YES

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


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (0,false)->3, (2,false)->4 },
it remains to prove termination of the 10-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  2 3 -> 0 3 4 ,
  2 3 -> 0 4 ,
  2 3 -> 2 ,
  2 1 -> 0 1 4 ,
  2 1 -> 2 ,
  3 1 ->= 1 4 3 ,
  4 3 ->= 3 3 4 ,
  4 1 ->= 3 1 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 0 |
| 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 0 |
| 0 1 |
 \   /

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


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


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

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

The system is trivially terminating.