YES

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


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 8 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 5 |
| 0 1 |
 \   /

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

The system is trivially terminating.