YES

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 49-rule system
{ 0 0 1 -> 0 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 1 0 -> 2 0 3 1 2 0 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 0 5 1 -> 0 0 3 1 2 5 ,
  0 1 1 0 -> 1 2 0 0 1 2 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 1 5 0 -> 1 2 5 0 0 3 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 0 1 0 -> 0 3 5 1 2 0 ,
  5 0 1 0 -> 1 5 2 0 3 0 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 0 5 5 1 -> 1 0 0 3 5 5 ,
  0 1 0 5 0 -> 0 1 5 2 0 0 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 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 1 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 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 1 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 |
 \         /
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 1 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 1 |
| 0 1 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 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 1 0 -> 2 0 3 1 2 0 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 0 5 1 -> 0 0 3 1 2 5 ,
  0 1 1 0 -> 1 2 0 0 1 2 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 0 1 0 -> 0 3 5 1 2 0 ,
  5 0 1 0 -> 1 5 2 0 3 0 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 0 5 5 1 -> 1 0 0 3 5 5 ,
  0 1 0 5 0 -> 0 1 5 2 0 0 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 1 }


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 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 1 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 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 1 |
| 0 1 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 47-rule system
{ 0 0 1 -> 0 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 1 0 -> 2 0 3 1 2 0 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 0 5 1 -> 0 0 3 1 2 5 ,
  0 1 1 0 -> 1 2 0 0 1 2 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 0 1 0 -> 0 3 5 1 2 0 ,
  5 0 1 0 -> 1 5 2 0 3 0 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 0 5 5 1 -> 1 0 0 3 5 5 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 45-rule system
{ 0 0 1 -> 0 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 1 0 -> 2 0 3 1 2 0 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 0 5 1 -> 0 0 3 1 2 5 ,
  0 1 1 0 -> 1 2 0 0 1 2 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 0 5 5 1 -> 1 0 0 3 5 5 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

0 is interpreted by
 /             \
| 1 0 1 0 1 0 0 |
| 0 1 0 0 0 0 0 |
| 0 0 0 1 0 0 1 |
| 0 1 0 0 0 0 0 |
| 0 0 0 0 0 1 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 |
| 0 1 0 0 0 0 0 |
| 0 0 0 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 |
| 0 0 0 1 0 0 0 |
 \             /
2 is interpreted by
 /             \
| 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 0 0 0 0 0 0 |
| 0 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 |
 \             /
3 is interpreted by
 /             \
| 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 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 |
| 0 1 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 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 |
| 0 1 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 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 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 1 1 0 -> 1 2 0 0 1 2 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 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 1 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 1 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 1 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 |
 \         /
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 1 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 1 |
 \         /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 41-rule system
{ 0 0 1 -> 0 1 2 0 3 ,
  0 0 1 -> 0 1 2 0 3 2 ,
  0 0 1 -> 1 2 0 0 3 2 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 0 2 1 -> 2 2 0 3 0 1 ,
  0 0 4 1 -> 1 4 0 3 0 3 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 1 0 -> 0 4 0 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  0 5 0 1 -> 0 2 0 3 5 1 ,
  0 5 0 1 -> 5 2 0 3 0 1 ,
  0 5 1 0 -> 0 1 2 0 3 5 ,
  0 5 1 0 -> 2 0 1 3 5 0 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 0 -> 0 4 1 2 0 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 1 5 0 -> 1 2 0 5 4 ,
  4 1 5 0 -> 1 4 0 3 5 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 1 5 0 0 -> 1 2 0 4 5 0 ,
  4 1 5 5 0 -> 5 1 3 0 5 4 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 1 0 -> 1 2 0 1 4 3 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 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 1 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 1 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 |
 \         /
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 1 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 1 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 0 1 |
| 0 0 1 0 0 |
 \         /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 26-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  5 4 1 0 -> 0 1 2 4 5 2 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 3 1 5 0 -> 5 1 0 3 2 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 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 1 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 0 0 0 |
| 0 1 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 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 1 0 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 0 0 |
| 0 0 1 0 0 |
 \         /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 24-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 ,
  4 4 1 0 5 -> 4 0 5 3 4 1 }


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 1 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
 \           /
1 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 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 1 0 0 0 |
| 0 2 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 1 0 0 1 |
| 0 1 0 0 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 |
 \           /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 23-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  0 4 1 -> 4 0 3 1 ,
  0 4 1 -> 2 4 0 3 2 1 ,
  0 4 1 -> 2 4 0 5 3 1 ,
  0 4 1 -> 4 2 1 2 0 3 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  0 2 4 1 -> 4 0 5 3 1 2 ,
  0 4 2 1 -> 4 0 3 2 2 1 ,
  0 4 2 1 -> 4 0 3 5 1 2 ,
  0 4 4 1 -> 2 4 0 3 4 1 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 3 1 0 -> 1 4 2 0 3 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  4 3 1 0 -> 2 1 4 2 0 3 ,
  4 3 1 0 -> 2 2 4 0 1 3 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 4 1 4 1 -> 4 4 0 1 2 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 }


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 1 0 1 0 |
| 0 1 0 0 0 |
| 0 0 1 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 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 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 2 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 11-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 3 1 0 0 -> 0 0 3 0 1 2 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 }


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 1 0 0 1 |
| 0 1 0 0 0 0 |
 \           /
1 is interpreted by
 /           \
| 1 0 0 1 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 |
 \           /
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 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 10-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  4 3 1 0 -> 2 0 2 1 3 4 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 ,
  4 3 1 0 1 -> 1 1 2 3 0 4 }


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 1 0 0 |
| 0 0 0 0 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 1 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 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 1 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 8-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  4 1 0 -> 1 2 0 4 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  4 1 0 1 -> 1 1 2 0 4 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 ,
  0 5 5 4 1 -> 4 1 0 5 5 3 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 1 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 2 0 0 0 |
| 0 1 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 5-rule system
{ 0 0 1 -> 1 2 0 0 3 2 ,
  0 0 1 1 -> 1 2 0 0 3 1 ,
  0 1 4 1 -> 0 1 2 4 1 2 ,
  4 0 5 1 -> 1 4 0 5 3 2 ,
  0 2 5 0 1 -> 2 0 3 5 0 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


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


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 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 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 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 |
 \           /

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

The system is trivially terminating.