YES

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,false)->4 },
it remains to prove termination of the 9-rule system
{ 0 1 -> 2 3 3 ,
  0 1 -> 0 3 ,
  0 1 -> 0 ,
  2 4 -> 2 ,
  0 3 -> 0 4 3 ,
  0 3 -> 0 ,
  3 1 ->= 1 3 3 ,
  1 4 ->= 4 1 ,
  3 3 ->= 3 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 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, 4->1, 0->2, 3->3, 1->4 }, 
it remains to prove termination of the 6-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 1 3 ,
  2 3 -> 2 ,
  3 4 ->= 4 3 3 ,
  4 1 ->= 1 4 ,
  3 3 ->= 3 1 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 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

After renaming modulo { 0->0, 1->1, 3->2, 4->3 }, 
it remains to prove termination of the 4-rule system
{ 0 1 -> 0 ,
  2 3 ->= 3 2 2 ,
  3 1 ->= 1 3 ,
  2 2 ->= 2 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 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 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /

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

The system is trivially terminating.