YES

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 25-rule system
{ 0 0 1 2 1 -> 1 0 1 1 0 ,
  0 3 1 2 4 -> 0 5 1 4 ,
  4 3 0 1 1 -> 5 4 5 2 ,
  4 3 4 2 2 -> 0 5 0 2 ,
  2 1 1 4 0 2 -> 1 1 5 3 5 ,
  2 2 4 1 3 4 2 -> 2 3 2 4 3 5 ,
  4 0 5 4 2 4 0 -> 0 1 2 2 2 2 0 ,
  4 2 4 2 5 1 0 1 5 -> 5 0 3 1 0 2 2 5 ,
  5 2 4 5 0 3 0 2 3 -> 5 3 2 1 0 1 3 4 0 ,
  1 4 1 3 2 3 3 1 2 1 -> 1 5 3 2 4 5 1 3 4 ,
  4 0 4 2 3 4 5 1 1 5 1 -> 5 4 3 2 2 3 2 1 2 4 0 ,
  4 5 2 2 5 4 4 3 4 5 4 -> 5 2 3 2 5 0 0 0 5 4 ,
  4 3 4 4 0 3 0 3 2 3 2 1 -> 5 5 5 5 5 0 2 2 4 4 2 0 ,
  5 3 4 4 3 3 5 2 5 2 1 1 4 2 -> 5 4 0 5 2 5 5 3 1 0 3 3 5 ,
  0 5 1 0 3 3 2 5 5 4 0 5 5 5 2 -> 1 0 1 3 4 5 3 3 3 2 2 3 3 5 2 ,
  4 5 3 2 1 1 5 2 2 3 4 3 2 3 1 -> 0 1 3 5 0 1 3 4 0 3 5 4 3 1 ,
  5 0 1 0 1 1 5 1 1 5 5 2 1 1 0 -> 5 1 5 1 1 1 3 0 3 3 3 3 1 0 ,
  5 3 0 4 4 1 1 5 3 4 1 1 2 3 2 -> 5 4 1 4 0 2 1 2 2 5 3 5 3 4 4 ,
  2 4 1 0 2 3 2 3 5 3 1 2 3 1 1 4 -> 2 2 2 1 4 5 0 1 0 3 1 3 5 1 2 ,
  0 1 1 3 2 2 0 0 0 5 0 2 4 3 3 0 1 -> 5 4 1 1 0 5 2 0 2 3 3 3 0 5 0 1 ,
  2 1 1 5 3 1 3 4 3 5 3 3 2 4 3 1 4 -> 1 0 1 0 0 2 1 3 2 2 0 3 0 5 2 4 ,
  2 4 3 5 0 2 5 5 1 5 0 4 4 4 1 4 3 -> 2 0 5 2 2 0 5 4 1 3 2 4 1 4 1 1 0 ,
  0 4 5 4 5 0 2 3 1 2 4 5 3 5 0 4 3 3 2 -> 1 0 2 4 5 5 2 2 4 2 1 1 4 0 1 2 3 0 2 5 ,
  4 5 1 0 2 0 5 4 5 4 4 2 5 5 2 3 5 4 2 3 -> 0 5 5 2 0 5 2 4 2 5 2 5 2 0 1 5 2 3 3 0 ,
  3 1 2 4 3 4 3 2 0 3 2 3 4 3 4 5 4 3 4 1 1 -> 3 4 0 0 2 4 5 0 0 4 3 5 4 3 0 3 2 2 1 1 }


The system was reversed.

After renaming modulo { 1->0, 2->1, 0->2, 4->3, 3->4, 5->5 }, 
it remains to prove termination of the 25-rule system
{ 0 1 0 2 2 -> 2 0 0 2 0 ,
  3 1 0 4 2 -> 3 0 5 2 ,
  0 0 2 4 3 -> 1 5 3 5 ,
  1 1 3 4 3 -> 1 2 5 2 ,
  1 2 3 0 0 1 -> 5 4 5 0 0 ,
  1 3 4 0 3 1 1 -> 5 4 3 1 4 1 ,
  2 3 1 3 5 2 3 -> 2 1 1 1 1 0 2 ,
  5 0 2 0 5 1 3 1 3 -> 5 1 1 2 0 4 2 5 ,
  4 1 2 4 2 5 3 1 5 -> 2 3 4 0 2 0 1 4 5 ,
  0 1 0 4 4 1 4 0 3 0 -> 3 4 0 5 3 1 4 5 0 ,
  0 5 0 0 5 3 4 1 3 2 3 -> 2 3 1 0 1 4 1 1 4 3 5 ,
  3 5 3 4 3 3 5 1 1 5 3 -> 3 5 2 2 2 5 1 4 1 5 ,
  0 1 4 1 4 2 4 2 3 3 4 3 -> 2 1 3 3 1 1 2 5 5 5 5 5 ,
  1 3 0 0 1 5 1 5 4 4 3 3 4 5 -> 5 4 4 2 0 4 5 5 1 5 2 3 5 ,
  1 5 5 5 2 3 5 5 1 4 4 2 0 5 2 -> 1 5 4 4 1 1 4 4 4 5 3 4 0 2 0 ,
  0 4 1 4 3 4 1 1 5 0 0 1 4 5 3 -> 0 4 3 5 4 2 3 4 0 2 5 4 0 2 ,
  2 0 0 1 5 5 0 0 5 0 0 2 0 2 5 -> 2 0 4 4 4 4 2 4 0 0 0 5 0 5 ,
  1 4 1 0 0 3 4 5 0 0 3 3 2 4 5 -> 3 3 4 5 4 5 1 1 0 1 2 3 0 3 5 ,
  3 0 0 4 1 0 4 5 4 1 4 1 2 0 3 1 -> 1 0 5 4 0 4 2 0 2 5 3 0 1 1 1 ,
  0 2 4 4 3 1 2 5 2 2 2 1 1 4 0 0 2 -> 0 2 5 2 4 4 4 1 2 1 5 2 0 0 3 5 ,
  3 0 4 3 1 4 4 5 4 3 4 0 4 5 0 0 1 -> 3 1 5 2 4 2 1 1 4 0 1 2 2 0 2 0 ,
  4 3 0 3 3 3 2 5 0 5 5 1 2 5 4 3 1 -> 2 0 0 3 0 3 1 4 0 3 5 2 1 1 5 2 1 ,
  1 4 4 3 2 5 4 5 3 1 0 4 1 2 5 3 5 3 2 -> 5 1 2 4 1 0 2 3 0 0 1 3 1 1 5 5 3 1 2 0 ,
  4 1 3 5 4 1 5 5 1 3 3 5 3 5 2 1 2 0 5 3 -> 2 4 4 1 5 0 2 1 5 1 5 1 3 1 5 2 1 5 5 2 ,
  0 0 3 4 3 5 3 4 3 4 1 4 2 1 4 3 4 3 1 0 4 -> 0 0 1 1 4 2 4 3 5 4 3 2 2 5 3 1 2 2 3 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 7 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 7 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 8 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 16:

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

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


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 |
 \   /

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


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 |
 \   /
5 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.