YES

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3 },
it remains to prove termination of the 6-rule system
{ 0 1 2 -> 0 1 1 ,
  0 1 2 -> 0 1 ,
  0 1 2 -> 0 ,
  0 3 -> 0 ,
  1 1 2 ->= 3 2 1 1 1 ,
  1 3 ->= 2 1 }


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

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

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

The system is trivially terminating.