YES

After renaming modulo { b->0, a->1 }, 
it remains to prove termination of the 8-rule system
{ 0 1 0 -> 0 1 1 1 0 ,
  0 1 1 1 0 1 1 0 -> 0 1 1 0 1 1 0 1 1 1 0 0 ,
  0 1 1 1 0 1 1 1 0 -> 0 ,
  0 1 1 1 0 0 0 -> 0 0 0 1 1 1 0 ,
  0 1 1 0 0 -> 0 ,
  0 0 1 1 0 -> 0 ,
  0 1 1 1 0 1 0 -> 0 ,
  0 1 0 1 1 1 0 -> 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

After renaming modulo { 0->0, 1->1 }, 
it remains to prove termination of the 5-rule system
{ 0 1 1 1 0 1 1 0 -> 0 1 1 0 1 1 0 1 1 1 0 0 ,
  0 1 1 1 0 1 1 1 0 -> 0 ,
  0 1 1 1 0 0 0 -> 0 0 0 1 1 1 0 ,
  0 1 1 0 0 -> 0 ,
  0 0 1 1 0 -> 0 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 9:

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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

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

The system is trivially terminating.