YES

After renaming modulo { 1->0, 4->1, 3->2, 2->3, 5->4, 0->5 }, 
it remains to prove termination of the 19-rule system
{ 0 1 -> 2 0 0 3 3 1 ,
  4 1 -> 1 3 2 0 0 0 ,
  5 2 5 -> 3 0 0 5 3 5 ,
  5 4 4 -> 0 5 0 2 1 3 ,
  0 4 1 -> 5 3 4 3 5 1 ,
  2 4 1 -> 1 0 2 1 3 2 ,
  1 0 1 -> 2 2 3 3 2 0 ,
  4 1 5 -> 3 1 5 1 1 5 ,
  4 1 5 -> 4 0 4 3 0 5 ,
  4 1 1 -> 1 0 0 2 3 1 ,
  4 4 1 -> 2 1 1 0 3 3 ,
  5 4 4 5 -> 5 3 5 5 2 5 ,
  5 4 4 1 -> 5 0 2 1 2 1 ,
  0 1 4 1 -> 5 1 4 5 3 0 ,
  0 1 4 4 -> 5 5 0 2 1 0 ,
  3 4 1 5 -> 5 1 0 3 1 5 ,
  1 2 5 4 -> 2 2 3 2 4 4 ,
  4 1 5 5 -> 0 5 1 5 3 3 ,
  4 1 5 3 -> 2 5 1 4 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 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 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 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 1 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 1 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 16-rule system
{ 0 1 -> 2 0 0 3 3 1 ,
  4 1 -> 1 3 2 0 0 0 ,
  5 2 5 -> 3 0 0 5 3 5 ,
  0 4 1 -> 5 3 4 3 5 1 ,
  2 4 1 -> 1 0 2 1 3 2 ,
  1 0 1 -> 2 2 3 3 2 0 ,
  4 1 5 -> 3 1 5 1 1 5 ,
  4 1 5 -> 4 0 4 3 0 5 ,
  4 1 1 -> 1 0 0 2 3 1 ,
  4 4 1 -> 2 1 1 0 3 3 ,
  0 1 4 1 -> 5 1 4 5 3 0 ,
  0 1 4 4 -> 5 5 0 2 1 0 ,
  3 4 1 5 -> 5 1 0 3 1 5 ,
  1 2 5 4 -> 2 2 3 2 4 4 ,
  4 1 5 5 -> 0 5 1 5 3 3 ,
  4 1 5 3 -> 2 5 1 4 5 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 0 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 1 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 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 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 15-rule system
{ 0 1 -> 2 0 0 3 3 1 ,
  4 1 -> 1 3 2 0 0 0 ,
  5 2 5 -> 3 0 0 5 3 5 ,
  0 4 1 -> 5 3 4 3 5 1 ,
  2 4 1 -> 1 0 2 1 3 2 ,
  1 0 1 -> 2 2 3 3 2 0 ,
  4 1 5 -> 3 1 5 1 1 5 ,
  4 1 5 -> 4 0 4 3 0 5 ,
  4 1 1 -> 1 0 0 2 3 1 ,
  4 4 1 -> 2 1 1 0 3 3 ,
  0 1 4 1 -> 5 1 4 5 3 0 ,
  0 1 4 4 -> 5 5 0 2 1 0 ,
  3 4 1 5 -> 5 1 0 3 1 5 ,
  4 1 5 5 -> 0 5 1 5 3 3 ,
  4 1 5 3 -> 2 5 1 4 5 3 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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


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

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

The system is trivially terminating.