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 1 0 2 -> 2 2 2 ,
  0 1 1 1 -> 3 1 0 ,
  4 5 1 4 -> 1 5 4 4 ,
  1 2 0 4 1 -> 2 5 2 2 ,
  1 5 1 0 3 -> 5 5 0 3 ,
  1 3 5 1 0 4 -> 4 0 0 0 1 4 ,
  3 3 1 4 5 4 5 5 -> 3 5 3 2 0 5 2 ,
  4 2 5 3 1 0 0 5 2 -> 4 4 1 5 3 5 3 2 ,
  2 2 1 1 0 2 0 1 2 3 -> 5 4 4 5 2 5 5 2 3 ,
  2 2 2 3 3 4 3 3 5 4 5 -> 5 5 4 2 5 3 5 3 2 0 5 ,
  4 2 1 1 5 1 0 0 0 2 5 -> 5 5 0 3 0 1 4 5 2 5 ,
  5 4 5 4 2 0 2 2 3 0 0 2 -> 5 3 4 5 0 3 2 1 1 2 2 ,
  0 2 1 1 3 1 5 0 5 2 3 1 4 -> 3 0 1 5 1 4 4 5 0 5 1 1 4 ,
  1 1 2 4 2 2 2 1 1 3 4 1 2 -> 1 5 0 3 4 1 0 5 2 2 2 3 ,
  1 4 0 0 2 4 0 3 3 2 0 3 1 -> 1 5 0 5 0 2 0 5 1 0 1 2 5 5 ,
  4 1 4 1 3 0 0 2 1 5 4 1 0 0 -> 2 3 0 2 5 4 4 3 0 4 1 2 0 ,
  4 2 4 4 0 0 0 4 0 3 5 0 3 3 -> 5 1 0 1 0 1 3 5 3 5 5 0 0 3 ,
  1 2 5 3 3 0 2 2 5 3 2 3 3 3 2 1 -> 1 1 0 0 4 1 2 1 0 5 0 0 3 5 0 4 1 ,
  3 1 2 5 0 3 4 3 1 5 4 1 5 2 0 5 -> 3 1 0 4 2 0 5 2 4 4 2 2 1 1 1 5 ,
  1 3 4 5 1 0 0 3 1 2 4 2 3 5 2 0 4 1 -> 1 3 0 0 4 2 2 5 3 1 0 1 2 1 5 0 1 4 1 ,
  1 0 3 3 2 5 0 0 3 0 3 2 4 1 4 0 2 4 2 -> 4 3 4 2 1 4 2 4 3 3 2 2 2 1 1 1 5 3 2 ,
  5 3 2 1 0 1 3 1 3 3 0 0 3 2 5 3 0 3 0 -> 5 1 0 3 2 4 0 0 3 2 1 5 1 3 0 5 1 3 1 ,
  0 2 2 3 3 5 0 0 5 0 3 1 3 0 1 2 1 5 5 1 -> 0 0 3 2 5 2 5 2 3 2 1 2 5 4 3 4 5 0 4 ,
  1 0 4 2 3 3 5 4 3 5 0 2 0 4 5 0 2 0 2 4 -> 4 5 4 5 4 1 1 2 5 0 4 3 1 5 4 3 1 5 4 0 4 ,
  1 4 2 3 1 3 4 2 4 1 5 1 4 0 4 5 2 0 0 3 4 -> 4 3 4 1 3 5 1 1 4 3 1 5 1 3 1 2 4 2 1 3 }


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 15 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 13 |
|  0  1 |
 \     /
2 is interpreted by
 /     \
|  1 14 |
|  0  1 |
 \     /
3 is interpreted by
 /     \
|  1 25 |
|  0  1 |
 \     /
4 is interpreted by
 /     \
|  1 17 |
|  0  1 |
 \     /
5 is interpreted by
 /     \
|  1 10 |
|  0  1 |
 \     /

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

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

The system is trivially terminating.