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 1 -> 0 1 2 2 }


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

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (0,4)->3, (1,0)->4, (1,1)->5, (1,2)->6, (1,4)->7, (2,0)->8, (2,1)->9, (2,2)->10, (2,4)->11, (3,0)->12, (3,1)->13, (3,2)->14, (3,4)->15 },
it remains to prove termination of the 64-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  4 2 -> 6 ,
  4 3 -> 7 ,
  8 0 -> 8 ,
  8 1 -> 9 ,
  8 2 -> 10 ,
  8 3 -> 11 ,
  12 0 -> 12 ,
  12 1 -> 13 ,
  12 2 -> 14 ,
  12 3 -> 15 ,
  0 0 0 -> 1 4 ,
  0 0 1 -> 1 5 ,
  0 0 2 -> 1 6 ,
  0 0 3 -> 1 7 ,
  4 0 0 -> 5 4 ,
  4 0 1 -> 5 5 ,
  4 0 2 -> 5 6 ,
  4 0 3 -> 5 7 ,
  8 0 0 -> 9 4 ,
  8 0 1 -> 9 5 ,
  8 0 2 -> 9 6 ,
  8 0 3 -> 9 7 ,
  12 0 0 -> 13 4 ,
  12 0 1 -> 13 5 ,
  12 0 2 -> 13 6 ,
  12 0 3 -> 13 7 ,
  1 6 8 -> 0 ,
  1 6 9 -> 1 ,
  1 6 10 -> 2 ,
  1 6 11 -> 3 ,
  5 6 8 -> 4 ,
  5 6 9 -> 5 ,
  5 6 10 -> 6 ,
  5 6 11 -> 7 ,
  9 6 8 -> 8 ,
  9 6 9 -> 9 ,
  9 6 10 -> 10 ,
  9 6 11 -> 11 ,
  13 6 8 -> 12 ,
  13 6 9 -> 13 ,
  13 6 10 -> 14 ,
  13 6 11 -> 15 ,
  2 9 4 -> 0 1 6 10 8 ,
  2 9 5 -> 0 1 6 10 9 ,
  2 9 6 -> 0 1 6 10 10 ,
  2 9 7 -> 0 1 6 10 11 ,
  6 9 4 -> 4 1 6 10 8 ,
  6 9 5 -> 4 1 6 10 9 ,
  6 9 6 -> 4 1 6 10 10 ,
  6 9 7 -> 4 1 6 10 11 ,
  10 9 4 -> 8 1 6 10 8 ,
  10 9 5 -> 8 1 6 10 9 ,
  10 9 6 -> 8 1 6 10 10 ,
  10 9 7 -> 8 1 6 10 11 ,
  14 9 4 -> 12 1 6 10 8 ,
  14 9 5 -> 12 1 6 10 9 ,
  14 9 6 -> 12 1 6 10 10 ,
  14 9 7 -> 12 1 6 10 11 }


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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 4->0, 1->1, 5->2, 8->3, 9->4, 0->5, 6->6, 10->7, 2->8 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  0 5 1 -> 2 2 ,
  3 5 1 -> 4 2 ,
  1 6 3 -> 5 ,
  1 6 7 -> 8 ,
  8 4 0 -> 5 1 6 7 3 ,
  8 4 2 -> 5 1 6 7 4 ,
  8 4 6 -> 5 1 6 7 7 ,
  6 4 0 -> 0 1 6 7 3 ,
  6 4 2 -> 0 1 6 7 4 ,
  6 4 6 -> 0 1 6 7 7 ,
  7 4 0 -> 3 1 6 7 3 ,
  7 4 2 -> 3 1 6 7 4 ,
  7 4 6 -> 3 1 6 7 7 }


Applying the dependency pairs transformation.

After renaming modulo { (1,true)->0, (6,false)->1, (7,false)->2, (8,true)->3, (4,false)->4, (0,false)->5, (3,false)->6, (6,true)->7, (7,true)->8, (3,true)->9, (2,false)->10, (0,true)->11, (1,false)->12, (5,false)->13, (8,false)->14 },
it remains to prove termination of the 55-rule system
{ 0 1 2 -> 3 ,
  3 4 5 -> 0 1 2 6 ,
  3 4 5 -> 7 2 6 ,
  3 4 5 -> 8 6 ,
  3 4 5 -> 9 ,
  3 4 10 -> 0 1 2 4 ,
  3 4 10 -> 7 2 4 ,
  3 4 10 -> 8 4 ,
  3 4 1 -> 0 1 2 2 ,
  3 4 1 -> 7 2 2 ,
  3 4 1 -> 8 2 ,
  3 4 1 -> 8 ,
  7 4 5 -> 11 12 1 2 6 ,
  7 4 5 -> 0 1 2 6 ,
  7 4 5 -> 7 2 6 ,
  7 4 5 -> 8 6 ,
  7 4 5 -> 9 ,
  7 4 10 -> 11 12 1 2 4 ,
  7 4 10 -> 0 1 2 4 ,
  7 4 10 -> 7 2 4 ,
  7 4 10 -> 8 4 ,
  7 4 1 -> 11 12 1 2 2 ,
  7 4 1 -> 0 1 2 2 ,
  7 4 1 -> 7 2 2 ,
  7 4 1 -> 8 2 ,
  7 4 1 -> 8 ,
  8 4 5 -> 9 12 1 2 6 ,
  8 4 5 -> 0 1 2 6 ,
  8 4 5 -> 7 2 6 ,
  8 4 5 -> 8 6 ,
  8 4 5 -> 9 ,
  8 4 10 -> 9 12 1 2 4 ,
  8 4 10 -> 0 1 2 4 ,
  8 4 10 -> 7 2 4 ,
  8 4 10 -> 8 4 ,
  8 4 1 -> 9 12 1 2 2 ,
  8 4 1 -> 0 1 2 2 ,
  8 4 1 -> 7 2 2 ,
  8 4 1 -> 8 2 ,
  8 4 1 -> 8 ,
  5 12 ->= 10 ,
  6 12 ->= 4 ,
  5 13 12 ->= 10 10 ,
  6 13 12 ->= 4 10 ,
  12 1 6 ->= 13 ,
  12 1 2 ->= 14 ,
  14 4 5 ->= 13 12 1 2 6 ,
  14 4 10 ->= 13 12 1 2 4 ,
  14 4 1 ->= 13 12 1 2 2 ,
  1 4 5 ->= 5 12 1 2 6 ,
  1 4 10 ->= 5 12 1 2 4 ,
  1 4 1 ->= 5 12 1 2 2 ,
  2 4 5 ->= 6 12 1 2 6 ,
  2 4 10 ->= 6 12 1 2 4 ,
  2 4 1 ->= 6 12 1 2 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 1 |
| 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 2 |
| 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 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 12->1, 10->2, 6->3, 4->4, 13->5, 1->6, 2->7, 14->8 }, 
it remains to prove termination of the 15-rule system
{ 0 1 ->= 2 ,
  3 1 ->= 4 ,
  0 5 1 ->= 2 2 ,
  3 5 1 ->= 4 2 ,
  1 6 3 ->= 5 ,
  1 6 7 ->= 8 ,
  8 4 0 ->= 5 1 6 7 3 ,
  8 4 2 ->= 5 1 6 7 4 ,
  8 4 6 ->= 5 1 6 7 7 ,
  6 4 0 ->= 0 1 6 7 3 ,
  6 4 2 ->= 0 1 6 7 4 ,
  6 4 6 ->= 0 1 6 7 7 ,
  7 4 0 ->= 3 1 6 7 3 ,
  7 4 2 ->= 3 1 6 7 4 ,
  7 4 6 ->= 3 1 6 7 7 }

The system is trivially terminating.