
-<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"/>
+<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"/>
+<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 </g>
 <!-- bag 2&#45;&gt;bag 1 -->
 <g id="edge1" class="edge">
 <title>bag 2&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"/>
-<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"/>
+<path fill="none" stroke="black" d="M142.99,-208.94C153.06,-237.49 167.75,-279.13 178.86,-310.6"/>
+<polygon fill="black" stroke="black" points="175.5,-311.58 182.12,-319.85 182.1,-309.25 175.5,-311.58"/>
 </g>
 <!-- sol2 -->
 <g id="node5" class="node">
 <title>sol2</title>
-<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"/>
-<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "/>
-<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "/>
-<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "/>
-<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "/>
-<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "/>
-<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "/>
-<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "/>
-<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "/>
-<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "/>
-<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "/>
-<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "/>
-<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "/>
-<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "/>
-<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "/>
-<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "/>
-<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "/>
-<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "/>
-<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "/>
-<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "/>
-<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "/>
-<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "/>
-<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "/>
-<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "/>
-<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "/>
-<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "/>
-<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"/>
+<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"/>
+<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"/>
+<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"/>
+<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"/>
+<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"/>
+<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"/>
+<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"/>
+<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"/>
+<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"/>
+<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"/>
+<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"/>
+<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"/>
+<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"/>
+<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"/>
+<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"/>
+<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"/>
+<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"/>
+<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"/>
+<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"/>
+<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"/>
+<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"/>
+<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"/>
+<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"/>
+<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"/>
+<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"/>
+<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 2&#45;&gt;sol2 -->
 <g id="edge4" class="edge">
 <title>bag 2&#45;&gt;sol2</title>
-<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"/>
-<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"/>
+<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"/>
+<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"/>
 </g>
 <!-- bag 3 -->
 <g id="node3" class="node">
 <title>bag 3</title>
-<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"/>
-<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"/>
-<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"/>
+<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"/>
+<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 </g>
 <!-- bag 3&#45;&gt;bag 1 -->
 <g id="edge2" class="edge">
 <title>bag 3&#45;&gt;bag 1</title>
-<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"/>
-<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"/>
+<path fill="none" stroke="black" d="M245.87,-208.94C235.8,-237.49 221.11,-279.13 210,-310.6"/>
+<polygon fill="black" stroke="black" points="206.76,-309.25 206.74,-319.85 213.36,-311.58 206.76,-309.25"/>
 </g>
 <!-- sol3 -->
 <g id="node7" class="node">
 <title>sol3</title>
-<path fill="white" stroke="black" d="M280,-272.5C280,-272.5 384,-272.5 384,-272.5 390,-272.5 396,-278.5 396,-284.5 396,-284.5 396,-396.5 396,-396.5 396,-402.5 390,-408.5 384,-408.5 384,-408.5 280,-408.5 280,-408.5 274,-408.5 268,-402.5 268,-396.5 268,-396.5 268,-284.5 268,-284.5 268,-278.5 274,-272.5 280,-272.5"/>
-<text text-anchor="middle" x="332" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
-<polyline fill="none" stroke="black" points="268,-391.5 396,-391.5 "/>
-<text text-anchor="middle" x="283" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="268,-374.5 298,-374.5 "/>
-<text text-anchor="middle" x="283" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="268,-357.5 298,-357.5 "/>
-<text text-anchor="middle" x="283" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="268,-340.5 298,-340.5 "/>
-<text text-anchor="middle" x="283" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="268,-323.5 298,-323.5 "/>
-<text text-anchor="middle" x="283" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="268,-306.5 298,-306.5 "/>
-<text text-anchor="middle" x="283" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="298,-289.5 298,-391.5 "/>
-<text text-anchor="middle" x="313" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-<polyline fill="none" stroke="black" points="298,-374.5 328,-374.5 "/>
-<text text-anchor="middle" x="313" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="298,-357.5 328,-357.5 "/>
-<text text-anchor="middle" x="313" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="298,-340.5 328,-340.5 "/>
-<text text-anchor="middle" x="313" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="298,-323.5 328,-323.5 "/>
-<text text-anchor="middle" x="313" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="298,-306.5 328,-306.5 "/>
-<text text-anchor="middle" x="313" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="328,-289.5 328,-391.5 "/>
-<text text-anchor="middle" x="343" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" points="328,-374.5 358,-374.5 "/>
-<text text-anchor="middle" x="343" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="328,-357.5 358,-357.5 "/>
-<text text-anchor="middle" x="343" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="328,-340.5 358,-340.5 "/>
-<text text-anchor="middle" x="343" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="328,-323.5 358,-323.5 "/>
-<text text-anchor="middle" x="343" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="328,-306.5 358,-306.5 "/>
-<text text-anchor="middle" x="343" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="358,-289.5 358,-391.5 "/>
-<text text-anchor="middle" x="377" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="358,-374.5 396,-374.5 "/>
-<text text-anchor="middle" x="377" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="358,-357.5 396,-357.5 "/>
-<text text-anchor="middle" x="377" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="358,-340.5 396,-340.5 "/>
-<text text-anchor="middle" x="377" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" points="358,-323.5 396,-323.5 "/>
-<text text-anchor="middle" x="377" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="358,-306.5 396,-306.5 "/>
-<text text-anchor="middle" x="377" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-<polyline fill="none" stroke="black" points="268,-289.5 396,-289.5 "/>
-<text text-anchor="middle" x="332" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 3</text>
+<path fill="white" stroke="black" d="M276,-283.96C276,-283.96 376.86,-283.96 376.86,-283.96 382.86,-283.96 388.86,-289.96 388.86,-295.96 388.86,-295.96 388.86,-415.48 388.86,-415.48 388.86,-421.48 382.86,-427.48 376.86,-427.48 376.86,-427.48 276,-427.48 276,-427.48 270,-427.48 264,-421.48 264,-415.48 264,-415.48 264,-295.96 264,-295.96 264,-289.96 270,-283.96 276,-283.96"/>
+<text text-anchor="middle" x="326.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
+<polyline fill="none" stroke="black" points="264,-409.54 388.86,-409.54"/>
+<text text-anchor="middle" x="278.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="264,-391.6 293.34,-391.6"/>
+<text text-anchor="middle" x="278.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="264,-373.66 293.34,-373.66"/>
+<text text-anchor="middle" x="278.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="264,-355.72 293.34,-355.72"/>
+<text text-anchor="middle" x="278.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="264,-337.78 293.34,-337.78"/>
+<text text-anchor="middle" x="278.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="264,-319.84 293.34,-319.84"/>
+<text text-anchor="middle" x="278.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="293.34,-301.9 293.34,-409.54"/>
+<text text-anchor="middle" x="308.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+<polyline fill="none" stroke="black" points="293.34,-391.6 322.68,-391.6"/>
+<text text-anchor="middle" x="308.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="293.34,-373.66 322.68,-373.66"/>
+<text text-anchor="middle" x="308.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="293.34,-355.72 322.68,-355.72"/>
+<text text-anchor="middle" x="308.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="293.34,-337.78 322.68,-337.78"/>
+<text text-anchor="middle" x="308.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="293.34,-319.84 322.68,-319.84"/>
+<text text-anchor="middle" x="308.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="322.68,-301.9 322.68,-409.54"/>
+<text text-anchor="middle" x="337.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" points="322.68,-391.6 352.02,-391.6"/>
+<text text-anchor="middle" x="337.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="322.68,-373.66 352.02,-373.66"/>
+<text text-anchor="middle" x="337.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="322.68,-355.72 352.02,-355.72"/>
+<text text-anchor="middle" x="337.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="322.68,-337.78 352.02,-337.78"/>
+<text text-anchor="middle" x="337.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="322.68,-319.84 352.02,-319.84"/>
+<text text-anchor="middle" x="337.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="352.02,-301.9 352.02,-409.54"/>
+<text text-anchor="middle" x="370.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="352.02,-391.6 388.86,-391.6"/>
+<text text-anchor="middle" x="370.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="352.02,-373.66 388.86,-373.66"/>
+<text text-anchor="middle" x="370.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="352.02,-355.72 388.86,-355.72"/>
+<text text-anchor="middle" x="370.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" points="352.02,-337.78 388.86,-337.78"/>
+<text text-anchor="middle" x="370.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="352.02,-319.84 388.86,-319.84"/>
+<text text-anchor="middle" x="370.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<polyline fill="none" stroke="black" points="264,-301.9 388.86,-301.9"/>
+<text text-anchor="middle" x="326.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 3</text>
 </g>
 <!-- bag 3&#45;&gt;sol3 -->
 <g id="edge6" class="edge">
 <title>bag 3&#45;&gt;sol3</title>
-<path fill="none" stroke="black" d="M273.69,-199.07C281.13,-216.97 290.87,-240.44 300.26,-263.06"/>
-<polygon fill="black" stroke="black" points="297.05,-264.44 304.11,-272.34 303.51,-261.76 297.05,-264.44"/>
+<path fill="none" stroke="black" d="M270.09,-208.94C277.07,-227.02 286.09,-250.34 294.85,-273.02"/>
+<polygon fill="black" stroke="black" points="291.57,-274.24 298.44,-282.3 298.1,-271.71 291.57,-274.24"/>
 </g>
 <!-- bag 4 -->
 <g id="node4" class="node">
 <title>bag 4</title>
-<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"/>
-<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"/>
-<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"/>
+<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"/>
+<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 </g>
 <!-- bag 4&#45;&gt;bag 3 -->
 <g id="edge3" class="edge">
 <title>bag 4&#45;&gt;bag 3</title>
-<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"/>
-<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"/>
+<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"/>
+<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"/>
 </g>
 <!-- sol4 -->
 <g id="node6" class="node">
 <title>sol4</title>
-<path fill="white" stroke="black" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"/>
-<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-<polyline fill="none" stroke="black" points="331,-218.5 459,-218.5 "/>
-<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-<polyline fill="none" stroke="black" points="331,-201.5 361,-201.5 "/>
-<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-184.5 361,-184.5 "/>
-<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-167.5 361,-167.5 "/>
-<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-150.5 361,-150.5 "/>
-<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="331,-133.5 361,-133.5 "/>
-<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-116.5 361,-218.5 "/>
-<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-<polyline fill="none" stroke="black" points="361,-201.5 391,-201.5 "/>
-<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="361,-184.5 391,-184.5 "/>
-<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-167.5 391,-167.5 "/>
-<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="361,-150.5 391,-150.5 "/>
-<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="361,-133.5 391,-133.5 "/>
-<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-116.5 391,-218.5 "/>
-<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-<polyline fill="none" stroke="black" points="391,-201.5 421,-201.5 "/>
-<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="391,-184.5 421,-184.5 "/>
-<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-167.5 421,-167.5 "/>
-<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-<polyline fill="none" stroke="black" points="391,-150.5 421,-150.5 "/>
-<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="391,-133.5 421,-133.5 "/>
-<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-<polyline fill="none" stroke="black" points="421,-116.5 421,-218.5 "/>
-<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-<polyline fill="none" stroke="black" points="421,-201.5 459,-201.5 "/>
-<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-184.5 459,-184.5 "/>
-<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-167.5 459,-167.5 "/>
-<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-<polyline fill="none" stroke="black" points="421,-150.5 459,-150.5 "/>
-<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="421,-133.5 459,-133.5 "/>
-<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-<polyline fill="none" stroke="black" points="331,-116.5 459,-116.5 "/>
-<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
+<path fill="white" stroke="black" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"/>
+<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+<polyline fill="none" stroke="black" points="327,-229.02 451.86,-229.02"/>
+<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+<polyline fill="none" stroke="black" points="327,-211.08 356.34,-211.08"/>
+<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-193.14 356.34,-193.14"/>
+<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-175.2 356.34,-175.2"/>
+<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-157.26 356.34,-157.26"/>
+<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="327,-139.32 356.34,-139.32"/>
+<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-121.38 356.34,-229.02"/>
+<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+<polyline fill="none" stroke="black" points="356.34,-211.08 385.68,-211.08"/>
+<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="356.34,-193.14 385.68,-193.14"/>
+<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-175.2 385.68,-175.2"/>
+<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="356.34,-157.26 385.68,-157.26"/>
+<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="356.34,-139.32 385.68,-139.32"/>
+<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-121.38 385.68,-229.02"/>
+<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+<polyline fill="none" stroke="black" points="385.68,-211.08 415.02,-211.08"/>
+<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="385.68,-193.14 415.02,-193.14"/>
+<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-175.2 415.02,-175.2"/>
+<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+<polyline fill="none" stroke="black" points="385.68,-157.26 415.02,-157.26"/>
+<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="385.68,-139.32 415.02,-139.32"/>
+<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<polyline fill="none" stroke="black" points="415.02,-121.38 415.02,-229.02"/>
+<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+<polyline fill="none" stroke="black" points="415.02,-211.08 451.86,-211.08"/>
+<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-193.14 451.86,-193.14"/>
+<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-175.2 451.86,-175.2"/>
+<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<polyline fill="none" stroke="black" points="415.02,-157.26 451.86,-157.26"/>
+<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="415.02,-139.32 451.86,-139.32"/>
+<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<polyline fill="none" stroke="black" points="327,-121.38 451.86,-121.38"/>
+<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min&#45;size: 2</text>
 </g>
 <!-- bag 4&#45;&gt;sol4 -->
 <g id="edge5" class="edge">
 <title>bag 4&#45;&gt;sol4</title>
-<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"/>
-<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"/>
+<path fill="none" stroke="black" d="M338.9,-67.23C342.61,-75.08 346.74,-83.82 350.99,-92.82"/>
+<polygon fill="black" stroke="black" points="347.74,-94.14 355.18,-101.68 354.07,-91.15 347.74,-94.14"/>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/combined1.svg b/test/expected_files/test_vc_multiple_and_join/combined1.svg
index 3935313..7751b40 100644
--- a/test/expected_files/test_vc_multiple_and_join/combined1.svg
+++ b/test/expected_files/test_vc_multiple_and_join/combined1.svg
@@ -1,228 +1,228 @@
 <?xml version="1.0" encoding="utf-8"?>
-<svg width="994pt" height="624pt" viewBox="0.0 0.0 994 624" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
-	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="1427pt" height="652pt" viewBox="0.0 0.0 1427 652" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
+	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 		<title>Tree-Decomposition</title>
-		<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"></polygon>
 		<g id="node1" class="node">
 			<title>bag 1</title>
-			<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"></path>
-			<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"></polygon>
-			<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-			<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-			<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+			<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"></path>
+			<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"></polygon>
+			<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+			<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+			<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 		</g>
 		<g id="node2" class="node">
 			<title>bag 2</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"></polygon>
-			<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-			<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-			<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"></polygon>
+			<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+			<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+			<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 		</g>
 		<g id="edge1" class="edge">
 			<title>bag 2-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"></path>
-			<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"></polygon>
+			<path fill="none" stroke="black" d="M143.13,-209.36C153.29,-238.13 168.06,-279.99 179.14,-311.4"></path>
+			<polygon fill="black" stroke="black" points="175.76,-312.35 182.39,-320.61 182.37,-310.02 175.76,-312.35"></polygon>
 		</g>
 		<g id="node3" class="node">
 			<title>bag 3</title>
-			<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"></polygon>
-			<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-			<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-			<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+			<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"></polygon>
+			<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+			<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+			<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 		</g>
 		<g id="edge2" class="edge">
 			<title>bag 3-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"></path>
-			<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"></polygon>
+			<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"></path>
+			<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"></polygon>
 		</g>
 		<g id="node4" class="node">
 			<title>bag 4</title>
-			<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"></path>
-			<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"></polygon>
-			<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-			<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-			<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+			<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"></path>
+			<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"></polygon>
+			<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+			<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+			<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 		</g>
 		<g id="edge3" class="edge">
 			<title>bag 4-&gt;bag 3</title>
-			<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"></path>
-			<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"></polygon>
+			<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"></path>
+			<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"></polygon>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(507.0 233.025) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 153.954)">
+	<g id="graph0" class="graph" transform="translate(499.86 161.205) scale(0.9999999999999997) scale(1 1) rotate(0) translate(4 325.97)">
 		<title>graph</title>
-		<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"></polygon>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"></path>
+			<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="black" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"></path>
+			<path fill="none" stroke="black" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"></path>
+			<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"></path>
 		</g>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"></path>
+			<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"></path>
+			<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="black" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"></path>
+			<path fill="none" stroke="black" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"></path>
+			<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"></path>
+			<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"></path>
+			<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"></path>
+			<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"></path>
+			<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"></path>
+			<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>1</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node2" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node3" class="node">
 			<title>3</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node4" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node5" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(778.0 210.705) scale(1.0000000000000002) scale(1 1) rotate(0) translate(104.28 101.294)">
+	<g id="graph0" class="graph" transform="translate(1027.0 130.235) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 387.53)">
 		<title>graph_sorted</title>
-		<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"></polygon>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"></path>
+			<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"></path>
 		</g>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"></path>
+			<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="black" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"></path>
+			<path fill="none" stroke="black" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"></path>
+			<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"></path>
+			<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="black" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"></path>
+			<path fill="none" stroke="black" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"></path>
+			<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"></path>
+			<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"></path>
+			<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"></path>
+			<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"></path>
+			<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"></path>
+			<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node2" class="node">
 			<title>1</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="79.2938" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node3" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node4" class="node">
 			<title>3</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-269.1" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node5" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="365.82" cy="-191.76" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
 </svg>
\ No newline at end of file
diff --git a/test/expected_files/test_vc_multiple_and_join/combined2.svg b/test/expected_files/test_vc_multiple_and_join/combined2.svg
index 045271b..8080e79 100644
--- a/test/expected_files/test_vc_multiple_and_join/combined2.svg
+++ b/test/expected_files/test_vc_multiple_and_join/combined2.svg
@@ -1,288 +1,288 @@
 <?xml version="1.0" encoding="utf-8"?>
-<svg width="994pt" height="624pt" viewBox="0.0 0.0 994 624" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
-	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="1427pt" height="652pt" viewBox="0.0 0.0 1427 652" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
+	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 		<title>Tree-Decomposition</title>
-		<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"></polygon>
 		<g id="node1" class="node">
 			<title>bag 1</title>
-			<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"></path>
-			<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"></polygon>
-			<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-			<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-			<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+			<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"></path>
+			<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"></polygon>
+			<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+			<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+			<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 		</g>
 		<g id="node2" class="node">
 			<title>bag 2</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"></polygon>
-			<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-			<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-			<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"></polygon>
+			<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+			<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+			<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 		</g>
 		<g id="edge1" class="edge">
 			<title>bag 2-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"></path>
-			<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"></polygon>
+			<path fill="none" stroke="black" d="M143.13,-209.36C153.29,-238.13 168.06,-279.99 179.14,-311.4"></path>
+			<polygon fill="black" stroke="black" points="175.76,-312.35 182.39,-320.61 182.37,-310.02 175.76,-312.35"></polygon>
 		</g>
 		<g id="node5" class="node">
 			<title>sol2</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"></path>
-			<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-			<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-			<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-391.5 128,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-374.5 30,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-357.5 30,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-340.5 30,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-323.5 30,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-306.5 30,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-289.5 30,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-374.5 60,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-357.5 60,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-340.5 60,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-323.5 60,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="30,-306.5 60,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-289.5 60,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-374.5 90,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-357.5 90,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-340.5 90,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-323.5 90,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="60,-306.5 90,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-289.5 90,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-374.5 128,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-357.5 128,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-340.5 128,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-323.5 128,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="90,-306.5 128,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-289.5 128,-289.5 "></polyline>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"></path>
+			<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+			<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+			<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-409.54 124.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-391.6 29.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-373.66 29.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-355.72 29.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-337.78 29.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-319.84 29.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-301.9 29.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-391.6 58.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-373.66 58.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-355.72 58.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-337.78 58.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="29.34,-319.84 58.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-301.9 58.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-391.6 88.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-373.66 88.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-355.72 88.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-337.78 88.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="58.68,-319.84 88.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-301.9 88.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-391.6 124.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-373.66 124.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-355.72 124.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-337.78 124.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="88.02,-319.84 124.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="0,-301.9 124.86,-301.9"></polyline>
 		</g>
 		<g id="edge4" class="edge">
 			<title>bag 2-&gt;sol2</title>
-			<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"></path>
-			<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"></polygon>
+			<path fill="none" stroke="black" d="M118.61,-209.36C111.68,-227.29 102.79,-250.3 94.13,-272.7"></path>
+			<polygon fill="black" stroke="black" points="90.93,-271.28 90.59,-281.86 97.46,-273.8 90.93,-271.28"></polygon>
 		</g>
 		<g id="node3" class="node">
 			<title>bag 3</title>
-			<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"></polygon>
-			<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-			<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-			<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+			<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"></polygon>
+			<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+			<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+			<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 		</g>
 		<g id="edge2" class="edge">
 			<title>bag 3-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"></path>
-			<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"></polygon>
+			<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"></path>
+			<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"></polygon>
 		</g>
 		<g id="node4" class="node">
 			<title>bag 4</title>
-			<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"></path>
-			<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"></polygon>
-			<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-			<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-			<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+			<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"></path>
+			<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"></polygon>
+			<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+			<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+			<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 		</g>
 		<g id="edge3" class="edge">
 			<title>bag 4-&gt;bag 3</title>
-			<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"></path>
-			<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"></polygon>
+			<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"></path>
+			<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"></polygon>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(507.0 233.025) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 153.954)">
+	<g id="graph0" class="graph" transform="translate(499.86 161.205) scale(0.9999999999999997) scale(1 1) rotate(0) translate(4 325.97)">
 		<title>graph</title>
-		<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"></polygon>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"></path>
+			<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"></path>
 		</g>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"></path>
+			<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="black" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"></path>
+			<path fill="none" stroke="black" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"></path>
+			<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"></path>
+			<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"></path>
+			<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"></path>
+			<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>1</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node2" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node3" class="node">
 			<title>3</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node4" class="node">
 			<title>4</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node5" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(778.0 210.705) scale(1.0000000000000002) scale(1 1) rotate(0) translate(104.28 101.294)">
+	<g id="graph0" class="graph" transform="translate(1027.0 130.235) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 387.53)">
 		<title>graph_sorted</title>
-		<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"></polygon>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"></path>
+			<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"></path>
 		</g>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"></path>
+			<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="black" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"></path>
+			<path fill="none" stroke="black" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"></path>
+			<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"></path>
+			<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"></path>
+			<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"></path>
+			<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node2" class="node">
 			<title>1</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node3" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node4" class="node">
 			<title>3</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node5" class="node">
 			<title>4</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="-79.294" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-365.53" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="-63.5907" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-331.11" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="365.82" cy="-191.76" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
 </svg>
\ No newline at end of file
diff --git a/test/expected_files/test_vc_multiple_and_join/combined3.svg b/test/expected_files/test_vc_multiple_and_join/combined3.svg
index 3fec518..cd52f24 100644
--- a/test/expected_files/test_vc_multiple_and_join/combined3.svg
+++ b/test/expected_files/test_vc_multiple_and_join/combined3.svg
@@ -1,348 +1,348 @@
 <?xml version="1.0" encoding="utf-8"?>
-<svg width="994pt" height="624pt" viewBox="0.0 0.0 994 624" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
-	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="1427pt" height="652pt" viewBox="0.0 0.0 1427 652" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
+	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 		<title>Tree-Decomposition</title>
-		<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"></polygon>
 		<g id="node1" class="node">
 			<title>bag 1</title>
-			<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"></path>
-			<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"></polygon>
-			<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-			<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-			<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+			<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"></path>
+			<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"></polygon>
+			<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+			<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+			<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 		</g>
 		<g id="node2" class="node">
 			<title>bag 2</title>
-			<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"></polygon>
-			<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-			<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-			<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+			<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"></polygon>
+			<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+			<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+			<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 		</g>
 		<g id="edge1" class="edge">
 			<title>bag 2-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"></path>
-			<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"></polygon>
+			<path fill="none" stroke="black" d="M142.99,-208.94C153.12,-237.67 167.94,-279.65 179.07,-311.2"></path>
+			<polygon fill="black" stroke="black" points="175.71,-312.19 182.34,-320.46 182.31,-309.86 175.71,-312.19"></polygon>
 		</g>
 		<g id="node5" class="node">
 			<title>sol2</title>
-			<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"></path>
-			<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-			<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-			<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "></polyline>
+			<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"></path>
+			<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+			<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+			<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"></polyline>
 		</g>
 		<g id="edge4" class="edge">
 			<title>bag 2-&gt;sol2</title>
-			<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"></path>
-			<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"></polygon>
+			<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"></path>
+			<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"></polygon>
 		</g>
 		<g id="node3" class="node">
 			<title>bag 3</title>
-			<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"></polygon>
-			<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-			<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-			<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+			<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"></polygon>
+			<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+			<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+			<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 		</g>
 		<g id="edge2" class="edge">
 			<title>bag 3-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"></path>
-			<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"></polygon>
+			<path fill="none" stroke="black" d="M245.87,-208.94C235.74,-237.67 220.92,-279.65 209.79,-311.2"></path>
+			<polygon fill="black" stroke="black" points="206.55,-309.86 206.52,-320.46 213.15,-312.19 206.55,-309.86"></polygon>
 		</g>
 		<g id="node4" class="node">
 			<title>bag 4</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"></path>
-			<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"></polygon>
-			<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-			<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-			<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"></path>
+			<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"></polygon>
+			<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+			<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+			<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 		</g>
 		<g id="edge3" class="edge">
 			<title>bag 4-&gt;bag 3</title>
-			<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"></path>
-			<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"></polygon>
+			<path fill="none" stroke="black" d="M307.62,-67.94C298.66,-86.91 287.35,-110.86 277.73,-131.22"></path>
+			<polygon fill="black" stroke="black" points="274.63,-129.58 273.53,-140.12 280.96,-132.57 274.63,-129.58"></polygon>
 		</g>
 		<g id="node6" class="node">
 			<title>sol4</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"></path>
-			<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-			<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-			<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-218.5 459,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-201.5 361,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-184.5 361,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-167.5 361,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-150.5 361,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-133.5 361,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-116.5 361,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-201.5 391,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-184.5 391,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-167.5 391,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-150.5 391,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="361,-133.5 391,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-116.5 391,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-201.5 421,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-184.5 421,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-167.5 421,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-150.5 421,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="391,-133.5 421,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-116.5 421,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-201.5 459,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-184.5 459,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-167.5 459,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-150.5 459,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="421,-133.5 459,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="331,-116.5 459,-116.5 "></polyline>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"></path>
+			<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+			<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+			<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-229.02 451.86,-229.02"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-211.08 356.34,-211.08"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-193.14 356.34,-193.14"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-175.2 356.34,-175.2"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-157.26 356.34,-157.26"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-139.32 356.34,-139.32"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-121.38 356.34,-229.02"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-211.08 385.68,-211.08"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-193.14 385.68,-193.14"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-175.2 385.68,-175.2"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-157.26 385.68,-157.26"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="356.34,-139.32 385.68,-139.32"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-121.38 385.68,-229.02"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-211.08 415.02,-211.08"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-193.14 415.02,-193.14"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-175.2 415.02,-175.2"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-157.26 415.02,-157.26"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="385.68,-139.32 415.02,-139.32"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-121.38 415.02,-229.02"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-211.08 451.86,-211.08"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-193.14 451.86,-193.14"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-175.2 451.86,-175.2"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-157.26 451.86,-157.26"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="415.02,-139.32 451.86,-139.32"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="327,-121.38 451.86,-121.38"></polyline>
 		</g>
 		<g id="edge5" class="edge">
 			<title>bag 4-&gt;sol4</title>
-			<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"></path>
-			<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"></polygon>
+			<path fill="none" stroke="black" d="M339.24,-67.94C342.8,-75.48 346.74,-83.81 350.79,-92.39"></path>
+			<polygon fill="black" stroke="black" points="347.5,-93.62 354.94,-101.17 353.83,-90.63 347.5,-93.62"></polygon>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(507.0 233.025) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 153.954)">
+	<g id="graph0" class="graph" transform="translate(499.86 161.205) scale(0.9999999999999997) scale(1 1) rotate(0) translate(4 325.97)">
 		<title>graph</title>
-		<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"></polygon>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="black" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"></path>
+			<path fill="none" stroke="black" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"></path>
+			<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"></path>
 		</g>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"></path>
+			<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"></path>
+			<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"></path>
+			<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"></path>
+			<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"></path>
+			<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>1</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node2" class="node">
 			<title>2</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node3" class="node">
 			<title>3</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node4" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node5" class="node">
 			<title>7</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(778.0 210.705) scale(1.0000000000000002) scale(1 1) rotate(0) translate(104.28 101.294)">
+	<g id="graph0" class="graph" transform="translate(1027.0 130.235) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 387.53)">
 		<title>graph_sorted</title>
-		<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"></polygon>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"></path>
 		</g>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="black" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"></path>
+			<path fill="none" stroke="black" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"></path>
+			<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"></path>
+			<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"></path>
+			<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"></path>
+			<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"></path>
+			<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"></path>
+			<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>7</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="63.5891" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-52.42" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node2" class="node">
 			<title>1</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node3" class="node">
 			<title>2</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="35.2894" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-114.44" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node4" class="node">
 			<title>3</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-269.1" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node5" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
 </svg>
\ No newline at end of file
diff --git a/test/expected_files/test_vc_multiple_and_join/combined4.svg b/test/expected_files/test_vc_multiple_and_join/combined4.svg
index 8e179c8..d51ed35 100644
--- a/test/expected_files/test_vc_multiple_and_join/combined4.svg
+++ b/test/expected_files/test_vc_multiple_and_join/combined4.svg
@@ -1,408 +1,408 @@
 <?xml version="1.0" encoding="utf-8"?>
-<svg width="994pt" height="624pt" viewBox="0.0 0.0 994 624" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
-	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="1427pt" height="652pt" viewBox="0.0 0.0 1427 652" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
+	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 		<title>Tree-Decomposition</title>
-		<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"></polygon>
 		<g id="node1" class="node">
 			<title>bag 1</title>
-			<path fill="white" stroke="black" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"></path>
-			<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"></polygon>
-			<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-			<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-			<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+			<path fill="white" stroke="black" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"></path>
+			<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"></polygon>
+			<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+			<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+			<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 		</g>
 		<g id="node2" class="node">
 			<title>bag 2</title>
-			<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"></polygon>
-			<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-			<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-			<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+			<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"></polygon>
+			<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+			<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+			<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 		</g>
 		<g id="edge1" class="edge">
 			<title>bag 2-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"></path>
-			<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"></polygon>
+			<path fill="none" stroke="black" d="M142.99,-208.94C153.12,-237.67 167.94,-279.65 179.07,-311.2"></path>
+			<polygon fill="black" stroke="black" points="175.71,-312.19 182.34,-320.46 182.31,-309.86 175.71,-312.19"></polygon>
 		</g>
 		<g id="node5" class="node">
 			<title>sol2</title>
-			<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"></path>
-			<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-			<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-			<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "></polyline>
+			<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"></path>
+			<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+			<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+			<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"></polyline>
 		</g>
 		<g id="edge4" class="edge">
 			<title>bag 2-&gt;sol2</title>
-			<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"></path>
-			<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"></polygon>
+			<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"></path>
+			<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"></polygon>
 		</g>
 		<g id="node3" class="node">
 			<title>bag 3</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"></polygon>
-			<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-			<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-			<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"></polygon>
+			<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+			<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+			<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 		</g>
 		<g id="edge2" class="edge">
 			<title>bag 3-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"></path>
-			<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"></polygon>
+			<path fill="none" stroke="black" d="M245.73,-209.36C235.57,-238.13 220.8,-279.99 209.72,-311.4"></path>
+			<polygon fill="black" stroke="black" points="206.49,-310.02 206.47,-320.61 213.1,-312.35 206.49,-310.02"></polygon>
 		</g>
 		<g id="node7" class="node">
 			<title>sol3</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M280,-272.5C280,-272.5 384,-272.5 384,-272.5 390,-272.5 396,-278.5 396,-284.5 396,-284.5 396,-396.5 396,-396.5 396,-402.5 390,-408.5 384,-408.5 384,-408.5 280,-408.5 280,-408.5 274,-408.5 268,-402.5 268,-396.5 268,-396.5 268,-284.5 268,-284.5 268,-278.5 274,-272.5 280,-272.5"></path>
-			<text text-anchor="middle" x="332" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
-			<text text-anchor="middle" x="283" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="283" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="313" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="313" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="313" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="343" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="343" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="343" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="377" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="377" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="377" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="332" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 3</text>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-391.5 396,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-374.5 298,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-357.5 298,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-340.5 298,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-323.5 298,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-306.5 298,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-289.5 298,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-374.5 328,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-357.5 328,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-340.5 328,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-323.5 328,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="298,-306.5 328,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-289.5 328,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-374.5 358,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-357.5 358,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-340.5 358,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-323.5 358,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="328,-306.5 358,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-289.5 358,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-374.5 396,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-357.5 396,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-340.5 396,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-323.5 396,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="358,-306.5 396,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="268,-289.5 396,-289.5 "></polyline>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M276,-283.96C276,-283.96 376.86,-283.96 376.86,-283.96 382.86,-283.96 388.86,-289.96 388.86,-295.96 388.86,-295.96 388.86,-415.48 388.86,-415.48 388.86,-421.48 382.86,-427.48 376.86,-427.48 376.86,-427.48 276,-427.48 276,-427.48 270,-427.48 264,-421.48 264,-415.48 264,-415.48 264,-295.96 264,-295.96 264,-289.96 270,-283.96 276,-283.96"></path>
+			<text text-anchor="middle" x="326.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
+			<text text-anchor="middle" x="278.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="278.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="308.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="308.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="308.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="337.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="337.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="337.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="370.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="370.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="370.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="326.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 3</text>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-409.54 388.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-391.6 293.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-373.66 293.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-355.72 293.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-337.78 293.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-319.84 293.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-301.9 293.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-391.6 322.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-373.66 322.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-355.72 322.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-337.78 322.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="293.34,-319.84 322.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-301.9 322.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-391.6 352.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-373.66 352.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-355.72 352.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-337.78 352.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="322.68,-319.84 352.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-301.9 352.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-391.6 388.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-373.66 388.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-355.72 388.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-337.78 388.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="352.02,-319.84 388.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="264,-301.9 388.86,-301.9"></polyline>
 		</g>
 		<g id="edge6" class="edge">
 			<title>bag 3-&gt;sol3</title>
-			<path fill="none" stroke="black" d="M273.69,-199.07C281.13,-216.97 290.87,-240.44 300.26,-263.06"></path>
-			<polygon fill="black" stroke="black" points="297.05,-264.44 304.11,-272.34 303.51,-261.76 297.05,-264.44"></polygon>
+			<path fill="none" stroke="black" d="M270.25,-209.36C277.18,-227.29 286.07,-250.3 294.73,-272.7"></path>
+			<polygon fill="black" stroke="black" points="291.4,-273.8 298.27,-281.86 297.93,-271.28 291.4,-273.8"></polygon>
 		</g>
 		<g id="node4" class="node">
 			<title>bag 4</title>
-			<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"></path>
-			<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"></polygon>
-			<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-			<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-			<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+			<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"></path>
+			<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"></polygon>
+			<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+			<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+			<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 		</g>
 		<g id="edge3" class="edge">
 			<title>bag 4-&gt;bag 3</title>
-			<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"></path>
-			<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"></polygon>
+			<path fill="none" stroke="black" d="M307.96,-67.23C299,-86.19 287.62,-110.28 277.93,-130.8"></path>
+			<polygon fill="black" stroke="black" points="274.79,-129.26 273.68,-139.79 281.12,-132.24 274.79,-129.26"></polygon>
 		</g>
 		<g id="node6" class="node">
 			<title>sol4</title>
-			<path fill="white" stroke="black" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"></path>
-			<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-			<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-			<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" points="331,-218.5 459,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-201.5 361,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-184.5 361,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-167.5 361,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-150.5 361,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-133.5 361,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-116.5 361,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-201.5 391,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-184.5 391,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-167.5 391,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-150.5 391,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-133.5 391,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-116.5 391,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-201.5 421,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-184.5 421,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-167.5 421,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-150.5 421,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-133.5 421,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-116.5 421,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-201.5 459,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-184.5 459,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-167.5 459,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-150.5 459,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-133.5 459,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-116.5 459,-116.5 "></polyline>
+			<path fill="white" stroke="black" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"></path>
+			<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+			<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+			<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" points="327,-229.02 451.86,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="327,-211.08 356.34,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="327,-193.14 356.34,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="327,-175.2 356.34,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="327,-157.26 356.34,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="327,-139.32 356.34,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-121.38 356.34,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-211.08 385.68,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-193.14 385.68,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-175.2 385.68,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-157.26 385.68,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-139.32 385.68,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-121.38 385.68,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-211.08 415.02,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-193.14 415.02,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-175.2 415.02,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-157.26 415.02,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-139.32 415.02,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-121.38 415.02,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-211.08 451.86,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-193.14 451.86,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-175.2 451.86,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-157.26 451.86,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-139.32 451.86,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="327,-121.38 451.86,-121.38"></polyline>
 		</g>
 		<g id="edge5" class="edge">
 			<title>bag 4-&gt;sol4</title>
-			<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"></path>
-			<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"></polygon>
+			<path fill="none" stroke="black" d="M338.9,-67.23C342.61,-75.08 346.74,-83.82 350.99,-92.82"></path>
+			<polygon fill="black" stroke="black" points="347.74,-94.14 355.18,-101.68 354.07,-91.15 347.74,-94.14"></polygon>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(507.0 233.025) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 153.954)">
+	<g id="graph0" class="graph" transform="translate(499.86 161.205) scale(0.9999999999999997) scale(1 1) rotate(0) translate(4 325.97)">
 		<title>graph</title>
-		<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"></polygon>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"></path>
+			<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"></path>
 		</g>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"></path>
+			<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"></path>
+			<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"></path>
+			<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"></path>
+			<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"></path>
+			<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"></path>
+			<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"></path>
+			<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>1</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node2" class="node">
 			<title>2</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node3" class="node">
 			<title>3</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node4" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node5" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(778.0 210.705) scale(1.0000000000000002) scale(1 1) rotate(0) translate(104.28 101.294)">
+	<g id="graph0" class="graph" transform="translate(1027.0 130.235) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 387.53)">
 		<title>graph_sorted</title>
-		<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"></polygon>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"></path>
+			<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"></path>
 		</g>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"></path>
+			<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"></path>
+			<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"></path>
+			<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"></path>
+			<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"></path>
+			<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"></path>
+			<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"></path>
+			<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node2" class="node">
 			<title>1</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node3" class="node">
 			<title>2</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="35.2894" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-114.44" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node4" class="node">
 			<title>3</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node5" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
 </svg>
\ No newline at end of file
diff --git a/test/expected_files/test_vc_multiple_and_join/combined5.svg b/test/expected_files/test_vc_multiple_and_join/combined5.svg
index ec73d6a..68173f4 100644
--- a/test/expected_files/test_vc_multiple_and_join/combined5.svg
+++ b/test/expected_files/test_vc_multiple_and_join/combined5.svg
@@ -1,500 +1,500 @@
 <?xml version="1.0" encoding="utf-8"?>
-<svg width="994pt" height="624pt" viewBox="0.0 0.0 994 624" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
-	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 620)">
+<svg width="1427pt" height="652pt" viewBox="0.0 0.0 1427 652" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" preserveAspectRatio="xMinYMin">
+	<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 648.38)">
 		<title>Tree-Decomposition</title>
-		<polygon fill="white" stroke="transparent" points="-4,4 -4,-620 463,-620 463,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-648.38 455.86,-648.38 455.86,4 -4,4"></polygon>
 		<g id="node1" class="node">
 			<title>bag 1</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M237.5,-372C237.5,-372 158.5,-372 158.5,-372 152.5,-372 146.5,-366 146.5,-360 146.5,-360 146.5,-321 146.5,-321 146.5,-315 152.5,-309 158.5,-309 158.5,-309 237.5,-309 237.5,-309 243.5,-309 249.5,-315 249.5,-321 249.5,-321 249.5,-360 249.5,-360 249.5,-366 243.5,-372 237.5,-372"></path>
-			<polygon fill="white" stroke="transparent" points="155,-351.5 155,-370.5 242,-370.5 242,-351.5 155,-351.5"></polygon>
-			<text text-anchor="start" x="183" y="-357.3" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
-			<text text-anchor="start" x="169" y="-334.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
-			<text text-anchor="start" x="157" y="-315.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M233.6,-389.19C233.6,-389.19 155.26,-389.19 155.26,-389.19 149.26,-389.19 143.26,-383.19 143.26,-377.19 143.26,-377.19 143.26,-334.25 143.26,-334.25 143.26,-328.25 149.26,-322.25 155.26,-322.25 155.26,-322.25 233.6,-322.25 233.6,-322.25 239.6,-322.25 245.6,-328.25 245.6,-334.25 245.6,-334.25 245.6,-377.19 245.6,-377.19 245.6,-383.19 239.6,-389.19 233.6,-389.19"></path>
+			<polygon fill="white" stroke="none" points="151.18,-367.97 151.18,-388.47 237.68,-388.47 237.68,-367.97 151.18,-367.97"></polygon>
+			<text text-anchor="start" x="179.43" y="-373.17" font-family="Times New Roman,serif" font-size="14.00">bag 1</text>
+			<text text-anchor="start" x="165.18" y="-348.67" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 5, 6]</text>
+			<text text-anchor="start" x="153.18" y="-328.17" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0009s</text>
 		</g>
 		<g id="node8" class="node">
 			<title>sol1</title>
-			<path fill="yellow" stroke="black" stroke-width="2.5" d="M131,-445.5C131,-445.5 265,-445.5 265,-445.5 271,-445.5 277,-451.5 277,-457.5 277,-457.5 277,-603.5 277,-603.5 277,-609.5 271,-615.5 265,-615.5 265,-615.5 131,-615.5 131,-615.5 125,-615.5 119,-609.5 119,-603.5 119,-603.5 119,-457.5 119,-457.5 119,-451.5 125,-445.5 131,-445.5"></path>
-			<text text-anchor="middle" x="198" y="-603.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 1</text>
-			<text text-anchor="middle" x="134" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="134" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="134" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="134" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="134" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="134" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="134" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="134" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="164" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="164" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="164" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="164" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="164" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="164" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="164" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="164" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="194" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-			<text text-anchor="middle" x="194" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="194" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="194" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="194" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="194" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="194" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="194" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="224" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="224" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="224" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="258" y="-586.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="258" y="-569.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-			<text text-anchor="middle" x="258" y="-552.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-			<text text-anchor="middle" x="258" y="-535.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="258" y="-518.3" font-family="Times New Roman,serif" font-size="14.00">6</text>
-			<text text-anchor="middle" x="258" y="-501.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-			<text text-anchor="middle" x="258" y="-484.3" font-family="Times New Roman,serif" font-size="14.00">5</text>
-			<text text-anchor="middle" x="258" y="-467.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="198" y="-450.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 4</text>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-598.5 277,-598.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-581.5 149,-581.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-564.5 149,-564.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-547.5 149,-547.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-530.5 149,-530.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-513.5 149,-513.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-496.5 149,-496.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-479.5 149,-479.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-462.5 149,-598.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-581.5 179,-581.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-564.5 179,-564.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-547.5 179,-547.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-530.5 179,-530.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-513.5 179,-513.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-496.5 179,-496.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="149,-479.5 179,-479.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-462.5 179,-598.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-581.5 209,-581.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-564.5 209,-564.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-547.5 209,-547.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-530.5 209,-530.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-513.5 209,-513.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-496.5 209,-496.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="179,-479.5 209,-479.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-462.5 209,-598.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-581.5 239,-581.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-564.5 239,-564.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-547.5 239,-547.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-530.5 239,-530.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-513.5 239,-513.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-496.5 239,-496.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="209,-479.5 239,-479.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-462.5 239,-598.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-581.5 277,-581.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-564.5 277,-564.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-547.5 277,-547.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-530.5 277,-530.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-513.5 277,-513.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-496.5 277,-496.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="239,-479.5 277,-479.5 "></polyline>
-			<polyline fill="none" stroke="black" stroke-width="2.5" points="119,-462.5 277,-462.5 "></polyline>
+			<path fill="yellow" stroke="black" stroke-width="2.5" d="M129.33,-464.48C129.33,-464.48 259.53,-464.48 259.53,-464.48 265.53,-464.48 271.53,-470.48 271.53,-476.48 271.53,-476.48 271.53,-631.88 271.53,-631.88 271.53,-637.88 265.53,-643.88 259.53,-643.88 259.53,-643.88 129.33,-643.88 129.33,-643.88 123.33,-643.88 117.33,-637.88 117.33,-631.88 117.33,-631.88 117.33,-476.48 117.33,-476.48 117.33,-470.48 123.33,-464.48 129.33,-464.48"></path>
+			<text text-anchor="middle" x="194.43" y="-629.86" font-family="Times New Roman,serif" font-size="14.00">sol bag 1</text>
+			<text text-anchor="middle" x="132" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="132" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="132" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="132" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="132" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="132" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="132" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="132" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="161.34" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="161.34" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="161.34" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="161.34" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="161.34" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="161.34" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="161.34" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="161.34" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="190.68" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+			<text text-anchor="middle" x="190.68" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="190.68" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="190.68" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="190.68" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="190.68" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="190.68" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="190.68" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="220.02" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="220.02" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="220.02" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="253.11" y="-611.92" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="253.11" y="-593.98" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<text text-anchor="middle" x="253.11" y="-576.04" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<text text-anchor="middle" x="253.11" y="-558.1" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="253.11" y="-540.16" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<text text-anchor="middle" x="253.11" y="-522.22" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<text text-anchor="middle" x="253.11" y="-504.28" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<text text-anchor="middle" x="253.11" y="-486.34" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="194.43" y="-468.4" font-family="Times New Roman,serif" font-size="14.00">min-size: 4</text>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-625.94 271.53,-625.94"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-608 146.67,-608"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-590.06 146.67,-590.06"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-572.12 146.67,-572.12"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-554.18 146.67,-554.18"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-536.24 146.67,-536.24"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-518.3 146.67,-518.3"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-500.36 146.67,-500.36"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-482.42 146.67,-625.94"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-608 176.01,-608"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-590.06 176.01,-590.06"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-572.12 176.01,-572.12"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-554.18 176.01,-554.18"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-536.24 176.01,-536.24"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-518.3 176.01,-518.3"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="146.67,-500.36 176.01,-500.36"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-482.42 176.01,-625.94"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-608 205.35,-608"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-590.06 205.35,-590.06"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-572.12 205.35,-572.12"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-554.18 205.35,-554.18"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-536.24 205.35,-536.24"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-518.3 205.35,-518.3"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="176.01,-500.36 205.35,-500.36"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-482.42 205.35,-625.94"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-608 234.69,-608"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-590.06 234.69,-590.06"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-572.12 234.69,-572.12"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-554.18 234.69,-554.18"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-536.24 234.69,-536.24"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-518.3 234.69,-518.3"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="205.35,-500.36 234.69,-500.36"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-482.42 234.69,-625.94"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-608 271.53,-608"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-590.06 271.53,-590.06"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-572.12 271.53,-572.12"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-554.18 271.53,-554.18"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-536.24 271.53,-536.24"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-518.3 271.53,-518.3"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="234.69,-500.36 271.53,-500.36"></polyline>
+			<polyline fill="none" stroke="black" stroke-width="2.5" points="117.33,-482.42 271.53,-482.42"></polyline>
 		</g>
 		<g id="edge7" class="edge">
 			<title>bag 1-&gt;sol1</title>
-			<path fill="none" stroke="black" d="M198,-372.12C198,-389.53 198,-412.35 198,-435.2"></path>
-			<polygon fill="black" stroke="black" points="194.5,-435.33 198,-445.33 201.5,-435.33 194.5,-435.33"></polygon>
+			<path fill="none" stroke="black" d="M194.43,-390.05C194.43,-407.47 194.43,-429.81 194.43,-452.34"></path>
+			<polygon fill="black" stroke="black" points="190.93,-452.24 194.43,-462.24 197.93,-452.24 190.93,-452.24"></polygon>
 		</g>
 		<g id="node2" class="node">
 			<title>bag 2</title>
-			<path fill="white" stroke="black" d="M173.5,-199C173.5,-199 94.5,-199 94.5,-199 88.5,-199 82.5,-193 82.5,-187 82.5,-187 82.5,-148 82.5,-148 82.5,-142 88.5,-136 94.5,-136 94.5,-136 173.5,-136 173.5,-136 179.5,-136 185.5,-142 185.5,-148 185.5,-148 185.5,-187 185.5,-187 185.5,-193 179.5,-199 173.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="91,-178.5 91,-197.5 178,-197.5 178,-178.5 91,-178.5"></polygon>
-			<text text-anchor="start" x="119" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
-			<text text-anchor="start" x="105" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
-			<text text-anchor="start" x="93" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
+			<path fill="white" stroke="black" d="M170.6,-208.67C170.6,-208.67 92.26,-208.67 92.26,-208.67 86.26,-208.67 80.26,-202.67 80.26,-196.67 80.26,-196.67 80.26,-153.73 80.26,-153.73 80.26,-147.73 86.26,-141.73 92.26,-141.73 92.26,-141.73 170.6,-141.73 170.6,-141.73 176.6,-141.73 182.6,-147.73 182.6,-153.73 182.6,-153.73 182.6,-196.67 182.6,-196.67 182.6,-202.67 176.6,-208.67 170.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="88.18,-187.45 88.18,-207.95 174.68,-207.95 174.68,-187.45 88.18,-187.45"></polygon>
+			<text text-anchor="start" x="116.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 2</text>
+			<text text-anchor="start" x="102.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 3, 4, 5]</text>
+			<text text-anchor="start" x="90.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0026s</text>
 		</g>
 		<g id="edge1" class="edge">
 			<title>bag 2-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M145.44,-199.07C155.92,-227.07 171.5,-268.7 182.98,-299.37"></path>
-			<polygon fill="black" stroke="black" points="179.77,-300.77 186.55,-308.91 186.32,-298.31 179.77,-300.77"></polygon>
+			<path fill="none" stroke="black" d="M142.99,-208.94C153.06,-237.49 167.75,-279.13 178.86,-310.6"></path>
+			<polygon fill="black" stroke="black" points="175.5,-311.58 182.12,-319.85 182.1,-309.25 175.5,-311.58"></polygon>
 		</g>
 		<g id="node5" class="node">
 			<title>sol2</title>
-			<path fill="white" stroke="black" d="M12,-272.5C12,-272.5 116,-272.5 116,-272.5 122,-272.5 128,-278.5 128,-284.5 128,-284.5 128,-396.5 128,-396.5 128,-402.5 122,-408.5 116,-408.5 116,-408.5 12,-408.5 12,-408.5 6,-408.5 0,-402.5 0,-396.5 0,-396.5 0,-284.5 0,-284.5 0,-278.5 6,-272.5 12,-272.5"></path>
-			<text text-anchor="middle" x="64" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
-			<text text-anchor="middle" x="15" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="15" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="15" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="45" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="45" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="45" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v5</text>
-			<text text-anchor="middle" x="75" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="75" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="75" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="109" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="109" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="109" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="109" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="64" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" points="0,-391.5 128,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-374.5 30,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-357.5 30,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-340.5 30,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-323.5 30,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-306.5 30,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-289.5 30,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-374.5 60,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-357.5 60,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-340.5 60,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-323.5 60,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="30,-306.5 60,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-289.5 60,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-374.5 90,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-357.5 90,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-340.5 90,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-323.5 90,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="60,-306.5 90,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-289.5 90,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-374.5 128,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-357.5 128,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-340.5 128,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-323.5 128,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="90,-306.5 128,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="0,-289.5 128,-289.5 "></polyline>
+			<path fill="white" stroke="black" d="M12,-283.96C12,-283.96 112.86,-283.96 112.86,-283.96 118.86,-283.96 124.86,-289.96 124.86,-295.96 124.86,-295.96 124.86,-415.48 124.86,-415.48 124.86,-421.48 118.86,-427.48 112.86,-427.48 112.86,-427.48 12,-427.48 12,-427.48 6,-427.48 0,-421.48 0,-415.48 0,-415.48 0,-295.96 0,-295.96 0,-289.96 6,-283.96 12,-283.96"></path>
+			<text text-anchor="middle" x="62.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 2</text>
+			<text text-anchor="middle" x="14.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="14.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="14.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="44.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="44.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="44.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v5</text>
+			<text text-anchor="middle" x="73.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="73.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="73.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="106.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="106.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="106.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="106.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="62.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" points="0,-409.54 124.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="0,-391.6 29.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="0,-373.66 29.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="0,-355.72 29.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="0,-337.78 29.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="0,-319.84 29.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-301.9 29.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-391.6 58.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-373.66 58.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-355.72 58.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-337.78 58.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="29.34,-319.84 58.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-301.9 58.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-391.6 88.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-373.66 88.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-355.72 88.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-337.78 88.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="58.68,-319.84 88.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-301.9 88.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-391.6 124.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-373.66 124.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-355.72 124.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-337.78 124.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="88.02,-319.84 124.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="0,-301.9 124.86,-301.9"></polyline>
 		</g>
 		<g id="edge4" class="edge">
 			<title>bag 2-&gt;sol2</title>
-			<path fill="none" stroke="black" d="M121.49,-199.07C114.16,-216.97 104.55,-240.44 95.29,-263.06"></path>
-			<polygon fill="black" stroke="black" points="92.04,-261.76 91.49,-272.34 98.52,-264.41 92.04,-261.76"></polygon>
+			<path fill="none" stroke="black" d="M118.77,-208.94C111.79,-227.02 102.77,-250.34 94.01,-273.02"></path>
+			<polygon fill="black" stroke="black" points="90.76,-271.71 90.42,-282.3 97.29,-274.24 90.76,-271.71"></polygon>
 		</g>
 		<g id="node3" class="node">
 			<title>bag 3</title>
-			<path fill="white" stroke="black" d="M300.5,-199C300.5,-199 221.5,-199 221.5,-199 215.5,-199 209.5,-193 209.5,-187 209.5,-187 209.5,-148 209.5,-148 209.5,-142 215.5,-136 221.5,-136 221.5,-136 300.5,-136 300.5,-136 306.5,-136 312.5,-142 312.5,-148 312.5,-148 312.5,-187 312.5,-187 312.5,-193 306.5,-199 300.5,-199"></path>
-			<polygon fill="white" stroke="transparent" points="218,-178.5 218,-197.5 305,-197.5 305,-178.5 218,-178.5"></polygon>
-			<text text-anchor="start" x="246" y="-184.3" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
-			<text text-anchor="start" x="232" y="-161.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
-			<text text-anchor="start" x="220" y="-142.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
+			<path fill="white" stroke="black" d="M296.6,-208.67C296.6,-208.67 218.26,-208.67 218.26,-208.67 212.26,-208.67 206.26,-202.67 206.26,-196.67 206.26,-196.67 206.26,-153.73 206.26,-153.73 206.26,-147.73 212.26,-141.73 218.26,-141.73 218.26,-141.73 296.6,-141.73 296.6,-141.73 302.6,-141.73 308.6,-147.73 308.6,-153.73 308.6,-153.73 308.6,-196.67 308.6,-196.67 308.6,-202.67 302.6,-208.67 296.6,-208.67"></path>
+			<polygon fill="white" stroke="none" points="214.18,-187.45 214.18,-207.95 300.68,-207.95 300.68,-187.45 214.18,-187.45"></polygon>
+			<text text-anchor="start" x="242.43" y="-192.65" font-family="Times New Roman,serif" font-size="14.00">bag 3</text>
+			<text text-anchor="start" x="228.18" y="-168.15" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 3, 6]</text>
+			<text text-anchor="start" x="216.18" y="-147.65" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0020s</text>
 		</g>
 		<g id="edge2" class="edge">
 			<title>bag 3-&gt;bag 1</title>
-			<path fill="none" stroke="black" d="M249.74,-199.07C239.42,-227.07 224.08,-268.7 212.79,-299.37"></path>
-			<polygon fill="black" stroke="black" points="209.44,-298.31 209.27,-308.91 216.01,-300.73 209.44,-298.31"></polygon>
+			<path fill="none" stroke="black" d="M245.87,-208.94C235.8,-237.49 221.11,-279.13 210,-310.6"></path>
+			<polygon fill="black" stroke="black" points="206.76,-309.25 206.74,-319.85 213.36,-311.58 206.76,-309.25"></polygon>
 		</g>
 		<g id="node7" class="node">
 			<title>sol3</title>
-			<path fill="white" stroke="black" d="M280,-272.5C280,-272.5 384,-272.5 384,-272.5 390,-272.5 396,-278.5 396,-284.5 396,-284.5 396,-396.5 396,-396.5 396,-402.5 390,-408.5 384,-408.5 384,-408.5 280,-408.5 280,-408.5 274,-408.5 268,-402.5 268,-396.5 268,-396.5 268,-284.5 268,-284.5 268,-278.5 274,-272.5 280,-272.5"></path>
-			<text text-anchor="middle" x="332" y="-396.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
-			<text text-anchor="middle" x="283" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="283" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="283" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v3</text>
-			<text text-anchor="middle" x="313" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="313" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="313" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="313" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="343" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="343" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="343" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="343" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="377" y="-379.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="377" y="-362.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-345.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-328.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="377" y="-311.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="377" y="-294.3" font-family="Times New Roman,serif" font-size="14.00">4</text>
-			<text text-anchor="middle" x="332" y="-277.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 3</text>
-			<polyline fill="none" stroke="black" points="268,-391.5 396,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-374.5 298,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-357.5 298,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-340.5 298,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-323.5 298,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-306.5 298,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-289.5 298,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-374.5 328,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-357.5 328,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-340.5 328,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-323.5 328,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="298,-306.5 328,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-289.5 328,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-374.5 358,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-357.5 358,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-340.5 358,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-323.5 358,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="328,-306.5 358,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-289.5 358,-391.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-374.5 396,-374.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-357.5 396,-357.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-340.5 396,-340.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-323.5 396,-323.5 "></polyline>
-			<polyline fill="none" stroke="black" points="358,-306.5 396,-306.5 "></polyline>
-			<polyline fill="none" stroke="black" points="268,-289.5 396,-289.5 "></polyline>
+			<path fill="white" stroke="black" d="M276,-283.96C276,-283.96 376.86,-283.96 376.86,-283.96 382.86,-283.96 388.86,-289.96 388.86,-295.96 388.86,-295.96 388.86,-415.48 388.86,-415.48 388.86,-421.48 382.86,-427.48 376.86,-427.48 376.86,-427.48 276,-427.48 276,-427.48 270,-427.48 264,-421.48 264,-415.48 264,-415.48 264,-295.96 264,-295.96 264,-289.96 270,-283.96 276,-283.96"></path>
+			<text text-anchor="middle" x="326.43" y="-413.46" font-family="Times New Roman,serif" font-size="14.00">sol bag 3</text>
+			<text text-anchor="middle" x="278.67" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="278.67" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="278.67" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v3</text>
+			<text text-anchor="middle" x="308.01" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="308.01" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="308.01" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="308.01" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="337.35" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="337.35" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="337.35" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="337.35" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="370.44" y="-395.52" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="370.44" y="-377.58" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-359.64" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-341.7" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="370.44" y="-323.76" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="370.44" y="-305.82" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<text text-anchor="middle" x="326.43" y="-287.88" font-family="Times New Roman,serif" font-size="14.00">min-size: 3</text>
+			<polyline fill="none" stroke="black" points="264,-409.54 388.86,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="264,-391.6 293.34,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="264,-373.66 293.34,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="264,-355.72 293.34,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="264,-337.78 293.34,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="264,-319.84 293.34,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-301.9 293.34,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-391.6 322.68,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-373.66 322.68,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-355.72 322.68,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-337.78 322.68,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="293.34,-319.84 322.68,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-301.9 322.68,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-391.6 352.02,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-373.66 352.02,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-355.72 352.02,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-337.78 352.02,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="322.68,-319.84 352.02,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-301.9 352.02,-409.54"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-391.6 388.86,-391.6"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-373.66 388.86,-373.66"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-355.72 388.86,-355.72"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-337.78 388.86,-337.78"></polyline>
+			<polyline fill="none" stroke="black" points="352.02,-319.84 388.86,-319.84"></polyline>
+			<polyline fill="none" stroke="black" points="264,-301.9 388.86,-301.9"></polyline>
 		</g>
 		<g id="edge6" class="edge">
 			<title>bag 3-&gt;sol3</title>
-			<path fill="none" stroke="black" d="M273.69,-199.07C281.13,-216.97 290.87,-240.44 300.26,-263.06"></path>
-			<polygon fill="black" stroke="black" points="297.05,-264.44 304.11,-272.34 303.51,-261.76 297.05,-264.44"></polygon>
+			<path fill="none" stroke="black" d="M270.09,-208.94C277.07,-227.02 286.09,-250.34 294.85,-273.02"></path>
+			<polygon fill="black" stroke="black" points="291.57,-274.24 298.44,-282.3 298.1,-271.71 291.57,-274.24"></polygon>
 		</g>
 		<g id="node4" class="node">
 			<title>bag 4</title>
-			<path fill="white" stroke="black" d="M367.5,-63C367.5,-63 288.5,-63 288.5,-63 282.5,-63 276.5,-57 276.5,-51 276.5,-51 276.5,-12 276.5,-12 276.5,-6 282.5,0 288.5,0 288.5,0 367.5,0 367.5,0 373.5,0 379.5,-6 379.5,-12 379.5,-12 379.5,-51 379.5,-51 379.5,-57 373.5,-63 367.5,-63"></path>
-			<polygon fill="white" stroke="transparent" points="285,-42.5 285,-61.5 372,-61.5 372,-42.5 285,-42.5"></polygon>
-			<text text-anchor="start" x="313" y="-48.3" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
-			<text text-anchor="start" x="299" y="-25.3" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
-			<text text-anchor="start" x="287" y="-6.3" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
+			<path fill="white" stroke="black" d="M362.6,-66.94C362.6,-66.94 284.26,-66.94 284.26,-66.94 278.26,-66.94 272.26,-60.94 272.26,-54.94 272.26,-54.94 272.26,-12 272.26,-12 272.26,-6 278.26,0 284.26,0 284.26,0 362.6,0 362.6,0 368.6,0 374.6,-6 374.6,-12 374.6,-12 374.6,-54.94 374.6,-54.94 374.6,-60.94 368.6,-66.94 362.6,-66.94"></path>
+			<polygon fill="white" stroke="none" points="280.18,-45.72 280.18,-66.22 366.68,-66.22 366.68,-45.72 280.18,-45.72"></polygon>
+			<text text-anchor="start" x="308.43" y="-50.92" font-family="Times New Roman,serif" font-size="14.00">bag 4</text>
+			<text text-anchor="start" x="294.18" y="-26.42" font-family="Times New Roman,serif" font-size="14.00">[1, 2, 6, 7]</text>
+			<text text-anchor="start" x="282.18" y="-5.92" font-family="Times New Roman,serif" font-size="14.00">dtime=0.0017s</text>
 		</g>
 		<g id="edge3" class="edge">
 			<title>bag 4-&gt;bag 3</title>
-			<path fill="none" stroke="black" d="M312.63,-63.24C303.18,-82.14 290.98,-106.54 280.81,-126.88"></path>
-			<polygon fill="black" stroke="black" points="277.64,-125.39 276.3,-135.9 283.9,-128.52 277.64,-125.39"></polygon>
+			<path fill="none" stroke="black" d="M307.96,-67.23C298.94,-86.33 287.46,-110.63 277.72,-131.25"></path>
+			<polygon fill="black" stroke="black" points="274.56,-129.74 273.45,-140.28 280.89,-132.73 274.56,-129.74"></polygon>
 		</g>
 		<g id="node6" class="node">
 			<title>sol4</title>
-			<path fill="white" stroke="black" d="M343,-99.5C343,-99.5 447,-99.5 447,-99.5 453,-99.5 459,-105.5 459,-111.5 459,-111.5 459,-223.5 459,-223.5 459,-229.5 453,-235.5 447,-235.5 447,-235.5 343,-235.5 343,-235.5 337,-235.5 331,-229.5 331,-223.5 331,-223.5 331,-111.5 331,-111.5 331,-105.5 337,-99.5 343,-99.5"></path>
-			<text text-anchor="middle" x="395" y="-223.3" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
-			<text text-anchor="middle" x="346" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v1</text>
-			<text text-anchor="middle" x="346" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="346" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v2</text>
-			<text text-anchor="middle" x="376" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="376" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="376" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">v6</text>
-			<text text-anchor="middle" x="406" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
-			<text text-anchor="middle" x="406" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="406" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
-			<text text-anchor="middle" x="440" y="-206.3" font-family="Times New Roman,serif" font-size="14.00">size</text>
-			<text text-anchor="middle" x="440" y="-189.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-172.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-155.3" font-family="Times New Roman,serif" font-size="14.00">2</text>
-			<text text-anchor="middle" x="440" y="-138.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="440" y="-121.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
-			<text text-anchor="middle" x="395" y="-104.3" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
-			<polyline fill="none" stroke="black" points="331,-218.5 459,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-201.5 361,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-184.5 361,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-167.5 361,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-150.5 361,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-133.5 361,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-116.5 361,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-201.5 391,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-184.5 391,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-167.5 391,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-150.5 391,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="361,-133.5 391,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-116.5 391,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-201.5 421,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-184.5 421,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-167.5 421,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-150.5 421,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="391,-133.5 421,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-116.5 421,-218.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-201.5 459,-201.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-184.5 459,-184.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-167.5 459,-167.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-150.5 459,-150.5 "></polyline>
-			<polyline fill="none" stroke="black" points="421,-133.5 459,-133.5 "></polyline>
-			<polyline fill="none" stroke="black" points="331,-116.5 459,-116.5 "></polyline>
+			<path fill="white" stroke="black" d="M339,-103.44C339,-103.44 439.86,-103.44 439.86,-103.44 445.86,-103.44 451.86,-109.44 451.86,-115.44 451.86,-115.44 451.86,-234.96 451.86,-234.96 451.86,-240.96 445.86,-246.96 439.86,-246.96 439.86,-246.96 339,-246.96 339,-246.96 333,-246.96 327,-240.96 327,-234.96 327,-234.96 327,-115.44 327,-115.44 327,-109.44 333,-103.44 339,-103.44"></path>
+			<text text-anchor="middle" x="389.43" y="-232.94" font-family="Times New Roman,serif" font-size="14.00">sol bag 4</text>
+			<text text-anchor="middle" x="341.67" y="-215" font-family="Times New Roman,serif" font-size="14.00">v1</text>
+			<text text-anchor="middle" x="341.67" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="341.67" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-215" font-family="Times New Roman,serif" font-size="14.00">v2</text>
+			<text text-anchor="middle" x="371.01" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="371.01" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="371.01" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-215" font-family="Times New Roman,serif" font-size="14.00">v6</text>
+			<text text-anchor="middle" x="400.35" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">0</text>
+			<text text-anchor="middle" x="400.35" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="400.35" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<text text-anchor="middle" x="433.44" y="-215" font-family="Times New Roman,serif" font-size="14.00">size</text>
+			<text text-anchor="middle" x="433.44" y="-197.06" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-179.12" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-161.18" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<text text-anchor="middle" x="433.44" y="-143.24" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="433.44" y="-125.3" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<text text-anchor="middle" x="389.43" y="-107.36" font-family="Times New Roman,serif" font-size="14.00">min-size: 2</text>
+			<polyline fill="none" stroke="black" points="327,-229.02 451.86,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="327,-211.08 356.34,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="327,-193.14 356.34,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="327,-175.2 356.34,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="327,-157.26 356.34,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="327,-139.32 356.34,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-121.38 356.34,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-211.08 385.68,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-193.14 385.68,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-175.2 385.68,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-157.26 385.68,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="356.34,-139.32 385.68,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-121.38 385.68,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-211.08 415.02,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-193.14 415.02,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-175.2 415.02,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-157.26 415.02,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="385.68,-139.32 415.02,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-121.38 415.02,-229.02"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-211.08 451.86,-211.08"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-193.14 451.86,-193.14"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-175.2 451.86,-175.2"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-157.26 451.86,-157.26"></polyline>
+			<polyline fill="none" stroke="black" points="415.02,-139.32 451.86,-139.32"></polyline>
+			<polyline fill="none" stroke="black" points="327,-121.38 451.86,-121.38"></polyline>
 		</g>
 		<g id="edge5" class="edge">
 			<title>bag 4-&gt;sol4</title>
-			<path fill="none" stroke="black" d="M343.37,-63.24C347.47,-71.44 352.09,-80.67 356.83,-90.16"></path>
-			<polygon fill="black" stroke="black" points="353.8,-91.93 361.41,-99.31 360.06,-88.8 353.8,-91.93"></polygon>
+			<path fill="none" stroke="black" d="M338.9,-67.23C342.61,-75.08 346.74,-83.82 350.99,-92.82"></path>
+			<polygon fill="black" stroke="black" points="347.74,-94.14 355.18,-101.68 354.07,-91.15 347.74,-94.14"></polygon>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(507.0 233.025) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 153.954)">
+	<g id="graph0" class="graph" transform="translate(499.86 161.205) scale(0.9999999999999997) scale(1 1) rotate(0) translate(4 325.97)">
 		<title>graph</title>
-		<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"></polygon>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"></path>
+			<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"></path>
+			<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"></path>
 		</g>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"></path>
+			<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"></path>
+			<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"></path>
+			<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"></path>
+			<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"></path>
+			<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"></path>
+			<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>1</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node2" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node3" class="node">
 			<title>3</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node4" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node5" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
-	<g id="graph0" class="graph" transform="translate(778.0 210.705) scale(1.0000000000000002) scale(1 1) rotate(0) translate(104.28 101.294)">
+	<g id="graph0" class="graph" transform="translate(1027.0 130.235) scale(1.0000000000000002) scale(1 1) rotate(0) translate(4 387.53)">
 		<title>graph_sorted</title>
-		<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"></polygon>
+		<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"></polygon>
 		<g id="edge9" class="edge">
 			<title>1--7</title>
-			<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"></path>
+			<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"></path>
 		</g>
 		<g id="edge1" class="edge">
 			<title>1--2</title>
-			<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"></path>
+			<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"></path>
 		</g>
 		<g id="edge12" class="edge">
 			<title>1--3</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"></path>
 		</g>
 		<g id="edge5" class="edge">
 			<title>1--4</title>
-			<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"></path>
+			<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"></path>
 		</g>
 		<g id="edge4" class="edge">
 			<title>1--5</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"></path>
 		</g>
 		<g id="edge11" class="edge">
 			<title>1--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"></path>
 		</g>
 		<g id="edge3" class="edge">
 			<title>2--7</title>
-			<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"></path>
+			<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"></path>
 		</g>
 		<g id="edge6" class="edge">
 			<title>2--3</title>
-			<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"></path>
+			<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"></path>
 		</g>
 		<g id="edge2" class="edge">
 			<title>3--4</title>
-			<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"></path>
+			<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"></path>
 		</g>
 		<g id="edge8" class="edge">
 			<title>4--5</title>
-			<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"></path>
+			<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"></path>
 		</g>
 		<g id="edge10" class="edge">
 			<title>5--6</title>
-			<path fill="none" stroke="red" stroke-width="2.2" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"></path>
+			<path fill="none" stroke="red" stroke-width="2.2" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"></path>
 		</g>
 		<g id="edge7" class="edge">
 			<title>6--7</title>
-			<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"></path>
+			<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"></path>
 		</g>
 		<g id="node1" class="node">
 			<title>7</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 		</g>
 		<g id="node2" class="node">
 			<title>1</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 		</g>
 		<g id="node3" class="node">
 			<title>2</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 		</g>
 		<g id="node4" class="node">
 			<title>3</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 		</g>
 		<g id="node5" class="node">
 			<title>4</title>
-			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+			<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 		</g>
 		<g id="node6" class="node">
 			<title>5</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="-63.5907" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-331.11" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 		</g>
 		<g id="node7" class="node">
 			<title>6</title>
-			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"></ellipse>
-			<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+			<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"></ellipse>
+			<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 		</g>
 	</g>
 </svg>
\ No newline at end of file
diff --git a/test/expected_files/test_vc_multiple_and_join/graph1.svg b/test/expected_files/test_vc_multiple_and_join/graph1.svg
index 548b301..6d3efe8 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph1.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph1.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph Pages: 1 -->
-<svg width="232pt" height="158pt"
- viewBox="0.00 0.00 231.59 157.95" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 153.954)">
+<svg width="488pt" height="330pt"
+ viewBox="0.00 0.00 487.59 329.97" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 325.97)">
 <title>graph</title>
-<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"/>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"/>
 </g>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"/>
 </g>
 <!-- 1 -->
-<g id="node1" class="node"><title>1</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"/>
-<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node1" class="node">
+<title>1</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"/>
+<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node2" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"/>
-<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node2" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"/>
+<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node3" class="node"><title>3</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"/>
-<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node3" class="node">
+<title>3</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node4" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"/>
-<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node4" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"/>
+<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 7 -->
-<g id="node5" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"/>
-<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node5" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"/>
-<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"/>
+<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"/>
-<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph2.svg b/test/expected_files/test_vc_multiple_and_join/graph2.svg
index f0ba461..3ed11d9 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph2.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph2.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph Pages: 1 -->
-<svg width="232pt" height="158pt"
- viewBox="0.00 0.00 231.59 157.95" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 153.954)">
+<svg width="488pt" height="330pt"
+ viewBox="0.00 0.00 487.59 329.97" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 325.97)">
 <title>graph</title>
-<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"/>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"/>
 </g>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"/>
 </g>
 <!-- 1 -->
-<g id="node1" class="node"><title>1</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"/>
-<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node1" class="node">
+<title>1</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"/>
+<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node2" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"/>
-<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node2" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"/>
+<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node3" class="node"><title>3</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"/>
-<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node3" class="node">
+<title>3</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node4" class="node"><title>4</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"/>
-<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node4" class="node">
+<title>4</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"/>
+<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 7 -->
-<g id="node5" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"/>
-<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node5" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"/>
-<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"/>
+<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"/>
-<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph3.svg b/test/expected_files/test_vc_multiple_and_join/graph3.svg
index 96d1005..191faf2 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph3.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph3.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph Pages: 1 -->
-<svg width="232pt" height="158pt"
- viewBox="0.00 0.00 231.59 157.95" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 153.954)">
+<svg width="488pt" height="330pt"
+ viewBox="0.00 0.00 487.59 329.97" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 325.97)">
 <title>graph</title>
-<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"/>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"/>
 </g>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"/>
 </g>
 <!-- 1 -->
-<g id="node1" class="node"><title>1</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"/>
-<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node1" class="node">
+<title>1</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"/>
+<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node2" class="node"><title>2</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"/>
-<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node2" class="node">
+<title>2</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"/>
+<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node3" class="node"><title>3</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"/>
-<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node3" class="node">
+<title>3</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node4" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"/>
-<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node4" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"/>
+<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 7 -->
-<g id="node5" class="node"><title>7</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"/>
-<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node5" class="node">
+<title>7</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"/>
-<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"/>
+<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"/>
-<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph4.svg b/test/expected_files/test_vc_multiple_and_join/graph4.svg
index d36118b..385570f 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph4.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph4.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph Pages: 1 -->
-<svg width="232pt" height="158pt"
- viewBox="0.00 0.00 231.59 157.95" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 153.954)">
+<svg width="488pt" height="330pt"
+ viewBox="0.00 0.00 487.59 329.97" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 325.97)">
 <title>graph</title>
-<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"/>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"/>
 </g>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"/>
 </g>
 <!-- 1 -->
-<g id="node1" class="node"><title>1</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"/>
-<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node1" class="node">
+<title>1</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"/>
+<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node2" class="node"><title>2</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"/>
-<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node2" class="node">
+<title>2</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"/>
+<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node3" class="node"><title>3</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"/>
-<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node3" class="node">
+<title>3</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node4" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"/>
-<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node4" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"/>
+<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 7 -->
-<g id="node5" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"/>
-<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node5" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"/>
-<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"/>
+<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"/>
-<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph5.svg b/test/expected_files/test_vc_multiple_and_join/graph5.svg
index e4e0160..5734227 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph5.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph5.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph Pages: 1 -->
-<svg width="232pt" height="158pt"
- viewBox="0.00 0.00 231.59 157.95" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 153.954)">
+<svg width="488pt" height="330pt"
+ viewBox="0.00 0.00 487.59 329.97" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 325.97)">
 <title>graph</title>
-<polygon fill="white" stroke="none" points="-4,4 -4,-153.954 227.589,-153.954 227.589,4 -4,4"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-325.97 483.59,-325.97 483.59,4 -4,4"/>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M76.4943,-55.0728C68.7196,-52.0652 60.091,-48.7274 52.3421,-45.7298"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M186.64,-124.74C152.51,-111.54 90.46,-87.53 56.22,-74.29"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M77.4582,-74.0894C68.6417,-77.8984 58.5689,-82.2501 49.7537,-86.0585"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M187.49,-144.13C152.24,-159.36 85.68,-188.11 50.37,-203.36"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M97.2193,-82.3958C95.6095,-92.1094 93.6323,-104.04 92.0212,-113.762"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M207.64,-152.9C202.21,-185.65 191.1,-252.69 185.7,-285.31"/>
 </g>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M111.162,-47.5546C113.941,-43.3109 116.925,-38.7536 119.699,-34.5188"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M221.98,-116.95C236.35,-95 261.12,-57.18 275.51,-35.2"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M114.542,-79.848C121.67,-87.6131 130.263,-96.9732 137.381,-104.727"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M225.56,-150.19C250.44,-177.29 300.35,-231.67 325.11,-258.64"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M127.325,-63.9362C140.462,-63.7826 156.205,-63.5985 169.36,-63.4447"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M238.5,-133.75C285.03,-133.2 378.24,-132.11 424.8,-131.57"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M28.3588,-54.7686C28.1206,-61.978 27.8467,-70.267 27.6075,-77.5056"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M31.29,-83.7C30.34,-112.28 28.56,-166.31 27.62,-194.8"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M55.1107,-31.8719C70.274,-29.0824 89.3028,-25.5819 104.451,-22.7951"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M58.7,-59.96C107.65,-50.95 210.99,-31.94 259.96,-22.93"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M47.6472,-107.898C54.4113,-111.832 61.9184,-116.199 68.6601,-120.12"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M47.99,-225.67C77.68,-242.94 131.67,-274.34 161.46,-291.67"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M115.197,-127.054C118.548,-126.426 121.98,-125.784 125.333,-125.157"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M209.26,-298.98C238.15,-293.58 284,-285 312.95,-279.58"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M164.386,-104.025C170.514,-96.2421 177.835,-86.9447 183.947,-79.1824"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M352.9,-257.85C374.65,-230.23 417.81,-175.41 439.5,-147.86"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M177.478,-50.074C168.788,-44.139 158.525,-37.1295 149.813,-31.1794"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M432.91,-117.81C401,-96.01 338.32,-53.2 306.42,-31.42"/>
 </g>
 <!-- 1 -->
-<g id="node1" class="node"><title>1</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="100.226" cy="-64.2531" rx="27" ry="18"/>
-<text text-anchor="middle" x="100.226" y="-60.5531" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node1" class="node">
+<title>1</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="210.76" cy="-134.07" rx="27" ry="18"/>
+<text text-anchor="middle" x="210.76" y="-129.02" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node2" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="28.9565" cy="-36.6834" rx="27" ry="18"/>
-<text text-anchor="middle" x="28.9565" y="-32.9834" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node2" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="31.91" cy="-64.89" rx="27" ry="18"/>
+<text text-anchor="middle" x="31.91" y="-59.84" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node3" class="node"><title>3</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-95.8887" rx="27" ry="18"/>
-<text text-anchor="middle" x="27" y="-92.1887" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node3" class="node">
+<title>3</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="27" cy="-213.46" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-208.41" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node4" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="89.0062" cy="-131.954" rx="27" ry="18"/>
-<text text-anchor="middle" x="89.0062" y="-128.254" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node4" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="182.61" cy="-303.97" rx="27" ry="18"/>
+<text text-anchor="middle" x="182.61" y="-298.92" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 7 -->
-<g id="node5" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="130.517" cy="-18" rx="27" ry="18"/>
-<text text-anchor="middle" x="130.517" y="-14.3" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node5" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="286.78" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="286.78" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="151.62" cy="-120.238" rx="27" ry="18"/>
-<text text-anchor="middle" x="151.62" y="-116.538" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="339.74" cy="-274.57" rx="27" ry="18"/>
+<text text-anchor="middle" x="339.74" y="-269.52" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="196.589" cy="-63.1264" rx="27" ry="18"/>
-<text text-anchor="middle" x="196.589" y="-59.4264" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="yellow" stroke="black" stroke-width="2.2" cx="452.59" cy="-131.25" rx="27" ry="18"/>
+<text text-anchor="middle" x="452.59" y="-126.2" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted1 b/test/expected_files/test_vc_multiple_and_join/graph_sorted1
index c0cdf42..bc6e88a 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted1
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted1
@@ -1,13 +1,13 @@
 strict graph graph_sorted {
 	graph [K=2 fontsize=18 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	7 [pos="2.097100,0.468120!"]
-	1 [pos="1.141400,0.250000!"]
-	2 [pos="0.375000,0.861170!"]
-	3 [pos="0.375000,1.841400!"]
-	4 [pos="1.141400,2.452600!"]
-	5 [pos="2.097100,2.234500!"]
-	6 [pos="2.522400,1.351300!"]
+	7 [pos="4.592900,0.784260!"]
+	1 [pos="2.252100,0.250000!"]
+	2 [pos="0.375000,1.747000!"]
+	3 [pos="0.375000,4.147900!"]
+	4 [pos="2.252100,5.644900!"]
+	5 [pos="4.592900,5.110600!"]
+	6 [pos="5.634600,2.947400!"]
 	1 -- 2
 	3 -- 4
 	2 -- 7
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted1.svg b/test/expected_files/test_vc_multiple_and_join/graph_sorted1.svg
index 7048b11..a6ea1d3 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted1.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted1.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph_sorted Pages: 1 -->
-<svg width="217pt" height="203pt"
- viewBox="0.00 0.00 216.61 202.59" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(104.28 101.294)">
+<svg width="401pt" height="392pt"
+ viewBox="0.00 0.00 400.82 391.53" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 387.53)">
 <title>graph_sorted</title>
-<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"/>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"/>
 </g>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"/>
 </g>
 <!-- 7 -->
-<g id="node1" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node1" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 1 -->
-<g id="node2" class="node"><title>1</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="79.2938" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node2" class="node">
+<title>1</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node3" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node3" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node4" class="node"><title>3</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node4" class="node">
+<title>3</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-269.1" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node5" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node5" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"/>
-<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="365.82" cy="-191.76" rx="27" ry="18"/>
+<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted2 b/test/expected_files/test_vc_multiple_and_join/graph_sorted2
index 2ebaf9e..8e80553 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted2
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted2
@@ -1,13 +1,13 @@
 strict graph graph_sorted {
 	graph [K=2 fontsize=18 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	7 [pos="2.097100,0.468120!"]
-	1 [pos="1.141400,0.250000!"]
-	2 [pos="0.375000,0.861170!"]
-	3 [pos="0.375000,1.841400!"]
-	4 [pos="1.141400,2.452600!"]
-	5 [pos="2.097100,2.234500!"]
-	6 [pos="2.522400,1.351300!"]
+	7 [pos="4.592900,0.784260!"]
+	1 [pos="2.252100,0.250000!"]
+	2 [pos="0.375000,1.747000!"]
+	3 [pos="0.375000,4.147900!"]
+	4 [pos="2.252100,5.644900!"]
+	5 [pos="4.592900,5.110600!"]
+	6 [pos="5.634600,2.947400!"]
 	1 -- 2
 	3 -- 4
 	2 -- 7
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted2.svg b/test/expected_files/test_vc_multiple_and_join/graph_sorted2.svg
index 2acef2b..6d71370 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted2.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted2.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph_sorted Pages: 1 -->
-<svg width="217pt" height="203pt"
- viewBox="0.00 0.00 216.61 202.59" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(104.28 101.294)">
+<svg width="401pt" height="392pt"
+ viewBox="0.00 0.00 400.82 391.53" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 387.53)">
 <title>graph_sorted</title>
-<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"/>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"/>
 </g>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"/>
 </g>
 <!-- 7 -->
-<g id="node1" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node1" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 1 -->
-<g id="node2" class="node"><title>1</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node2" class="node">
+<title>1</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node3" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node3" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node4" class="node"><title>3</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node4" class="node">
+<title>3</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node5" class="node"><title>4</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="-79.294" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node5" class="node">
+<title>4</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-365.53" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="-63.5907" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-331.11" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"/>
-<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="365.82" cy="-191.76" rx="27" ry="18"/>
+<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted3 b/test/expected_files/test_vc_multiple_and_join/graph_sorted3
index 3b7d32e..ab397ea 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted3
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted3
@@ -1,13 +1,13 @@
 strict graph graph_sorted {
 	graph [K=2 fontsize=18 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	7 [pos="2.097100,0.468120!"]
-	1 [pos="1.141400,0.250000!"]
-	2 [pos="0.375000,0.861170!"]
-	3 [pos="0.375000,1.841400!"]
-	4 [pos="1.141400,2.452600!"]
-	5 [pos="2.097100,2.234500!"]
-	6 [pos="2.522400,1.351300!"]
+	7 [pos="4.592900,0.784260!"]
+	1 [pos="2.252100,0.250000!"]
+	2 [pos="0.375000,1.747000!"]
+	3 [pos="0.375000,4.147900!"]
+	4 [pos="2.252100,5.644900!"]
+	5 [pos="4.592900,5.110600!"]
+	6 [pos="5.634600,2.947400!"]
 	1 -- 2
 	3 -- 4
 	2 -- 7
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted3.svg b/test/expected_files/test_vc_multiple_and_join/graph_sorted3.svg
index 70ff87a..935c43d 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted3.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted3.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph_sorted Pages: 1 -->
-<svg width="217pt" height="203pt"
- viewBox="0.00 0.00 216.61 202.59" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(104.28 101.294)">
+<svg width="401pt" height="392pt"
+ viewBox="0.00 0.00 400.82 391.53" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 387.53)">
 <title>graph_sorted</title>
-<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"/>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"/>
 </g>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"/>
 </g>
 <!-- 7 -->
-<g id="node1" class="node"><title>7</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="63.5891" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node1" class="node">
+<title>7</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-52.42" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 1 -->
-<g id="node2" class="node"><title>1</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node2" class="node">
+<title>1</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node3" class="node"><title>2</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="35.2894" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node3" class="node">
+<title>2</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-114.44" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node4" class="node"><title>3</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node4" class="node">
+<title>3</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-269.1" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node5" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node5" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"/>
-<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"/>
+<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted4 b/test/expected_files/test_vc_multiple_and_join/graph_sorted4
index 2c39ccb..70f8b9a 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted4
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted4
@@ -1,13 +1,13 @@
 strict graph graph_sorted {
 	graph [K=2 fontsize=18 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	7 [pos="2.097100,0.468120!"]
-	1 [pos="1.141400,0.250000!"]
-	2 [pos="0.375000,0.861170!"]
-	3 [pos="0.375000,1.841400!"]
-	4 [pos="1.141400,2.452600!"]
-	5 [pos="2.097100,2.234500!"]
-	6 [pos="2.522400,1.351300!"]
+	7 [pos="4.592900,0.784260!"]
+	1 [pos="2.252100,0.250000!"]
+	2 [pos="0.375000,1.747000!"]
+	3 [pos="0.375000,4.147900!"]
+	4 [pos="2.252100,5.644900!"]
+	5 [pos="4.592900,5.110600!"]
+	6 [pos="5.634600,2.947400!"]
 	1 -- 2
 	3 -- 4
 	2 -- 7
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted4.svg b/test/expected_files/test_vc_multiple_and_join/graph_sorted4.svg
index e0feb09..4604411 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted4.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted4.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph_sorted Pages: 1 -->
-<svg width="217pt" height="203pt"
- viewBox="0.00 0.00 216.61 202.59" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(104.28 101.294)">
+<svg width="401pt" height="392pt"
+ viewBox="0.00 0.00 400.82 391.53" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 387.53)">
 <title>graph_sorted</title>
-<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"/>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"/>
 </g>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="black" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="black" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"/>
 </g>
 <!-- 7 -->
-<g id="node1" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node1" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 1 -->
-<g id="node2" class="node"><title>1</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node2" class="node">
+<title>1</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node3" class="node"><title>2</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="35.2894" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node3" class="node">
+<title>2</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-114.44" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node4" class="node"><title>3</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node4" class="node">
+<title>3</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node5" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node5" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="-63.5907" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-331.11" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"/>
-<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"/>
+<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted5 b/test/expected_files/test_vc_multiple_and_join/graph_sorted5
index 49751a1..a780f61 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted5
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted5
@@ -1,13 +1,13 @@
 strict graph graph_sorted {
 	graph [K=2 fontsize=18 outputorder=edgesfirst overlap=false]
 	node [fillcolor=white fontcolor=black penwidth=2.2 style=filled]
-	7 [pos="2.097100,0.468120!"]
-	1 [pos="1.141400,0.250000!"]
-	2 [pos="0.375000,0.861170!"]
-	3 [pos="0.375000,1.841400!"]
-	4 [pos="1.141400,2.452600!"]
-	5 [pos="2.097100,2.234500!"]
-	6 [pos="2.522400,1.351300!"]
+	7 [pos="4.592900,0.784260!"]
+	1 [pos="2.252100,0.250000!"]
+	2 [pos="0.375000,1.747000!"]
+	3 [pos="0.375000,4.147900!"]
+	4 [pos="2.252100,5.644900!"]
+	5 [pos="4.592900,5.110600!"]
+	6 [pos="5.634600,2.947400!"]
 	1 -- 2
 	3 -- 4
 	2 -- 7
diff --git a/test/expected_files/test_vc_multiple_and_join/graph_sorted5.svg b/test/expected_files/test_vc_multiple_and_join/graph_sorted5.svg
index 144fc9b..9db0ad9 100644
--- a/test/expected_files/test_vc_multiple_and_join/graph_sorted5.svg
+++ b/test/expected_files/test_vc_multiple_and_join/graph_sorted5.svg
@@ -1,96 +1,115 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN"
  "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd">
-<!-- Generated by graphviz version 2.38.0 (20140413.2041)
+<!-- Generated by graphviz version 12.2.1 (20241206.2353)
  -->
 <!-- Title: graph_sorted Pages: 1 -->
-<svg width="217pt" height="203pt"
- viewBox="0.00 0.00 216.61 202.59" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
-<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(104.28 101.294)">
+<svg width="401pt" height="392pt"
+ viewBox="0.00 0.00 400.82 391.53" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
+<g id="graph0" class="graph" transform="scale(1 1) rotate(0) translate(4 387.53)">
 <title>graph_sorted</title>
-<polygon fill="white" stroke="none" points="-104.28,101.294 -104.28,-101.294 112.334,-101.294 112.334,101.294 -104.28,101.294"/>
+<polygon fill="white" stroke="none" points="-4,4 -4,-387.53 396.82,-387.53 396.82,4 -4,4"/>
 <!-- 1&#45;&#45;7 -->
-<g id="edge9" class="edge"><title>1&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M7.52374,73.4459C13.1789,72.1553 19.1734,70.7871 24.8384,69.4942"/>
+<g id="edge9" class="edge">
+<title>1&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M174.19,-23.99C201.69,-30.27 244.66,-40.08 272.24,-46.37"/>
 </g>
 <!-- 1&#45;&#45;2 -->
-<g id="edge1" class="edge"><title>1&#45;&#45;2</title>
-<path fill="none" stroke="black" d="M-35.5584,65.3705C-41.9997,60.2339 -49.2964,54.4151 -55.7444,49.2731"/>
+<g id="edge1" class="edge">
+<title>1&#45;&#45;2</title>
+<path fill="none" stroke="black" d="M129.82,-32.44C106.89,-50.72 67.63,-82.03 44.83,-100.21"/>
 </g>
 <!-- 1&#45;&#45;3 -->
-<g id="edge12" class="edge"><title>1&#45;&#45;3</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-26.4796,61.8914C-36.9115,40.23 -54.6167,3.46571 -65.0009,-18.0967"/>
+<g id="edge12" class="edge">
+<title>1&#45;&#45;3</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M139.22,-36.06C116.91,-82.39 57.84,-205.05 35.62,-251.2"/>
 </g>
 <!-- 1&#45;&#45;4 -->
-<g id="edge5" class="edge"><title>1&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-18.0988,61.1018C-18.0988,30.6734 -18.0988,-30.214 -18.0988,-60.8256"/>
+<g id="edge5" class="edge">
+<title>1&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M147.92,-36.93C147.92,-97.56 147.92,-286.45 147.92,-346.8"/>
 </g>
 <!-- 1&#45;&#45;5 -->
-<g id="edge4" class="edge"><title>1&#45;&#45;5</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-9.79864,62.0586C3.42708,34.5955 29.138,-18.7929 42.3822,-46.2944"/>
+<g id="edge4" class="edge">
+<title>1&#45;&#45;5</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M156.46,-35.73C182.94,-90.71 263.47,-257.94 290.08,-313.19"/>
 </g>
 <!-- 1&#45;&#45;6 -->
-<g id="edge11" class="edge"><title>1&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M-0.779014,65.4818C17.3599,51.0167 45.6893,28.4249 63.8786,13.9196"/>
+<g id="edge11" class="edge">
+<title>1&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M165.75,-32.22C206.61,-64.8 306.64,-144.57 347.74,-177.35"/>
 </g>
 <!-- 2&#45;&#45;7 -->
-<g id="edge3" class="edge"><title>2&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M-47.5887,41.1531C-26.3086,46.01 3.78266,52.878 25.0536,57.7329"/>
+<g id="edge3" class="edge">
+<title>2&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M53.05,-108.49C104.86,-96.66 220.28,-70.32 272.34,-58.44"/>
 </g>
 <!-- 2&#45;&#45;3 -->
-<g id="edge6" class="edge"><title>2&#45;&#45;3</title>
-<path fill="none" stroke="black" d="M-73.2798,17.1141C-73.2798,6.6584 -73.2798,-6.44199 -73.2798,-16.9284"/>
+<g id="edge6" class="edge">
+<title>2&#45;&#45;3</title>
+<path fill="none" stroke="black" d="M27,-133.4C27,-163.25 27,-220.82 27,-250.46"/>
 </g>
 <!-- 3&#45;&#45;4 -->
-<g id="edge2" class="edge"><title>3&#45;&#45;4</title>
-<path fill="none" stroke="black" d="M-55.8202,-49.2114C-49.3789,-54.3483 -42.0822,-60.1674 -35.6342,-65.3096"/>
+<g id="edge2" class="edge">
+<title>3&#45;&#45;4</title>
+<path fill="none" stroke="black" d="M45.1,-283.54C68.03,-301.82 107.29,-333.13 130.09,-351.31"/>
 </g>
 <!-- 4&#45;&#45;5 -->
-<g id="edge8" class="edge"><title>4&#45;&#45;5</title>
-<path fill="none" stroke="black" d="M7.52374,-73.4467C13.1789,-72.1561 19.1734,-70.7881 24.8384,-69.4953"/>
+<g id="edge8" class="edge">
+<title>4&#45;&#45;5</title>
+<path fill="none" stroke="black" d="M174.19,-359.54C201.69,-353.26 244.66,-343.45 272.24,-337.16"/>
 </g>
 <!-- 5&#45;&#45;6 -->
-<g id="edge10" class="edge"><title>5&#45;&#45;6</title>
-<path fill="none" stroke="red" stroke-width="2.2" d="M59.0794,-46.2143C63.4001,-37.2416 68.6569,-26.3252 72.9762,-17.3555"/>
+<g id="edge10" class="edge">
+<title>5&#45;&#45;6</title>
+<path fill="none" stroke="red" stroke-width="2.2" d="M307.35,-313.18C320.23,-286.43 344.35,-236.34 357.22,-209.63"/>
 </g>
 <!-- 6&#45;&#45;7 -->
-<g id="edge7" class="edge"><title>6&#45;&#45;7</title>
-<path fill="none" stroke="black" d="M72.966,17.3759C68.6453,26.3484 63.3885,37.2646 59.0692,46.2341"/>
+<g id="edge7" class="edge">
+<title>6&#45;&#45;7</title>
+<path fill="none" stroke="black" d="M357.18,-173.83C344.3,-147.08 320.18,-97 307.31,-70.28"/>
 </g>
 <!-- 7 -->
-<g id="node1" class="node"><title>7</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="50.7118" cy="63.5891" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="67.2891" font-family="Times New Roman,serif" font-size="14.00">7</text>
+<g id="node1" class="node">
+<title>7</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="298.71" cy="-52.42" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-47.37" font-family="Times New Roman,serif" font-size="14.00">7</text>
 </g>
 <!-- 1 -->
-<g id="node2" class="node"><title>1</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-18.0988" cy="79.2938" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="82.9938" font-family="Times New Roman,serif" font-size="14.00">1</text>
+<g id="node2" class="node">
+<title>1</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="147.92" cy="-18" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-12.95" font-family="Times New Roman,serif" font-size="14.00">1</text>
 </g>
 <!-- 2 -->
-<g id="node3" class="node"><title>2</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-73.2798" cy="35.2894" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="38.9894" font-family="Times New Roman,serif" font-size="14.00">2</text>
+<g id="node3" class="node">
+<title>2</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="27" cy="-114.44" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-109.39" font-family="Times New Roman,serif" font-size="14.00">2</text>
 </g>
 <!-- 3 -->
-<g id="node4" class="node"><title>3</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="-73.2798" cy="-35.2874" rx="27" ry="18"/>
-<text text-anchor="middle" x="-73.2798" y="-31.5874" font-family="Times New Roman,serif" font-size="14.00">3</text>
+<g id="node4" class="node">
+<title>3</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="27" cy="-269.1" rx="27" ry="18"/>
+<text text-anchor="middle" x="27" y="-264.05" font-family="Times New Roman,serif" font-size="14.00">3</text>
 </g>
 <!-- 4 -->
-<g id="node5" class="node"><title>4</title>
-<ellipse fill="white" stroke="black" stroke-width="2.2" cx="-18.0988" cy="-79.294" rx="27" ry="18"/>
-<text text-anchor="middle" x="-18.0988" y="-75.594" font-family="Times New Roman,serif" font-size="14.00">4</text>
+<g id="node5" class="node">
+<title>4</title>
+<ellipse fill="white" stroke="black" stroke-width="2.2" cx="147.92" cy="-365.53" rx="27" ry="18"/>
+<text text-anchor="middle" x="147.92" y="-360.48" font-family="Times New Roman,serif" font-size="14.00">4</text>
 </g>
 <!-- 5 -->
-<g id="node6" class="node"><title>5</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="50.7118" cy="-63.5907" rx="27" ry="18"/>
-<text text-anchor="middle" x="50.7118" y="-59.8907" font-family="Times New Roman,serif" font-size="14.00">5</text>
+<g id="node6" class="node">
+<title>5</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="298.71" cy="-331.11" rx="27" ry="18"/>
+<text text-anchor="middle" x="298.71" y="-326.06" font-family="Times New Roman,serif" font-size="14.00">5</text>
 </g>
 <!-- 6 -->
-<g id="node7" class="node"><title>6</title>
-<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="81.3336" cy="-0.000102858" rx="27" ry="18"/>
-<text text-anchor="middle" x="81.3336" y="3.6999" font-family="Times New Roman,serif" font-size="14.00">6</text>
+<g id="node7" class="node">
+<title>6</title>
+<ellipse fill="blue" stroke="black" stroke-width="2.2" stroke-dasharray="5,2" cx="365.82" cy="-191.76" rx="27" ry="18"/>
+<text text-anchor="middle" x="365.82" y="-186.71" font-family="Times New Roman,serif" font-size="14.00">6</text>
 </g>
 </g>
 </svg>
diff --git a/test/test_construct_dpdb.py b/test/test_construct_dpdb.py
index 2e991de..6bfd653 100644
--- a/test/test_construct_dpdb.py
+++ b/test/test_construct_dpdb.py
@@ -23,8 +23,9 @@
 
 import datetime
 from pathlib import Path
+from unittest.mock import PropertyMock
 
-import psycopg2 as pg
+import psycopg as pg
 
 from tdvisu import construct_dpdb_visu as module
 from tdvisu.construct_dpdb_visu import (
@@ -35,48 +36,52 @@
     IDpdbVisuConstruct,
     db_config,
     main,
-    read_cfg)
+    read_cfg,
+)
 
 DIR = Path(__file__).parent
-SECTION = 'postgresql'
+SECTION = "postgresql"
 
 
 def test_db_config():
     """Test reading the database configuration from the test file."""
-    result = read_cfg(DIR / 'database.ini', SECTION, True)
-    assert result == {'application_name': 'dpdb-admin',
-                      'host': 'localhost',
-                      'password': 'XXX',
-                      'port': '123',
-                      'user': 'postgres'
-                      }, "should be able to read from ini file"
-
-    result = db_config(DIR / 'database.ini', SECTION)
-    assert result == {'application_name': 'dpdb-admin',
-                      'database': DEFAULT_DBCONFIG['database'],
-                      'host': 'localhost',
-                      'password': 'XXX',
-                      'port': '123',
-                      'user': 'postgres'
-                      }, "should complete 'database' with default."
+    result = read_cfg(DIR / "database.ini", SECTION, True)
+    assert result == {
+        "application_name": "dpdb-admin",
+        "host": "localhost",
+        "password": "XXX",
+        "port": "123",
+        "user": "postgres",
+    }, "should be able to read from ini file"
+
+    result = db_config(DIR / "database.ini", SECTION)
+    assert result == {
+        "application_name": "dpdb-admin",
+        "database": DEFAULT_DBCONFIG["database"],
+        "host": "localhost",
+        "password": "XXX",
+        "port": "123",
+        "user": "postgres",
+    }, "should complete 'database' with default."
 
 
 def test_db2_config():
     """Test should use defaults when file not found."""
-    fixed_defaults = db_config(DIR / 'database2.ini', SECTION)
+    fixed_defaults = db_config(DIR / "database2.ini", SECTION)
     assert fixed_defaults == DEFAULT_DBCONFIG
 
 
 def test_db_passwd_config():
     """Test should add password from file to defaults."""
-    insert_passwd = db_config(DIR / 'db_password.ini', SECTION)
-    assert insert_passwd == {'application_name': 'dpdb-admin',
-                             'database': 'logicsem',
-                             'host': 'localhost',
-                             'password': 'XXX',
-                             'port': 5432,
-                             'user': 'postgres'
-                             }
+    insert_passwd = db_config(DIR / "db_password.ini", SECTION)
+    assert insert_passwd == {
+        "application_name": "dpdb-admin",
+        "database": "logicsem",
+        "host": "localhost",
+        "password": "XXX",
+        "port": 5432,
+        "user": "postgres",
+    }
 
 
 def test_problem_interface():
@@ -89,64 +94,76 @@ def test_problem_interface():
 def test_main(mocker, tmp_path):
     """Test behaviour of construct_dpdb_visu.main"""
 
-    mock_connect = mocker.patch('tdvisu.construct_dpdb_visu.pg.connect')
-    ta_status = mock_connect.return_value.__enter__.return_value.get_transaction_status
-    ta_status.return_value = pg.extensions.TRANSACTION_STATUS_IDLE
+    mock_connect = mocker.patch("tdvisu.construct_dpdb_visu.pg.connect")
+    mock_status = mocker.patch(
+        "tdvisu.construct_dpdb_visu.pg.connect.return_value.__enter__.return_value.info"
+    )
+    type(mock_status).status = PropertyMock(
+        side_effect=[pg.pq.ConnStatus.BAD, pg.pq.ConnStatus.OK]
+    )
 
     query_problem = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_problem',
-        return_value='Sat')
-    query_num_vars = mocker.patch('tdvisu.construct_dpdb_visu.query_num_vars',
-                                  return_value=8)
+        "tdvisu.construct_dpdb_visu.query_problem", return_value="Sat"
+    )
+    query_num_vars = mocker.patch(
+        "tdvisu.construct_dpdb_visu.query_num_vars", return_value=8
+    )
     query_td_node_status_ordered = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_td_node_status_ordered',
-        return_value=[(3,), (5,), (4,), (2,), (1,)])
+        "tdvisu.construct_dpdb_visu.query_td_node_status_ordered",
+        return_value=[(3,), (5,), (4,), (2,), (1,)],
+    )
     query_sat_clause = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_sat_clause',
-        return_value=[(True, None, None, True, None, True, None, None, None, None),
-                      (True, None, None, None, False,
-                       None, None, None, None, None),
-                      (False, None, None, None, None,
-                       None, True, None, None, None),
-                      (None, True, True, None, None, None, None, None, None, None),
-                      (None, True, None, None, True, None, None, None, None, None),
-                      (None, True, None, None, None,
-                       False, None, None, None, None),
-                      (None, None, True, None, None,
-                       None, None, False, None, None),
-                      (None, None, None, True, None,
-                       None, None, False, None, None),
-                      (None, None, None, False, None,
-                       True, None, None, None, None),
-                      (None, None, None, False, None, None, True, None, None, None)])
+        "tdvisu.construct_dpdb_visu.query_sat_clause",
+        return_value=[
+            (True, None, None, True, None, True, None, None, None, None),
+            (True, None, None, None, False, None, None, None, None, None),
+            (False, None, None, None, None, None, True, None, None, None),
+            (None, True, True, None, None, None, None, None, None, None),
+            (None, True, None, None, True, None, None, None, None, None),
+            (None, True, None, None, None, False, None, None, None, None),
+            (None, None, True, None, None, None, None, False, None, None),
+            (None, None, None, True, None, None, None, False, None, None),
+            (None, None, None, False, None, True, None, None, None, None),
+            (None, None, None, False, None, None, True, None, None, None),
+        ],
+    )
 
     query_td_bag_grouped = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_td_bag_grouped', return_value=[[1, 2, 3, 4, 5]])
+        "tdvisu.construct_dpdb_visu.query_td_bag_grouped",
+        return_value=[[1, 2, 3, 4, 5]],
+    )
     query_td_node_status = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_td_node_status',
+        "tdvisu.construct_dpdb_visu.query_td_node_status",
         return_value=(
             "2020-07-13 02:06:18.053880",
-            datetime.timedelta(
-                microseconds=768)))
-    query_td_bag = mocker.patch('tdvisu.construct_dpdb_visu.query_td_bag',
-                                return_value=[(1,), (2,), (4,), (6,)])
+            datetime.timedelta(microseconds=768),
+        ),
+    )
+    query_td_bag = mocker.patch(
+        "tdvisu.construct_dpdb_visu.query_td_bag", return_value=[(1,), (2,), (4,), (6,)]
+    )
     query_column_name = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_column_name', return_value=[
-            ('v1',), ('v2',), ('v4',), ('v6',)])
+        "tdvisu.construct_dpdb_visu.query_column_name",
+        return_value=[("v1",), ("v2",), ("v4",), ("v6",)],
+    )
     query_bag = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_bag',
-        return_value=[(False, None, False, None),
-                      (True, None, True, None),
-                      (False, None, True, None),
-                      (True, None, False, None)])
+        "tdvisu.construct_dpdb_visu.query_bag",
+        return_value=[
+            (False, None, False, None),
+            (True, None, True, None),
+            (False, None, True, None),
+            (True, None, False, None),
+        ],
+    )
 
     query_edgearray = mocker.patch(
-        'tdvisu.construct_dpdb_visu.query_edgearray', return_value=[
-            (2, 1), (3, 2), (4, 2), (5, 4)])
+        "tdvisu.construct_dpdb_visu.query_edgearray",
+        return_value=[(2, 1), (3, 2), (4, 2), (5, 4)],
+    )
     # set cmd-arguments
-    outfile = str(tmp_path / 'test_main.json')
+    outfile = str(tmp_path / "test_main.json")
     # one mocked run
-    main(['1', '--outfile', outfile])
+    main(["1", "--outfile", outfile])
 
     # Assertions
     mock_connect.assert_called_once()
@@ -166,7 +183,7 @@ def test_init(mocker):
     """Test that main is called correctly if called as __main__."""
     expected = -1000
     main = mocker.patch.object(module, "main", return_value=expected)
-    mock_exit = mocker.patch.object(module.sys, 'exit')
+    mock_exit = mocker.patch.object(module.sys, "exit")
     mocker.patch.object(module, "__name__", "__main__")
     module.init()
 
diff --git a/test/test_reader.py b/test/test_reader.py
index 50bb064..fb7934f 100644
--- a/test/test_reader.py
+++ b/test/test_reader.py
@@ -21,7 +21,6 @@
 
 """
 import logging
-
 from pathlib import Path
 
 import pytest
@@ -31,7 +30,7 @@
 
 def test_reader_valid_input():
     """Create and test the reader on valid input from a file."""
-    twfile = Path(__file__).parent / 'grda16.tw'
+    twfile = Path(__file__).parent / "grda16.tw"
     # from filename
     reader = TwReader.from_filename(twfile)
     _reader_assertions(reader)
@@ -51,7 +50,7 @@ def test_reader_valid_input():
 
 def test_reader_commented_body():
     """Create and test the reader on valid input from a file with comments in the body."""
-    twfile = Path(__file__).parent / 'grda16_comments.tw'
+    twfile = Path(__file__).parent / "grda16_comments.tw"
     # from filename
     reader = TwReader.from_filename(twfile)
     _reader_assertions(reader)
@@ -77,7 +76,7 @@ def test_dimacsreader_has_body():
 
 def test_reader_inval_preamble(caplog):
     """Test message when a unexpected token in the preamble was encountered."""
-    twfile = Path(__file__).parent / 'grda16.tw'
+    twfile = Path(__file__).parent / "grda16.tw"
     # from string
     with open(twfile) as file:
         content = "invalid preamble\n" + file.read()
@@ -86,7 +85,8 @@ def test_reader_inval_preamble(caplog):
         assert (
             "reader.py",
             logging.WARN,
-            "Invalid content in preamble at line 0: invalid preamble") in caplog.record_tuples
+            "Invalid content in preamble at line 0: invalid preamble",
+        ) in caplog.record_tuples
 
 
 def test_reader_no_type_found(caplog):
@@ -94,9 +94,11 @@ def test_reader_no_type_found(caplog):
     content = "c no preamble\n"
     with pytest.raises(SystemExit) as pytest_wrapped_e:
         TwReader.from_string(content)  # should raise SystemExit
-        assert ("reader.py",
-                logging.ERROR,
-                "No type found in DIMACS file!") in caplog.record_tuples
+        assert (
+            "reader.py",
+            logging.ERROR,
+            "No type found in DIMACS file!",
+        ) in caplog.record_tuples
         assert pytest_wrapped_e.type == SystemExit
         assert pytest_wrapped_e.value.code == 1
 
@@ -106,26 +108,26 @@ def test_dimacs_wrong_type_found(caplog):
     content = "p wrong 16 31\n1 2\n2 1\n"
     with pytest.raises(SystemExit) as pytest_wrapped_e:
         TwReader.from_string(content)  # should raise SystemExit
-        assert ("reader.py",
-                logging.ERROR,
-                "Not a tw file!") in caplog.record_tuples
+        assert ("reader.py", logging.ERROR, "Not a tw file!") in caplog.record_tuples
         assert pytest_wrapped_e.type == SystemExit
         assert pytest_wrapped_e.value.code == 1
 
 
 def test_dimacs_col_long_line(caplog):
     """Test message when long line was read in the body."""
-    colfile = Path(__file__).parent / 'col_with_long_line.col'
+    colfile = Path(__file__).parent / "col_with_long_line.col"
 
     TwReader.from_filename(colfile)  # should raise SystemExit
     assert (
         "reader.py",
         logging.WARN,
-        "Expected exactly 2 vertices at line 1, but 3 found") in caplog.record_tuples
+        "Expected exactly 2 vertices at line 1, but 3 found",
+    ) in caplog.record_tuples
     assert (
         "reader.py",
         logging.WARN,
-        "Expected exactly 2 vertices at line 1, but 3 found") in caplog.record_tuples
+        "Expected exactly 2 vertices at line 1, but 3 found",
+    ) in caplog.record_tuples
 
 
 def test_dimacs_fewer_edges(caplog):
@@ -135,7 +137,8 @@ def test_dimacs_fewer_edges(caplog):
     assert (
         "reader.py",
         logging.WARN,
-        "Number of edges mismatch preamble (2 vs 3)") in caplog.record_tuples
+        "Number of edges mismatch preamble (2 vs 3)",
+    ) in caplog.record_tuples
     assert reader.num_vertices == 3
     assert reader.num_edges == 3
     assert len(reader.edges) == 2
@@ -146,18 +149,63 @@ def _reader_assertions(reader: TwReader):
     as well as the number of vertices and number of edges.
     """
 
-    expected_edges = {(1, 2), (2, 1), (2, 3), (3, 2), (3, 4), (3, 5),
-                      (4, 3), (4, 5), (4, 6), (5, 3), (5, 4), (6, 4),
-                      (6, 7), (6, 15), (7, 6), (7, 8), (7, 14), (8, 7),
-                      (8, 9), (9, 8), (9, 10), (9, 11), (10, 9),
-                      (11, 9), (11, 12), (11, 14), (12, 11), (12, 13),
-                      (12, 14), (13, 12), (14, 7), (14, 11), (14, 12),
-                      (15, 6), (15, 16), (16, 15)}
-
-    expected_adj = {1: {2}, 2: {1, 3}, 3: {2, 4, 5}, 4: {3, 5, 6},
-                    5: {3, 4}, 6: {4, 7, 15}, 7: {6, 8, 14}, 8: {7, 9},
-                    9: {8, 10, 11}, 10: {9}, 11: {9, 12, 14}, 12: {11, 13, 14},
-                    13: {12}, 14: {7, 11, 12}, 15: {6, 16}, 16: {15}}
+    expected_edges = {
+        (1, 2),
+        (2, 1),
+        (2, 3),
+        (3, 2),
+        (3, 4),
+        (3, 5),
+        (4, 3),
+        (4, 5),
+        (4, 6),
+        (5, 3),
+        (5, 4),
+        (6, 4),
+        (6, 7),
+        (6, 15),
+        (7, 6),
+        (7, 8),
+        (7, 14),
+        (8, 7),
+        (8, 9),
+        (9, 8),
+        (9, 10),
+        (9, 11),
+        (10, 9),
+        (11, 9),
+        (11, 12),
+        (11, 14),
+        (12, 11),
+        (12, 13),
+        (12, 14),
+        (13, 12),
+        (14, 7),
+        (14, 11),
+        (14, 12),
+        (15, 6),
+        (15, 16),
+        (16, 15),
+    }
+
+    expected_adj = {
+        1: {2},
+        2: {1, 3},
+        3: {2, 4, 5},
+        4: {3, 5, 6},
+        5: {3, 4},
+        6: {4, 7, 15},
+        7: {6, 8, 14},
+        8: {7, 9},
+        9: {8, 10, 11},
+        10: {9},
+        11: {9, 12, 14},
+        12: {11, 13, 14},
+        13: {12},
+        14: {7, 11, 12},
+        15: {6, 16},
+        16: {15},
+    }
 
     assert reader.num_vertices == 16
     assert reader.num_edges == 36