YES

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


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 -> ,
  2 1 -> 1 2 0 1 2 0 ,
  2 0 -> }


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

After renaming modulo { (2,0)->0, (0,1)->1, (1,1)->2, (2,1)->3, (1,2)->4, (2,2)->5, (1,4)->6, (2,4)->7, (0,2)->8, (0,4)->9 },
it remains to prove termination of the 21-rule system
{ 0 1 2 -> 3 ,
  0 1 4 -> 5 ,
  0 1 6 -> 7 ,
  8 3 2 -> 1 4 0 1 4 0 1 ,
  8 3 4 -> 1 4 0 1 4 0 8 ,
  8 3 6 -> 1 4 0 1 4 0 9 ,
  4 3 2 -> 2 4 0 1 4 0 1 ,
  4 3 4 -> 2 4 0 1 4 0 8 ,
  4 3 6 -> 2 4 0 1 4 0 9 ,
  5 3 2 -> 3 4 0 1 4 0 1 ,
  5 3 4 -> 3 4 0 1 4 0 8 ,
  5 3 6 -> 3 4 0 1 4 0 9 ,
  8 0 1 -> 1 ,
  8 0 8 -> 8 ,
  8 0 9 -> 9 ,
  4 0 1 -> 2 ,
  4 0 8 -> 4 ,
  4 0 9 -> 6 ,
  5 0 1 -> 3 ,
  5 0 8 -> 5 ,
  5 0 9 -> 7 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 8->6, 6->7, 9->8 }, 
it remains to prove termination of the 19-rule system
{ 0 1 2 -> 3 ,
  0 1 4 -> 5 ,
  6 3 2 -> 1 4 0 1 4 0 1 ,
  6 3 4 -> 1 4 0 1 4 0 6 ,
  6 3 7 -> 1 4 0 1 4 0 8 ,
  4 3 2 -> 2 4 0 1 4 0 1 ,
  4 3 4 -> 2 4 0 1 4 0 6 ,
  4 3 7 -> 2 4 0 1 4 0 8 ,
  5 3 2 -> 3 4 0 1 4 0 1 ,
  5 3 4 -> 3 4 0 1 4 0 6 ,
  5 3 7 -> 3 4 0 1 4 0 8 ,
  6 0 1 -> 1 ,
  6 0 6 -> 6 ,
  6 0 8 -> 8 ,
  4 0 1 -> 2 ,
  4 0 6 -> 4 ,
  4 0 8 -> 7 ,
  5 0 1 -> 3 ,
  5 0 6 -> 5 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (4,false)->2, (5,true)->3, (6,true)->4, (3,false)->5, (2,false)->6, (4,true)->7, (0,false)->8, (6,false)->9, (7,false)->10, (8,false)->11, (5,false)->12 },
it remains to prove termination of the 62-rule system
{ 0 1 2 -> 3 ,
  4 5 6 -> 7 8 1 2 8 1 ,
  4 5 6 -> 0 1 2 8 1 ,
  4 5 6 -> 7 8 1 ,
  4 5 6 -> 0 1 ,
  4 5 2 -> 7 8 1 2 8 9 ,
  4 5 2 -> 0 1 2 8 9 ,
  4 5 2 -> 7 8 9 ,
  4 5 2 -> 0 9 ,
  4 5 2 -> 4 ,
  4 5 10 -> 7 8 1 2 8 11 ,
  4 5 10 -> 0 1 2 8 11 ,
  4 5 10 -> 7 8 11 ,
  4 5 10 -> 0 11 ,
  7 5 6 -> 7 8 1 2 8 1 ,
  7 5 6 -> 0 1 2 8 1 ,
  7 5 6 -> 7 8 1 ,
  7 5 6 -> 0 1 ,
  7 5 2 -> 7 8 1 2 8 9 ,
  7 5 2 -> 0 1 2 8 9 ,
  7 5 2 -> 7 8 9 ,
  7 5 2 -> 0 9 ,
  7 5 2 -> 4 ,
  7 5 10 -> 7 8 1 2 8 11 ,
  7 5 10 -> 0 1 2 8 11 ,
  7 5 10 -> 7 8 11 ,
  7 5 10 -> 0 11 ,
  3 5 6 -> 7 8 1 2 8 1 ,
  3 5 6 -> 0 1 2 8 1 ,
  3 5 6 -> 7 8 1 ,
  3 5 6 -> 0 1 ,
  3 5 2 -> 7 8 1 2 8 9 ,
  3 5 2 -> 0 1 2 8 9 ,
  3 5 2 -> 7 8 9 ,
  3 5 2 -> 0 9 ,
  3 5 2 -> 4 ,
  3 5 10 -> 7 8 1 2 8 11 ,
  3 5 10 -> 0 1 2 8 11 ,
  3 5 10 -> 7 8 11 ,
  3 5 10 -> 0 11 ,
  4 8 9 -> 4 ,
  7 8 9 -> 7 ,
  3 8 9 -> 3 ,
  8 1 6 ->= 5 ,
  8 1 2 ->= 12 ,
  9 5 6 ->= 1 2 8 1 2 8 1 ,
  9 5 2 ->= 1 2 8 1 2 8 9 ,
  9 5 10 ->= 1 2 8 1 2 8 11 ,
  2 5 6 ->= 6 2 8 1 2 8 1 ,
  2 5 2 ->= 6 2 8 1 2 8 9 ,
  2 5 10 ->= 6 2 8 1 2 8 11 ,
  12 5 6 ->= 5 2 8 1 2 8 1 ,
  12 5 2 ->= 5 2 8 1 2 8 9 ,
  12 5 10 ->= 5 2 8 1 2 8 11 ,
  9 8 1 ->= 1 ,
  9 8 9 ->= 9 ,
  9 8 11 ->= 11 ,
  2 8 1 ->= 6 ,
  2 8 9 ->= 2 ,
  2 8 11 ->= 10 ,
  12 8 1 ->= 5 ,
  12 8 9 ->= 12 }


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 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 4->0, 8->1, 9->2, 7->3, 3->4, 1->5, 6->6, 5->7, 2->8, 12->9, 10->10, 11->11 }, 
it remains to prove termination of the 22-rule system
{ 0 1 2 -> 0 ,
  3 1 2 -> 3 ,
  4 1 2 -> 4 ,
  1 5 6 ->= 7 ,
  1 5 8 ->= 9 ,
  2 7 6 ->= 5 8 1 5 8 1 5 ,
  2 7 8 ->= 5 8 1 5 8 1 2 ,
  2 7 10 ->= 5 8 1 5 8 1 11 ,
  8 7 6 ->= 6 8 1 5 8 1 5 ,
  8 7 8 ->= 6 8 1 5 8 1 2 ,
  8 7 10 ->= 6 8 1 5 8 1 11 ,
  9 7 6 ->= 7 8 1 5 8 1 5 ,
  9 7 8 ->= 7 8 1 5 8 1 2 ,
  9 7 10 ->= 7 8 1 5 8 1 11 ,
  2 1 5 ->= 5 ,
  2 1 2 ->= 2 ,
  2 1 11 ->= 11 ,
  8 1 5 ->= 6 ,
  8 1 2 ->= 8 ,
  8 1 11 ->= 10 ,
  9 1 5 ->= 7 ,
  9 1 2 ->= 9 }


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 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 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 0 |
| 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 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 3->0, 1->1, 2->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 -> 0 ,
  3 1 2 -> 3 ,
  1 4 5 ->= 6 ,
  1 4 7 ->= 8 ,
  2 6 5 ->= 4 7 1 4 7 1 4 ,
  2 6 7 ->= 4 7 1 4 7 1 2 ,
  2 6 9 ->= 4 7 1 4 7 1 10 ,
  7 6 5 ->= 5 7 1 4 7 1 4 ,
  7 6 7 ->= 5 7 1 4 7 1 2 ,
  7 6 9 ->= 5 7 1 4 7 1 10 ,
  8 6 5 ->= 6 7 1 4 7 1 4 ,
  8 6 7 ->= 6 7 1 4 7 1 2 ,
  8 6 9 ->= 6 7 1 4 7 1 10 ,
  2 1 4 ->= 4 ,
  2 1 2 ->= 2 ,
  2 1 10 ->= 10 ,
  7 1 4 ->= 5 ,
  7 1 2 ->= 7 ,
  7 1 10 ->= 9 ,
  8 1 4 ->= 6 ,
  8 1 2 ->= 8 }


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 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 1 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 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 0 |
| 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 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 3->0, 1->1, 2->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9 }, 
it remains to prove termination of the 20-rule system
{ 0 1 2 -> 0 ,
  1 3 4 ->= 5 ,
  1 3 6 ->= 7 ,
  2 5 4 ->= 3 6 1 3 6 1 3 ,
  2 5 6 ->= 3 6 1 3 6 1 2 ,
  2 5 8 ->= 3 6 1 3 6 1 9 ,
  6 5 4 ->= 4 6 1 3 6 1 3 ,
  6 5 6 ->= 4 6 1 3 6 1 2 ,
  6 5 8 ->= 4 6 1 3 6 1 9 ,
  7 5 4 ->= 5 6 1 3 6 1 3 ,
  7 5 6 ->= 5 6 1 3 6 1 2 ,
  7 5 8 ->= 5 6 1 3 6 1 9 ,
  2 1 3 ->= 3 ,
  2 1 2 ->= 2 ,
  2 1 9 ->= 9 ,
  6 1 3 ->= 4 ,
  6 1 2 ->= 6 ,
  6 1 9 ->= 8 ,
  7 1 3 ->= 5 ,
  7 1 2 ->= 7 }


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

After renaming modulo { 1->0, 3->1, 4->2, 5->3, 6->4, 7->5, 2->6, 8->7, 9->8 }, 
it remains to prove termination of the 19-rule system
{ 0 1 2 ->= 3 ,
  0 1 4 ->= 5 ,
  6 3 2 ->= 1 4 0 1 4 0 1 ,
  6 3 4 ->= 1 4 0 1 4 0 6 ,
  6 3 7 ->= 1 4 0 1 4 0 8 ,
  4 3 2 ->= 2 4 0 1 4 0 1 ,
  4 3 4 ->= 2 4 0 1 4 0 6 ,
  4 3 7 ->= 2 4 0 1 4 0 8 ,
  5 3 2 ->= 3 4 0 1 4 0 1 ,
  5 3 4 ->= 3 4 0 1 4 0 6 ,
  5 3 7 ->= 3 4 0 1 4 0 8 ,
  6 0 1 ->= 1 ,
  6 0 6 ->= 6 ,
  6 0 8 ->= 8 ,
  4 0 1 ->= 2 ,
  4 0 6 ->= 4 ,
  4 0 8 ->= 7 ,
  5 0 1 ->= 3 ,
  5 0 6 ->= 5 }

The system is trivially terminating.