YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 0 -> 1 1 2 ,
  2 -> ,
  2 1 -> 1 2 0 }


The system was reversed.

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (1,0)->3, (1,1)->4, (1,2)->5, (2,0)->6, (2,1)->7, (2,2)->8, (3,0)->9, (3,1)->10, (3,2)->11 },
it remains to prove termination of the 48-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 4 ,
  3 2 -> 5 ,
  6 0 -> 6 ,
  6 1 -> 7 ,
  6 2 -> 8 ,
  9 0 -> 9 ,
  9 1 -> 10 ,
  9 2 -> 11 ,
  0 0 0 -> 1 5 8 6 ,
  0 0 1 -> 1 5 8 7 ,
  0 0 2 -> 1 5 8 8 ,
  3 0 0 -> 4 5 8 6 ,
  3 0 1 -> 4 5 8 7 ,
  3 0 2 -> 4 5 8 8 ,
  6 0 0 -> 7 5 8 6 ,
  6 0 1 -> 7 5 8 7 ,
  6 0 2 -> 7 5 8 8 ,
  9 0 0 -> 10 5 8 6 ,
  9 0 1 -> 10 5 8 7 ,
  9 0 2 -> 10 5 8 8 ,
  1 3 -> 0 ,
  1 4 -> 1 ,
  1 5 -> 2 ,
  4 3 -> 3 ,
  4 4 -> 4 ,
  4 5 -> 5 ,
  7 3 -> 6 ,
  7 4 -> 7 ,
  7 5 -> 8 ,
  10 3 -> 9 ,
  10 4 -> 10 ,
  10 5 -> 11 ,
  2 7 3 -> 0 1 5 6 ,
  2 7 4 -> 0 1 5 7 ,
  2 7 5 -> 0 1 5 8 ,
  5 7 3 -> 3 1 5 6 ,
  5 7 4 -> 3 1 5 7 ,
  5 7 5 -> 3 1 5 8 ,
  8 7 3 -> 6 1 5 6 ,
  8 7 4 -> 6 1 5 7 ,
  8 7 5 -> 6 1 5 8 ,
  11 7 3 -> 9 1 5 6 ,
  11 7 4 -> 9 1 5 7 ,
  11 7 5 -> 9 1 5 8 }


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

After renaming modulo { 3->0, 1->1, 4->2, 6->3, 7->4, 0->5, 5->6, 8->7, 2->8 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  0 5 1 -> 2 6 7 4 ,
  3 5 1 -> 4 6 7 4 ,
  1 0 -> 5 ,
  1 6 -> 8 ,
  8 4 0 -> 5 1 6 3 ,
  8 4 2 -> 5 1 6 4 ,
  8 4 6 -> 5 1 6 7 ,
  6 4 0 -> 0 1 6 3 ,
  6 4 2 -> 0 1 6 4 ,
  6 4 6 -> 0 1 6 7 ,
  7 4 0 -> 3 1 6 3 ,
  7 4 2 -> 3 1 6 4 ,
  7 4 6 -> 3 1 6 7 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (5,false)->1, (1,false)->2, (6,true)->3, (7,false)->4, (4,false)->5, (7,true)->6, (3,true)->7, (1,true)->8, (6,false)->9, (8,true)->10, (0,false)->11, (3,false)->12, (2,false)->13, (8,false)->14 },
it remains to prove termination of the 50-rule system
{ 0 1 2 -> 3 4 5 ,
  0 1 2 -> 6 5 ,
  7 1 2 -> 3 4 5 ,
  7 1 2 -> 6 5 ,
  8 9 -> 10 ,
  10 5 11 -> 8 9 12 ,
  10 5 11 -> 3 12 ,
  10 5 11 -> 7 ,
  10 5 13 -> 8 9 5 ,
  10 5 13 -> 3 5 ,
  10 5 9 -> 8 9 4 ,
  10 5 9 -> 3 4 ,
  10 5 9 -> 6 ,
  3 5 11 -> 0 2 9 12 ,
  3 5 11 -> 8 9 12 ,
  3 5 11 -> 3 12 ,
  3 5 11 -> 7 ,
  3 5 13 -> 0 2 9 5 ,
  3 5 13 -> 8 9 5 ,
  3 5 13 -> 3 5 ,
  3 5 9 -> 0 2 9 4 ,
  3 5 9 -> 8 9 4 ,
  3 5 9 -> 3 4 ,
  3 5 9 -> 6 ,
  6 5 11 -> 7 2 9 12 ,
  6 5 11 -> 8 9 12 ,
  6 5 11 -> 3 12 ,
  6 5 11 -> 7 ,
  6 5 13 -> 7 2 9 5 ,
  6 5 13 -> 8 9 5 ,
  6 5 13 -> 3 5 ,
  6 5 9 -> 7 2 9 4 ,
  6 5 9 -> 8 9 4 ,
  6 5 9 -> 3 4 ,
  6 5 9 -> 6 ,
  11 2 ->= 13 ,
  12 2 ->= 5 ,
  11 1 2 ->= 13 9 4 5 ,
  12 1 2 ->= 5 9 4 5 ,
  2 11 ->= 1 ,
  2 9 ->= 14 ,
  14 5 11 ->= 1 2 9 12 ,
  14 5 13 ->= 1 2 9 5 ,
  14 5 9 ->= 1 2 9 4 ,
  9 5 11 ->= 11 2 9 12 ,
  9 5 13 ->= 11 2 9 5 ,
  9 5 9 ->= 11 2 9 4 ,
  4 5 11 ->= 12 2 9 12 ,
  4 5 13 ->= 12 2 9 5 ,
  4 5 9 ->= 12 2 9 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 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 2 |
| 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 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 11->0, 2->1, 13->2, 12->3, 5->4, 1->5, 9->6, 4->7, 14->8 }, 
it remains to prove termination of the 15-rule system
{ 0 1 ->= 2 ,
  3 1 ->= 4 ,
  0 5 1 ->= 2 6 7 4 ,
  3 5 1 ->= 4 6 7 4 ,
  1 0 ->= 5 ,
  1 6 ->= 8 ,
  8 4 0 ->= 5 1 6 3 ,
  8 4 2 ->= 5 1 6 4 ,
  8 4 6 ->= 5 1 6 7 ,
  6 4 0 ->= 0 1 6 3 ,
  6 4 2 ->= 0 1 6 4 ,
  6 4 6 ->= 0 1 6 7 ,
  7 4 0 ->= 3 1 6 3 ,
  7 4 2 ->= 3 1 6 4 ,
  7 4 6 ->= 3 1 6 7 }

The system is trivially terminating.