YES

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


Applying the dependency pairs transformation.

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

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

The system is trivially terminating.