YES

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 10:

0 is interpreted by
 /                   \
| 1 0 1 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 0 |
| 0 0 1 0 0 0 1 0 0 0 |
| 0 0 1 0 0 0 0 2 0 0 |
| 0 0 1 0 0 0 0 0 1 0 |
| 0 0 0 0 0 0 0 0 0 1 |
| 0 1 1 0 0 1 0 0 0 0 |
 \                   /
1 is interpreted by
 /                   \
| 1 0 0 0 0 0 0 0 0 0 |
| 0 1 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 1 0 0 0 0 0 0 |
 \                   /
2 is interpreted by
 /                   \
| 1 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 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 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 {  }, 
it remains to prove termination of the 0-rule system
{ }

The system is trivially terminating.