YES

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


The system was reversed.

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


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

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (3,false)->1, (4,true)->2, (5,false)->3, (6,false)->4, (5,true)->5, (1,false)->6, (7,false)->7, (7,true)->8, (0,false)->9, (1,true)->10, (8,false)->11, (9,false)->12, (2,false)->13, (4,false)->14 },
it remains to prove termination of the 48-rule system
{ 0 1 -> 2 3 4 ,
  0 1 -> 5 4 ,
  0 6 -> 2 3 7 ,
  0 6 -> 5 7 ,
  0 6 -> 8 ,
  5 4 1 -> 8 9 6 9 1 ,
  5 4 1 -> 0 6 9 1 ,
  5 4 1 -> 10 9 1 ,
  5 4 1 -> 0 1 ,
  5 4 11 -> 8 9 6 9 11 ,
  5 4 11 -> 0 6 9 11 ,
  5 4 11 -> 10 9 11 ,
  5 4 11 -> 0 11 ,
  5 4 6 -> 8 9 6 9 6 ,
  5 4 6 -> 0 6 9 6 ,
  5 4 6 -> 10 9 6 ,
  5 4 6 -> 0 6 ,
  5 4 6 -> 10 ,
  5 4 12 -> 8 9 6 9 12 ,
  5 4 12 -> 0 6 9 12 ,
  5 4 12 -> 10 9 12 ,
  5 4 12 -> 0 12 ,
  2 4 1 -> 0 6 9 1 ,
  2 4 1 -> 10 9 1 ,
  2 4 1 -> 0 1 ,
  2 4 11 -> 0 6 9 11 ,
  2 4 11 -> 10 9 11 ,
  2 4 11 -> 0 11 ,
  2 4 6 -> 0 6 9 6 ,
  2 4 6 -> 10 9 6 ,
  2 4 6 -> 0 6 ,
  2 4 6 -> 10 ,
  2 4 12 -> 0 6 9 12 ,
  2 4 12 -> 10 9 12 ,
  2 4 12 -> 0 12 ,
  9 6 ->= 13 ,
  9 1 ->= 14 3 4 ,
  9 6 ->= 14 3 7 ,
  3 4 1 ->= 7 9 6 9 1 ,
  3 4 11 ->= 7 9 6 9 11 ,
  3 4 6 ->= 7 9 6 9 6 ,
  3 4 12 ->= 7 9 6 9 12 ,
  14 4 1 ->= 13 9 6 9 1 ,
  14 4 11 ->= 13 9 6 9 11 ,
  14 4 6 ->= 13 9 6 9 6 ,
  14 4 12 ->= 13 9 6 9 12 ,
  6 13 9 ->= 1 ,
  7 13 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 4 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 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 0 |
| 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 2 |
| 0 1 |
 \   /

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

The system is trivially terminating.