YES

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 67-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  3 4 1 0 -> 3 1 2 4 0 ,
  3 4 1 0 -> 3 1 4 0 2 ,
  3 4 1 0 -> 3 1 5 4 0 ,
  3 4 1 0 -> 3 4 2 1 0 ,
  3 4 1 0 -> 3 1 1 5 4 0 ,
  3 4 1 0 -> 3 1 2 1 4 0 ,
  3 4 1 0 -> 3 1 2 5 4 0 ,
  3 4 1 0 -> 3 1 4 2 0 2 ,
  3 4 1 0 -> 3 1 5 4 0 2 ,
  3 4 1 0 -> 3 1 5 5 4 0 ,
  3 4 1 0 -> 3 4 2 1 1 0 ,
  3 4 1 0 -> 3 4 5 1 2 0 ,
  0 1 4 1 0 -> 0 1 1 4 0 2 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 3 0 1 0 -> 0 0 3 1 3 0 ,
  0 3 0 1 0 -> 0 0 3 3 1 0 ,
  0 3 0 1 0 -> 0 0 3 5 1 0 ,
  0 3 0 1 0 -> 2 0 0 3 1 0 ,
  0 3 4 1 0 -> 0 2 0 4 3 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 2 0 1 0 -> 0 2 3 1 5 0 ,
  3 2 0 1 0 -> 2 0 3 1 1 0 ,
  3 3 0 1 0 -> 3 1 2 0 3 0 ,
  3 3 0 1 0 -> 3 1 2 3 0 0 ,
  3 3 4 1 0 -> 3 1 2 4 3 0 ,
  3 3 4 1 0 -> 3 1 3 4 0 2 ,
  3 3 4 1 0 -> 3 1 4 3 1 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 }, 
it remains to prove termination of the 51-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 1 4 1 0 -> 0 1 1 4 0 2 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 3 0 1 0 -> 0 0 3 1 3 0 ,
  0 3 0 1 0 -> 0 0 3 3 1 0 ,
  0 3 0 1 0 -> 0 0 3 5 1 0 ,
  0 3 0 1 0 -> 2 0 0 3 1 0 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 2 0 1 0 -> 0 2 3 1 5 0 ,
  3 2 0 1 0 -> 2 0 3 1 1 0 ,
  3 3 0 1 0 -> 3 1 2 0 3 0 ,
  3 3 0 1 0 -> 3 1 2 3 0 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 1 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 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 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 1 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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 50-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 3 0 1 0 -> 0 0 3 1 3 0 ,
  0 3 0 1 0 -> 0 0 3 3 1 0 ,
  0 3 0 1 0 -> 0 0 3 5 1 0 ,
  0 3 0 1 0 -> 2 0 0 3 1 0 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 2 0 1 0 -> 0 2 3 1 5 0 ,
  3 2 0 1 0 -> 2 0 3 1 1 0 ,
  3 3 0 1 0 -> 3 1 2 0 3 0 ,
  3 3 0 1 0 -> 3 1 2 3 0 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 |
| 0 1 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 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 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 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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 48-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 3 0 1 0 -> 0 0 3 1 3 0 ,
  0 3 0 1 0 -> 0 0 3 3 1 0 ,
  0 3 0 1 0 -> 0 0 3 5 1 0 ,
  0 3 0 1 0 -> 2 0 0 3 1 0 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 3 0 1 0 -> 3 1 2 0 3 0 ,
  3 3 0 1 0 -> 3 1 2 3 0 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 46-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 3 0 1 0 -> 0 0 3 1 3 0 ,
  0 3 0 1 0 -> 0 0 3 3 1 0 ,
  0 3 0 1 0 -> 0 0 3 5 1 0 ,
  0 3 0 1 0 -> 2 0 0 3 1 0 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 1 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 0 0 0 0 |
 \           /
3 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 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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 42-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 0 1 0 -> 0 2 4 1 3 0 ,
  3 4 0 1 0 -> 3 1 4 0 0 2 ,
  3 4 0 1 0 -> 3 2 0 4 1 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 |
| 0 1 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 0 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 1 0 0 0 0 |
 \           /
4 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 |
 \           /
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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 39-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 0 1 0 -> 0 2 3 1 0 ,
  3 0 1 0 -> 3 1 0 0 2 ,
  3 0 1 0 -> 3 1 1 0 0 ,
  3 0 1 0 -> 3 1 2 0 0 ,
  3 0 1 0 -> 3 1 5 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 ,
  3 0 1 0 -> 5 0 3 1 0 ,
  3 0 1 0 -> 2 0 2 3 1 0 ,
  3 0 1 0 -> 2 2 0 3 1 0 ,
  3 0 1 0 -> 3 1 5 0 0 0 ,
  3 0 1 0 -> 3 1 5 0 2 0 ,
  3 0 1 0 -> 3 1 5 1 0 0 ,
  3 0 1 0 -> 3 1 5 2 0 0 ,
  3 0 1 0 -> 3 1 5 5 0 0 ,
  3 0 1 0 -> 3 2 2 1 0 0 ,
  3 0 1 0 -> 3 5 1 0 0 2 ,
  3 0 1 0 -> 3 5 1 5 0 0 ,
  3 0 1 0 -> 5 1 1 3 0 0 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 0 0 -> 3 1 3 0 0 0 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 1 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 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 }, 
it remains to prove termination of the 20-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  0 2 0 1 0 -> 0 2 0 0 3 1 ,
  0 2 0 1 0 -> 2 0 0 0 3 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 1 0 |
| 0 0 0 0 0 0 |
| 0 1 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 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 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 }, 
it remains to prove termination of the 18-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 1 1 0 -> 3 1 0 1 2 0 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 0 |
| 0 0 0 0 0 0 |
| 0 1 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 1 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 0 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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 17-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  0 5 0 1 0 -> 0 0 0 1 5 2 ,
  0 5 0 1 0 -> 0 0 1 5 1 0 ,
  0 5 0 1 0 -> 0 2 0 0 1 5 ,
  3 0 2 1 0 -> 2 0 3 1 1 0 ,
  3 0 2 1 0 -> 2 3 1 5 0 0 ,
  3 0 2 1 0 -> 3 1 2 0 1 0 ,
  3 0 2 1 0 -> 3 1 2 0 5 0 ,
  3 0 5 1 0 -> 3 1 5 2 0 0 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 0 |
| 0 0 0 0 0 0 |
| 0 1 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 1 0 |
| 0 0 0 0 0 0 |
| 0 0 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 |
 \           /

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


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 1 0 |
| 0 0 0 0 0 0 |
| 0 1 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 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 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 |
 \           /

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


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 0 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 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 1 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 }, 
it remains to prove termination of the 9-rule system
{ 0 0 1 0 -> 0 2 0 0 3 1 ,
  0 0 1 0 -> 0 2 0 4 1 0 ,
  0 0 1 0 -> 2 0 0 0 2 1 ,
  3 1 0 1 0 -> 2 0 3 1 1 0 ,
  3 1 0 1 0 -> 3 1 1 1 0 0 ,
  3 1 0 1 0 -> 3 1 2 1 0 0 ,
  3 1 4 1 0 -> 3 1 2 1 4 0 ,
  3 1 4 1 0 -> 3 1 5 1 4 0 ,
  3 4 4 1 0 -> 3 1 1 4 4 0 }


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 0 0 |
| 0 0 0 0 0 0 |
| 0 1 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 0 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 1 0 0 |
| 0 0 0 0 1 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 |
 \           /

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


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 1 1 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 |
 \           /
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 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 0 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 1 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 |
 \           /

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


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

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

The system is trivially terminating.