/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

After renaming modulo { a->0, b->1 }, 
it remains to prove termination of the 4-rule system
{ 0 1 1 1 -> 1 1 1 1 ,
  1 1 1 0 -> 1 0 1 0 ,
  1 1 0 0 -> 1 0 1 0 ,
  0 0 0 1 -> 0 1 0 0 }


The system was reversed.

After renaming modulo { 1->0, 0->1 }, 
it remains to prove termination of the 4-rule system
{ 0 0 0 1 -> 0 0 0 0 ,
  1 0 0 0 -> 1 0 1 0 ,
  1 1 0 0 -> 1 0 1 0 ,
  0 1 1 1 -> 1 1 0 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /

After renaming modulo { 0->0, 1->1 }, 
it remains to prove termination of the 3-rule system
{ 0 0 0 1 -> 0 0 0 0 ,
  1 0 0 0 -> 1 0 1 0 ,
  0 1 1 1 -> 1 1 0 1 }


Applying sparse tiling TRFC(2) [Geser/Hofbauer/Waldmann, FSCD 2019].

After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (1,1)->3, (1,3)->4, (0,3)->5, (2,0)->6, (2,1)->7 },
it remains to prove termination of the 27-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  0 0 0 1 3 -> 0 0 0 0 1 ,
  0 0 0 1 4 -> 0 0 0 0 5 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  2 0 0 1 3 -> 2 0 0 0 1 ,
  2 0 0 1 4 -> 2 0 0 0 5 ,
  6 0 0 1 2 -> 6 0 0 0 0 ,
  6 0 0 1 3 -> 6 0 0 0 1 ,
  6 0 0 1 4 -> 6 0 0 0 5 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 5 -> 1 2 1 2 5 ,
  3 2 0 0 0 -> 3 2 1 2 0 ,
  3 2 0 0 1 -> 3 2 1 2 1 ,
  3 2 0 0 5 -> 3 2 1 2 5 ,
  7 2 0 0 0 -> 7 2 1 2 0 ,
  7 2 0 0 1 -> 7 2 1 2 1 ,
  7 2 0 0 5 -> 7 2 1 2 5 ,
  0 1 3 3 2 -> 1 3 2 1 2 ,
  0 1 3 3 3 -> 1 3 2 1 3 ,
  0 1 3 3 4 -> 1 3 2 1 4 ,
  2 1 3 3 2 -> 3 3 2 1 2 ,
  2 1 3 3 3 -> 3 3 2 1 3 ,
  2 1 3 3 4 -> 3 3 2 1 4 ,
  6 1 3 3 2 -> 7 3 2 1 2 ,
  6 1 3 3 3 -> 7 3 2 1 3 ,
  6 1 3 3 4 -> 7 3 2 1 4 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 6->4, 5->5, 7->6, 4->7 }, 
it remains to prove termination of the 21-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  0 0 0 1 3 -> 0 0 0 0 1 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  2 0 0 1 3 -> 2 0 0 0 1 ,
  4 0 0 1 2 -> 4 0 0 0 0 ,
  4 0 0 1 3 -> 4 0 0 0 1 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 5 -> 1 2 1 2 5 ,
  3 2 0 0 0 -> 3 2 1 2 0 ,
  3 2 0 0 1 -> 3 2 1 2 1 ,
  3 2 0 0 5 -> 3 2 1 2 5 ,
  6 2 0 0 0 -> 6 2 1 2 0 ,
  6 2 0 0 1 -> 6 2 1 2 1 ,
  6 2 0 0 5 -> 6 2 1 2 5 ,
  0 1 3 3 2 -> 1 3 2 1 2 ,
  0 1 3 3 3 -> 1 3 2 1 3 ,
  0 1 3 3 7 -> 1 3 2 1 7 ,
  2 1 3 3 2 -> 3 3 2 1 2 ,
  2 1 3 3 3 -> 3 3 2 1 3 ,
  2 1 3 3 7 -> 3 3 2 1 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 4->3, 5->4, 3->5, 6->6, 7->7 }, 
it remains to prove termination of the 15-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  3 0 0 1 2 -> 3 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 4 -> 1 2 1 2 4 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  5 2 0 0 1 -> 5 2 1 2 1 ,
  5 2 0 0 4 -> 5 2 1 2 4 ,
  6 2 0 0 0 -> 6 2 1 2 0 ,
  6 2 0 0 1 -> 6 2 1 2 1 ,
  6 2 0 0 4 -> 6 2 1 2 4 ,
  2 1 5 5 2 -> 5 5 2 1 2 ,
  2 1 5 5 5 -> 5 5 2 1 5 ,
  2 1 5 5 7 -> 5 5 2 1 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 4->3, 5->4, 6->5, 7->6 }, 
it remains to prove termination of the 14-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 3 -> 1 2 1 2 3 ,
  4 2 0 0 0 -> 4 2 1 2 0 ,
  4 2 0 0 1 -> 4 2 1 2 1 ,
  4 2 0 0 3 -> 4 2 1 2 3 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  5 2 0 0 1 -> 5 2 1 2 1 ,
  5 2 0 0 3 -> 5 2 1 2 3 ,
  2 1 4 4 2 -> 4 4 2 1 2 ,
  2 1 4 4 4 -> 4 4 2 1 4 ,
  2 1 4 4 6 -> 4 4 2 1 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 13-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 3 -> 1 2 1 2 3 ,
  4 2 0 0 0 -> 4 2 1 2 0 ,
  4 2 0 0 3 -> 4 2 1 2 3 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  5 2 0 0 1 -> 5 2 1 2 1 ,
  5 2 0 0 3 -> 5 2 1 2 3 ,
  2 1 4 4 2 -> 4 4 2 1 2 ,
  2 1 4 4 4 -> 4 4 2 1 4 ,
  2 1 4 4 6 -> 4 4 2 1 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 12-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 3 -> 1 2 1 2 3 ,
  4 2 0 0 0 -> 4 2 1 2 0 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  5 2 0 0 1 -> 5 2 1 2 1 ,
  5 2 0 0 3 -> 5 2 1 2 3 ,
  2 1 4 4 2 -> 4 4 2 1 2 ,
  2 1 4 4 4 -> 4 4 2 1 4 ,
  2 1 4 4 6 -> 4 4 2 1 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 11-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 3 -> 1 2 1 2 3 ,
  4 2 0 0 0 -> 4 2 1 2 0 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  5 2 0 0 3 -> 5 2 1 2 3 ,
  2 1 4 4 2 -> 4 4 2 1 2 ,
  2 1 4 4 4 -> 4 4 2 1 4 ,
  2 1 4 4 6 -> 4 4 2 1 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 10-rule system
{ 0 0 0 1 2 -> 0 0 0 0 0 ,
  2 0 0 1 2 -> 2 0 0 0 0 ,
  1 2 0 0 0 -> 1 2 1 2 0 ,
  1 2 0 0 1 -> 1 2 1 2 1 ,
  1 2 0 0 3 -> 1 2 1 2 3 ,
  4 2 0 0 0 -> 4 2 1 2 0 ,
  5 2 0 0 0 -> 5 2 1 2 0 ,
  2 1 4 4 2 -> 4 4 2 1 2 ,
  2 1 4 4 4 -> 4 4 2 1 4 ,
  2 1 4 4 6 -> 4 4 2 1 6 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (2,true)->4, (1,true)->5, (3,false)->6, (4,true)->7, (5,true)->8, (4,false)->9, (6,false)->10, (5,false)->11 },
it remains to prove termination of the 58-rule system
{ 0 1 1 2 3 -> 0 1 1 1 1 ,
  0 1 1 2 3 -> 0 1 1 1 ,
  0 1 1 2 3 -> 0 1 1 ,
  0 1 1 2 3 -> 0 1 ,
  0 1 1 2 3 -> 0 ,
  4 1 1 2 3 -> 4 1 1 1 1 ,
  4 1 1 2 3 -> 0 1 1 1 ,
  4 1 1 2 3 -> 0 1 1 ,
  4 1 1 2 3 -> 0 1 ,
  4 1 1 2 3 -> 0 ,
  5 3 1 1 1 -> 5 3 2 3 1 ,
  5 3 1 1 1 -> 4 2 3 1 ,
  5 3 1 1 1 -> 5 3 1 ,
  5 3 1 1 1 -> 4 1 ,
  5 3 1 1 1 -> 0 ,
  5 3 1 1 2 -> 5 3 2 3 2 ,
  5 3 1 1 2 -> 4 2 3 2 ,
  5 3 1 1 2 -> 5 3 2 ,
  5 3 1 1 2 -> 4 2 ,
  5 3 1 1 2 -> 5 ,
  5 3 1 1 6 -> 5 3 2 3 6 ,
  5 3 1 1 6 -> 4 2 3 6 ,
  5 3 1 1 6 -> 5 3 6 ,
  5 3 1 1 6 -> 4 6 ,
  7 3 1 1 1 -> 7 3 2 3 1 ,
  7 3 1 1 1 -> 4 2 3 1 ,
  7 3 1 1 1 -> 5 3 1 ,
  7 3 1 1 1 -> 4 1 ,
  7 3 1 1 1 -> 0 ,
  8 3 1 1 1 -> 8 3 2 3 1 ,
  8 3 1 1 1 -> 4 2 3 1 ,
  8 3 1 1 1 -> 5 3 1 ,
  8 3 1 1 1 -> 4 1 ,
  8 3 1 1 1 -> 0 ,
  4 2 9 9 3 -> 7 9 3 2 3 ,
  4 2 9 9 3 -> 7 3 2 3 ,
  4 2 9 9 3 -> 4 2 3 ,
  4 2 9 9 3 -> 5 3 ,
  4 2 9 9 3 -> 4 ,
  4 2 9 9 9 -> 7 9 3 2 9 ,
  4 2 9 9 9 -> 7 3 2 9 ,
  4 2 9 9 9 -> 4 2 9 ,
  4 2 9 9 9 -> 5 9 ,
  4 2 9 9 9 -> 7 ,
  4 2 9 9 10 -> 7 9 3 2 10 ,
  4 2 9 9 10 -> 7 3 2 10 ,
  4 2 9 9 10 -> 4 2 10 ,
  4 2 9 9 10 -> 5 10 ,
  1 1 1 2 3 ->= 1 1 1 1 1 ,
  3 1 1 2 3 ->= 3 1 1 1 1 ,
  2 3 1 1 1 ->= 2 3 2 3 1 ,
  2 3 1 1 2 ->= 2 3 2 3 2 ,
  2 3 1 1 6 ->= 2 3 2 3 6 ,
  9 3 1 1 1 ->= 9 3 2 3 1 ,
  11 3 1 1 1 ->= 11 3 2 3 1 ,
  3 2 9 9 3 ->= 9 9 3 2 3 ,
  3 2 9 9 9 ->= 9 9 3 2 9 ,
  3 2 9 9 10 ->= 9 9 3 2 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 20-rule system
{ 0 1 1 2 3 -> 0 1 1 1 1 ,
  4 1 1 2 3 -> 4 1 1 1 1 ,
  5 3 1 1 1 -> 5 3 2 3 1 ,
  5 3 1 1 2 -> 5 3 2 3 2 ,
  5 3 1 1 6 -> 5 3 2 3 6 ,
  7 3 1 1 1 -> 7 3 2 3 1 ,
  8 3 1 1 1 -> 8 3 2 3 1 ,
  4 2 9 9 3 -> 7 9 3 2 3 ,
  4 2 9 9 9 -> 7 9 3 2 9 ,
  4 2 9 9 10 -> 7 9 3 2 10 ,
  1 1 1 2 3 ->= 1 1 1 1 1 ,
  3 1 1 2 3 ->= 3 1 1 1 1 ,
  2 3 1 1 1 ->= 2 3 2 3 1 ,
  2 3 1 1 2 ->= 2 3 2 3 2 ,
  2 3 1 1 6 ->= 2 3 2 3 6 ,
  9 3 1 1 1 ->= 9 3 2 3 1 ,
  11 3 1 1 1 ->= 11 3 2 3 1 ,
  3 2 9 9 3 ->= 9 9 3 2 3 ,
  3 2 9 9 9 ->= 9 9 3 2 9 ,
  3 2 9 9 10 ->= 9 9 3 2 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 2:

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 11->10, 10->11 }, 
it remains to prove termination of the 17-rule system
{ 0 1 1 2 3 -> 0 1 1 1 1 ,
  4 1 1 2 3 -> 4 1 1 1 1 ,
  5 3 1 1 1 -> 5 3 2 3 1 ,
  5 3 1 1 2 -> 5 3 2 3 2 ,
  5 3 1 1 6 -> 5 3 2 3 6 ,
  7 3 1 1 1 -> 7 3 2 3 1 ,
  8 3 1 1 1 -> 8 3 2 3 1 ,
  1 1 1 2 3 ->= 1 1 1 1 1 ,
  3 1 1 2 3 ->= 3 1 1 1 1 ,
  2 3 1 1 1 ->= 2 3 2 3 1 ,
  2 3 1 1 2 ->= 2 3 2 3 2 ,
  2 3 1 1 6 ->= 2 3 2 3 6 ,
  9 3 1 1 1 ->= 9 3 2 3 1 ,
  10 3 1 1 1 ->= 10 3 2 3 1 ,
  3 2 9 9 3 ->= 9 9 3 2 3 ,
  3 2 9 9 9 ->= 9 9 3 2 9 ,
  3 2 9 9 11 ->= 9 9 3 2 11 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
10 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
11 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 4->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 16-rule system
{ 0 1 1 2 3 -> 0 1 1 1 1 ,
  4 3 1 1 1 -> 4 3 2 3 1 ,
  4 3 1 1 2 -> 4 3 2 3 2 ,
  4 3 1 1 5 -> 4 3 2 3 5 ,
  6 3 1 1 1 -> 6 3 2 3 1 ,
  7 3 1 1 1 -> 7 3 2 3 1 ,
  1 1 1 2 3 ->= 1 1 1 1 1 ,
  3 1 1 2 3 ->= 3 1 1 1 1 ,
  2 3 1 1 1 ->= 2 3 2 3 1 ,
  2 3 1 1 2 ->= 2 3 2 3 2 ,
  2 3 1 1 5 ->= 2 3 2 3 5 ,
  8 3 1 1 1 ->= 8 3 2 3 1 ,
  9 3 1 1 1 ->= 9 3 2 3 1 ,
  3 2 8 8 3 ->= 8 8 3 2 3 ,
  3 2 8 8 8 ->= 8 8 3 2 8 ,
  3 2 8 8 10 ->= 8 8 3 2 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
10 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 4->0, 3->1, 1->2, 2->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9 }, 
it remains to prove termination of the 15-rule system
{ 0 1 2 2 2 -> 0 1 3 1 2 ,
  0 1 2 2 3 -> 0 1 3 1 3 ,
  0 1 2 2 4 -> 0 1 3 1 4 ,
  5 1 2 2 2 -> 5 1 3 1 2 ,
  6 1 2 2 2 -> 6 1 3 1 2 ,
  2 2 2 3 1 ->= 2 2 2 2 2 ,
  1 2 2 3 1 ->= 1 2 2 2 2 ,
  3 1 2 2 2 ->= 3 1 3 1 2 ,
  3 1 2 2 3 ->= 3 1 3 1 3 ,
  3 1 2 2 4 ->= 3 1 3 1 4 ,
  7 1 2 2 2 ->= 7 1 3 1 2 ,
  8 1 2 2 2 ->= 8 1 3 1 2 ,
  1 3 7 7 1 ->= 7 7 1 3 1 ,
  1 3 7 7 7 ->= 7 7 1 3 7 ,
  1 3 7 7 9 ->= 7 7 1 3 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, 
it remains to prove termination of the 14-rule system
{ 0 1 2 2 2 -> 0 1 3 1 2 ,
  0 1 2 2 4 -> 0 1 3 1 4 ,
  5 1 2 2 2 -> 5 1 3 1 2 ,
  6 1 2 2 2 -> 6 1 3 1 2 ,
  2 2 2 3 1 ->= 2 2 2 2 2 ,
  1 2 2 3 1 ->= 1 2 2 2 2 ,
  3 1 2 2 2 ->= 3 1 3 1 2 ,
  3 1 2 2 3 ->= 3 1 3 1 3 ,
  3 1 2 2 4 ->= 3 1 3 1 4 ,
  7 1 2 2 2 ->= 7 1 3 1 2 ,
  8 1 2 2 2 ->= 8 1 3 1 2 ,
  1 3 7 7 1 ->= 7 7 1 3 1 ,
  1 3 7 7 7 ->= 7 7 1 3 7 ,
  1 3 7 7 9 ->= 7 7 1 3 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 4->6, 7->7, 8->8, 9->9 }, 
it remains to prove termination of the 13-rule system
{ 0 1 2 2 2 -> 0 1 3 1 2 ,
  4 1 2 2 2 -> 4 1 3 1 2 ,
  5 1 2 2 2 -> 5 1 3 1 2 ,
  2 2 2 3 1 ->= 2 2 2 2 2 ,
  1 2 2 3 1 ->= 1 2 2 2 2 ,
  3 1 2 2 2 ->= 3 1 3 1 2 ,
  3 1 2 2 3 ->= 3 1 3 1 3 ,
  3 1 2 2 6 ->= 3 1 3 1 6 ,
  7 1 2 2 2 ->= 7 1 3 1 2 ,
  8 1 2 2 2 ->= 8 1 3 1 2 ,
  1 3 7 7 1 ->= 7 7 1 3 1 ,
  1 3 7 7 7 ->= 7 7 1 3 7 ,
  1 3 7 7 9 ->= 7 7 1 3 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 4->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 9->8 }, 
it remains to prove termination of the 12-rule system
{ 0 1 2 2 2 -> 0 1 3 1 2 ,
  4 1 2 2 2 -> 4 1 3 1 2 ,
  2 2 2 3 1 ->= 2 2 2 2 2 ,
  1 2 2 3 1 ->= 1 2 2 2 2 ,
  3 1 2 2 2 ->= 3 1 3 1 2 ,
  3 1 2 2 3 ->= 3 1 3 1 3 ,
  3 1 2 2 5 ->= 3 1 3 1 5 ,
  6 1 2 2 2 ->= 6 1 3 1 2 ,
  7 1 2 2 2 ->= 7 1 3 1 2 ,
  1 3 6 6 1 ->= 6 6 1 3 1 ,
  1 3 6 6 6 ->= 6 6 1 3 6 ,
  1 3 6 6 8 ->= 6 6 1 3 8 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 4->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7 }, 
it remains to prove termination of the 11-rule system
{ 0 1 2 2 2 -> 0 1 3 1 2 ,
  2 2 2 3 1 ->= 2 2 2 2 2 ,
  1 2 2 3 1 ->= 1 2 2 2 2 ,
  3 1 2 2 2 ->= 3 1 3 1 2 ,
  3 1 2 2 3 ->= 3 1 3 1 3 ,
  3 1 2 2 4 ->= 3 1 3 1 4 ,
  5 1 2 2 2 ->= 5 1 3 1 2 ,
  6 1 2 2 2 ->= 6 1 3 1 2 ,
  1 3 5 5 1 ->= 5 5 1 3 1 ,
  1 3 5 5 5 ->= 5 5 1 3 5 ,
  1 3 5 5 7 ->= 5 5 1 3 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 1 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
5 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
6 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 2->0, 3->1, 1->2, 4->3, 5->4, 6->5, 7->6 }, 
it remains to prove termination of the 10-rule system
{ 0 0 0 1 2 ->= 0 0 0 0 0 ,
  2 0 0 1 2 ->= 2 0 0 0 0 ,
  1 2 0 0 0 ->= 1 2 1 2 0 ,
  1 2 0 0 1 ->= 1 2 1 2 1 ,
  1 2 0 0 3 ->= 1 2 1 2 3 ,
  4 2 0 0 0 ->= 4 2 1 2 0 ,
  5 2 0 0 0 ->= 5 2 1 2 0 ,
  2 1 4 4 2 ->= 4 4 2 1 2 ,
  2 1 4 4 4 ->= 4 4 2 1 4 ,
  2 1 4 4 6 ->= 4 4 2 1 6 }

The system is trivially terminating.