YES

After renaming modulo { a->0, c->1, b->2 }, 
it remains to prove termination of the 3-rule system
{ 0 1 2 -> 2 0 2 0 ,
  0 0 -> 0 2 0 ,
  2 ->= 2 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 0 |
| 0 0 1 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 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 1 1 1 |
 \       /

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


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

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

The system is trivially terminating.