YES

After renaming modulo { b->0, a->1, c->2 }, 
it remains to prove termination of the 5-rule system
{ 0 1 1 -> 1 0 2 ,
  2 1 -> 1 2 ,
  0 2 1 -> 1 0 2 ,
  2 0 -> 0 1 ,
  1 2 0 -> 2 0 1 }


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (1,true)->3, (2,false)->4 },
it remains to prove termination of the 14-rule system
{ 0 1 2 -> 3 1 ,
  0 1 2 -> 0 ,
  0 4 -> 0 ,
  0 4 2 -> 3 1 ,
  0 4 2 -> 0 ,
  3 4 -> 0 2 ,
  3 4 -> 3 ,
  3 4 1 -> 0 2 4 ,
  3 4 1 -> 3 4 ,
  1 1 2 ->= 4 2 1 ,
  1 4 ->= 4 1 ,
  1 4 2 ->= 4 2 1 ,
  2 4 ->= 1 2 ,
  2 4 1 ->= 1 2 4 }


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

After renaming modulo { 3->0, 4->1, 0->2, 2->3, 1->4 }, 
it remains to prove termination of the 7-rule system
{ 0 1 -> 2 3 ,
  0 1 4 -> 2 3 1 ,
  4 4 3 ->= 1 3 4 ,
  4 1 ->= 1 4 ,
  4 1 3 ->= 1 3 4 ,
  3 1 ->= 4 3 ,
  3 1 4 ->= 4 3 1 }


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

After renaming modulo { 4->0, 3->1, 1->2 }, 
it remains to prove termination of the 5-rule system
{ 0 0 1 ->= 2 1 0 ,
  0 2 ->= 2 0 ,
  0 2 1 ->= 2 1 0 ,
  1 2 ->= 0 1 ,
  1 2 0 ->= 0 1 2 }

The system is trivially terminating.