YES

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


The system was reversed.

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


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, [0, 2]->4, [2, 0]->5, [1, 2]->6, [2, 1]->7, [2, 2]->8 },
it remains to prove termination of the 27-rule system
{ 0 1 2 3 -> 1 3 0 ,
  0 4 5 -> 0 1 3 0 ,
  1 3 ->= 1 6 7 3 ,
  0 1 2 2 -> 1 3 1 ,
  0 4 7 -> 0 1 3 1 ,
  1 2 ->= 1 6 7 2 ,
  0 1 2 6 -> 1 3 4 ,
  0 4 8 -> 0 1 3 4 ,
  1 6 ->= 1 6 7 6 ,
  3 1 2 3 -> 2 3 0 ,
  3 4 5 -> 3 1 3 0 ,
  2 3 ->= 2 6 7 3 ,
  3 1 2 2 -> 2 3 1 ,
  3 4 7 -> 3 1 3 1 ,
  2 2 ->= 2 6 7 2 ,
  3 1 2 6 -> 2 3 4 ,
  3 4 8 -> 3 1 3 4 ,
  2 6 ->= 2 6 7 6 ,
  5 1 2 3 -> 7 3 0 ,
  5 4 5 -> 5 1 3 0 ,
  7 3 ->= 7 6 7 3 ,
  5 1 2 2 -> 7 3 1 ,
  5 4 7 -> 5 1 3 1 ,
  7 2 ->= 7 6 7 2 ,
  5 1 2 6 -> 7 3 4 ,
  5 4 8 -> 5 1 3 4 ,
  7 6 ->= 7 6 7 6 }


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

After renaming modulo { 1->0, 3->1, 6->2, 7->3, 0->4, 4->5, 2->6, 5->7 }, 
it remains to prove termination of the 14-rule system
{ 0 1 ->= 0 2 3 1 ,
  4 5 3 -> 4 0 1 0 ,
  0 6 ->= 0 2 3 6 ,
  0 2 ->= 0 2 3 2 ,
  1 0 6 1 -> 6 1 4 ,
  6 1 ->= 6 2 3 1 ,
  1 5 3 -> 1 0 1 0 ,
  6 6 ->= 6 2 3 6 ,
  1 0 6 2 -> 6 1 5 ,
  6 2 ->= 6 2 3 2 ,
  3 1 ->= 3 2 3 1 ,
  7 5 3 -> 7 0 1 0 ,
  3 6 ->= 3 2 3 6 ,
  3 2 ->= 3 2 3 2 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 13-rule system
{ 0 1 ->= 0 2 3 1 ,
  4 5 3 -> 4 0 1 0 ,
  0 6 ->= 0 2 3 6 ,
  0 2 ->= 0 2 3 2 ,
  1 0 6 1 -> 6 1 4 ,
  6 1 ->= 6 2 3 1 ,
  1 5 3 -> 1 0 1 0 ,
  6 6 ->= 6 2 3 6 ,
  1 0 6 2 -> 6 1 5 ,
  6 2 ->= 6 2 3 2 ,
  3 1 ->= 3 2 3 1 ,
  3 6 ->= 3 2 3 6 ,
  3 2 ->= 3 2 3 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 11-rule system
{ 0 1 ->= 0 2 3 1 ,
  4 5 3 -> 4 0 1 0 ,
  0 6 ->= 0 2 3 6 ,
  0 2 ->= 0 2 3 2 ,
  1 5 3 -> 1 0 1 0 ,
  6 6 ->= 6 2 3 6 ,
  1 0 6 2 -> 6 1 5 ,
  6 2 ->= 6 2 3 2 ,
  3 1 ->= 3 2 3 1 ,
  3 6 ->= 3 2 3 6 ,
  3 2 ->= 3 2 3 2 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 6->4, 5->5 }, 
it remains to prove termination of the 10-rule system
{ 0 1 ->= 0 2 3 1 ,
  0 4 ->= 0 2 3 4 ,
  0 2 ->= 0 2 3 2 ,
  1 5 3 -> 1 0 1 0 ,
  4 4 ->= 4 2 3 4 ,
  1 0 4 2 -> 4 1 5 ,
  4 2 ->= 4 2 3 2 ,
  3 1 ->= 3 2 3 1 ,
  3 4 ->= 3 2 3 4 ,
  3 2 ->= 3 2 3 2 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 9-rule system
{ 0 1 ->= 0 2 3 1 ,
  0 4 ->= 0 2 3 4 ,
  0 2 ->= 0 2 3 2 ,
  1 5 3 -> 1 0 1 0 ,
  1 0 4 2 -> 4 1 5 ,
  4 2 ->= 4 2 3 2 ,
  3 1 ->= 3 2 3 1 ,
  3 4 ->= 3 2 3 4 ,
  3 2 ->= 3 2 3 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 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 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 1 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 |
| 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 1 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 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 0 |
| 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 |
 \             /
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 1 0 0 |
| 0 0 0 0 0 0 0 |
| 0 0 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 1 |
| 0 0 0 0 0 0 0 |
 \             /

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


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

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

The system is trivially terminating.