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 1 -> 2 2 2 ,
  2 2 2 2 -> 0 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 26 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 17 |
|  0  1 |
 \     /
2 is interpreted by
 /     \
|  1 11 |
|  0  1 |
 \     /

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

The system is trivially terminating.