YES

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


Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019].

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (0,false)->2, (2,false)->3, (3,false)->4 },
it remains to prove termination of the 13-rule system
{ 0 1 2 1 3 3 2 -> 0 1 2 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 ,
  0 1 2 1 3 3 2 -> 0 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 3 ,
  0 1 2 1 3 3 4 -> 0 1 2 1 2 1 4 ,
  0 1 2 1 3 3 4 -> 0 1 2 1 4 ,
  0 1 2 1 3 3 4 -> 0 1 4 ,
  2 1 2 1 3 3 2 ->= 3 3 3 2 1 2 1 2 1 2 ,
  2 1 2 1 3 3 3 ->= 3 3 3 2 1 2 1 2 1 3 ,
  2 1 2 1 3 3 4 ->= 3 3 3 2 1 2 1 2 1 4 }


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 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 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 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 |
 \               /
2 is interpreted by
 /               \
| 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 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 1 0 0 0 0 0 |
 \               /
3 is interpreted by
 /               \
| 1 0 0 1 0 1 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 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 0 |
 \               /
4 is interpreted by
 /               \
| 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 |
| 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 |
 \               /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4 }, 
it remains to prove termination of the 10-rule system
{ 0 1 2 1 3 3 2 -> 0 1 2 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 ,
  0 1 2 1 3 3 2 -> 0 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 3 ,
  2 1 2 1 3 3 2 ->= 3 3 3 2 1 2 1 2 1 2 ,
  2 1 2 1 3 3 3 ->= 3 3 3 2 1 2 1 2 1 3 ,
  2 1 2 1 3 3 4 ->= 3 3 3 2 1 2 1 2 1 4 }


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 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 |
 \               /
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 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 |
 \               /
2 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 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 |
 \               /
3 is interpreted by
 /               \
| 1 0 0 1 0 1 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 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 0 |
 \               /
4 is interpreted by
 /               \
| 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 |
| 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 |
 \               /

After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, 
it remains to prove termination of the 9-rule system
{ 0 1 2 1 3 3 2 -> 0 1 2 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 1 2 ,
  0 1 2 1 3 3 2 -> 0 1 2 ,
  0 1 2 1 3 3 2 -> 0 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 2 1 3 ,
  0 1 2 1 3 3 3 -> 0 1 3 ,
  2 1 2 1 3 3 2 ->= 3 3 3 2 1 2 1 2 1 2 ,
  2 1 2 1 3 3 3 ->= 3 3 3 2 1 2 1 2 1 3 }


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 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 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 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 |
 \               /
2 is interpreted by
 /               \
| 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 1 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 1 0 0 0 0 0 |
| 0 0 2 0 0 0 0 0 |
| 0 1 0 0 1 0 0 0 |
 \               /
3 is interpreted by
 /               \
| 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 |
| 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 1 0 |
| 0 0 0 1 0 1 0 1 |
| 0 0 0 0 0 0 0 0 |
 \               /

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

The system is trivially terminating.