YES

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


Applying context closure of depth 1 in the following form: System R over Sigma
maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2,
where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n})

After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 1]->2, [1, 0]->3 },
it remains to prove termination of the 8-rule system
{ 0 1 2 2 3 0 -> 0 ,
  0 ->= 0 1 3 0 ,
  0 1 2 2 3 1 -> 1 ,
  1 ->= 0 1 3 1 ,
  3 1 2 2 3 0 -> 3 ,
  3 ->= 3 1 3 0 ,
  3 1 2 2 3 1 -> 2 ,
  2 ->= 3 1 3 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.