YES

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


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (2,true)->4 },
it remains to prove termination of the 17-rule system
{ 0 1 2 2 2 2 1 1 -> 0 1 3 3 1 1 ,
  0 1 2 2 2 2 1 1 -> 0 3 3 1 1 ,
  0 1 2 2 2 2 1 1 -> 4 3 1 1 ,
  0 1 2 2 2 2 1 1 -> 4 1 1 ,
  0 1 2 2 2 2 1 1 -> 0 1 ,
  0 1 2 2 2 2 1 1 -> 0 ,
  4 3 1 1 -> 0 1 3 3 3 3 ,
  4 3 1 1 -> 0 3 3 3 3 ,
  4 3 1 1 -> 4 3 3 3 ,
  4 3 1 1 -> 4 3 3 ,
  4 3 1 1 -> 4 3 ,
  4 3 1 1 -> 4 ,
  4 3 3 3 3 3 -> 4 3 2 2 ,
  4 3 3 3 3 3 -> 4 2 2 ,
  1 1 2 2 2 2 1 1 ->= 2 2 1 1 3 3 1 1 ,
  3 3 1 1 ->= 1 1 3 3 3 3 ,
  3 3 3 3 3 3 ->= 2 2 3 3 2 2 }


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 { 0->0, 1->1, 2->2, 3->3, 4->4 }, 
it remains to prove termination of the 6-rule system
{ 0 1 2 2 2 2 1 1 -> 0 1 3 3 1 1 ,
  4 3 3 3 3 3 -> 4 3 2 2 ,
  4 3 3 3 3 3 -> 4 2 2 ,
  1 1 2 2 2 2 1 1 ->= 2 2 1 1 3 3 1 1 ,
  3 3 1 1 ->= 1 1 3 3 3 3 ,
  3 3 3 3 3 3 ->= 2 2 3 3 2 2 }


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 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 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 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 |
 \             /
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 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 0 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 1 0 0 0 |
| 0 0 0 0 1 0 0 |
| 0 0 0 0 0 1 0 |
| 0 0 0 0 0 0 1 |
| 0 1 0 0 0 0 0 |
 \             /
4 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 |
 \             /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 14:

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

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

The system is trivially terminating.