YES

After renaming modulo { a->0, s->1, b->2, c->3 }, 
it remains to prove termination of the 5-rule system
{ 0 1 -> 1 0 ,
  2 0 2 1 -> 0 2 1 0 ,
  2 0 2 2 -> 3 1 ,
  3 1 -> 0 2 0 2 ,
  0 2 0 0 -> 2 0 2 0 }


The system was reversed.

After renaming modulo { 1->0, 0->1, 2->2, 3->3 }, 
it remains to prove termination of the 5-rule system
{ 0 1 -> 1 0 ,
  0 2 1 2 -> 1 0 2 1 ,
  2 2 1 2 -> 0 3 ,
  0 3 -> 2 1 2 1 ,
  1 1 2 1 -> 1 2 1 2 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (0,false)->3, (2,false)->4, (2,true)->5, (3,false)->6 },
it remains to prove termination of the 20-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 0 ,
  0 4 1 4 -> 2 3 4 1 ,
  0 4 1 4 -> 0 4 1 ,
  0 4 1 4 -> 5 1 ,
  0 4 1 4 -> 2 ,
  5 4 1 4 -> 0 6 ,
  0 6 -> 5 1 4 1 ,
  0 6 -> 2 4 1 ,
  0 6 -> 5 1 ,
  0 6 -> 2 ,
  2 1 4 1 -> 2 4 1 4 ,
  2 1 4 1 -> 5 1 4 ,
  2 1 4 1 -> 2 4 ,
  2 1 4 1 -> 5 ,
  3 1 ->= 1 3 ,
  3 4 1 4 ->= 1 3 4 1 ,
  4 4 1 4 ->= 3 6 ,
  3 6 ->= 4 1 4 1 ,
  1 1 4 1 ->= 1 4 1 4 }


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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 7 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 4->1, 1->2, 0->3, 6->4, 2->5, 3->6 }, 
it remains to prove termination of the 8-rule system
{ 0 1 2 1 -> 3 4 ,
  3 4 -> 0 2 1 2 ,
  5 2 1 2 -> 5 1 2 1 ,
  6 2 ->= 2 6 ,
  6 1 2 1 ->= 2 6 1 2 ,
  1 1 2 1 ->= 6 4 ,
  6 4 ->= 1 2 1 2 ,
  2 2 1 2 ->= 2 1 2 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

After renaming modulo { 3->0, 4->1, 0->2, 2->3, 1->4, 5->5, 6->6 }, 
it remains to prove termination of the 7-rule system
{ 0 1 -> 2 3 4 3 ,
  5 3 4 3 -> 5 4 3 4 ,
  6 3 ->= 3 6 ,
  6 4 3 4 ->= 3 6 4 3 ,
  4 4 3 4 ->= 6 1 ,
  6 1 ->= 4 3 4 3 ,
  3 3 4 3 ->= 3 4 3 4 }


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

After renaming modulo { 5->0, 3->1, 4->2, 6->3, 1->4 }, 
it remains to prove termination of the 6-rule system
{ 0 1 2 1 -> 0 2 1 2 ,
  3 1 ->= 1 3 ,
  3 2 1 2 ->= 1 3 2 1 ,
  2 2 1 2 ->= 3 4 ,
  3 4 ->= 2 1 2 1 ,
  1 1 2 1 ->= 1 2 1 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

After renaming modulo { 3->0, 1->1, 2->2, 4->3 }, 
it remains to prove termination of the 5-rule system
{ 0 1 ->= 1 0 ,
  0 2 1 2 ->= 1 0 2 1 ,
  2 2 1 2 ->= 0 3 ,
  0 3 ->= 2 1 2 1 ,
  1 1 2 1 ->= 1 2 1 2 }

The system is trivially terminating.