YES

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,false)->2, (0,false)->3 },
it remains to prove termination of the 9-rule system
{ 0 1 2 1 -> 0 1 2 3 1 2 ,
  0 1 2 1 -> 0 1 2 ,
  0 1 2 1 -> 0 1 2 3 1 2 3 1 2 ,
  0 1 2 1 -> 0 1 2 3 1 2 3 1 2 3 1 2 ,
  0 1 2 1 -> 0 1 2 3 1 2 3 1 2 3 1 2 3 1 2 ,
  3 1 2 1 ->= 1 2 1 1 3 1 2 3 1 2 ,
  3 1 2 1 ->= 1 2 1 1 3 1 2 3 1 2 3 1 2 ,
  3 1 2 1 ->= 1 2 1 1 3 1 2 3 1 2 3 1 2 3 1 2 ,
  3 1 2 1 ->= 1 2 1 1 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 }


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

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

The system is trivially terminating.