YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 1 -> 1 1 0 2 ,
  1 1 -> 0 ,
  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 -> ,
  1 0 -> 2 0 1 1 ,
  1 1 -> 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 ,
  1 4 0 -> 2 8 1 5 4 ,
  1 4 1 -> 2 8 1 5 5 ,
  1 4 2 -> 2 8 1 5 6 ,
  1 4 3 -> 2 8 1 5 7 ,
  5 4 0 -> 6 8 1 5 4 ,
  5 4 1 -> 6 8 1 5 5 ,
  5 4 2 -> 6 8 1 5 6 ,
  5 4 3 -> 6 8 1 5 7 ,
  9 4 0 -> 10 8 1 5 4 ,
  9 4 1 -> 10 8 1 5 5 ,
  9 4 2 -> 10 8 1 5 6 ,
  9 4 3 -> 10 8 1 5 7 ,
  13 4 0 -> 14 8 1 5 4 ,
  13 4 1 -> 14 8 1 5 5 ,
  13 4 2 -> 14 8 1 5 6 ,
  13 4 3 -> 14 8 1 5 7 ,
  1 5 4 -> 0 0 ,
  1 5 5 -> 0 1 ,
  1 5 6 -> 0 2 ,
  1 5 7 -> 0 3 ,
  5 5 4 -> 4 0 ,
  5 5 5 -> 4 1 ,
  5 5 6 -> 4 2 ,
  5 5 7 -> 4 3 ,
  9 5 4 -> 8 0 ,
  9 5 5 -> 8 1 ,
  9 5 6 -> 8 2 ,
  9 5 7 -> 8 3 ,
  13 5 4 -> 12 0 ,
  13 5 5 -> 12 1 ,
  13 5 6 -> 12 2 ,
  13 5 7 -> 12 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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 4 |
| 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 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 8->0, 1->1, 9->2, 2->3, 10->4, 4->5, 0->6, 5->7, 6->8, 3->9, 7->10 }, 
it remains to prove termination of the 24-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  1 5 6 -> 3 0 1 7 5 ,
  1 5 1 -> 3 0 1 7 7 ,
  1 5 3 -> 3 0 1 7 8 ,
  1 5 9 -> 3 0 1 7 10 ,
  7 5 6 -> 8 0 1 7 5 ,
  7 5 1 -> 8 0 1 7 7 ,
  7 5 3 -> 8 0 1 7 8 ,
  7 5 9 -> 8 0 1 7 10 ,
  2 5 6 -> 4 0 1 7 5 ,
  2 5 1 -> 4 0 1 7 7 ,
  2 5 3 -> 4 0 1 7 8 ,
  2 5 9 -> 4 0 1 7 10 ,
  1 7 5 -> 6 6 ,
  1 7 7 -> 6 1 ,
  1 7 8 -> 6 3 ,
  1 7 10 -> 6 9 ,
  7 7 5 -> 5 6 ,
  7 7 7 -> 5 1 ,
  7 7 8 -> 5 3 ,
  7 7 10 -> 5 9 ,
  3 4 0 -> 6 ,
  8 4 0 -> 5 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (1,true)->3, (5,false)->4, (6,false)->5, (3,true)->6, (0,false)->7, (7,false)->8, (7,true)->9, (3,false)->10, (8,false)->11, (8,true)->12, (9,false)->13, (10,false)->14, (2,false)->15, (4,false)->16 },
it remains to prove termination of the 79-rule system
{ 0 1 -> 2 ,
  3 4 5 -> 6 7 1 8 4 ,
  3 4 5 -> 0 1 8 4 ,
  3 4 5 -> 3 8 4 ,
  3 4 5 -> 9 4 ,
  3 4 1 -> 6 7 1 8 8 ,
  3 4 1 -> 0 1 8 8 ,
  3 4 1 -> 3 8 8 ,
  3 4 1 -> 9 8 ,
  3 4 1 -> 9 ,
  3 4 10 -> 6 7 1 8 11 ,
  3 4 10 -> 0 1 8 11 ,
  3 4 10 -> 3 8 11 ,
  3 4 10 -> 9 11 ,
  3 4 10 -> 12 ,
  3 4 13 -> 6 7 1 8 14 ,
  3 4 13 -> 0 1 8 14 ,
  3 4 13 -> 3 8 14 ,
  3 4 13 -> 9 14 ,
  9 4 5 -> 12 7 1 8 4 ,
  9 4 5 -> 0 1 8 4 ,
  9 4 5 -> 3 8 4 ,
  9 4 5 -> 9 4 ,
  9 4 1 -> 12 7 1 8 8 ,
  9 4 1 -> 0 1 8 8 ,
  9 4 1 -> 3 8 8 ,
  9 4 1 -> 9 8 ,
  9 4 1 -> 9 ,
  9 4 10 -> 12 7 1 8 11 ,
  9 4 10 -> 0 1 8 11 ,
  9 4 10 -> 3 8 11 ,
  9 4 10 -> 9 11 ,
  9 4 10 -> 12 ,
  9 4 13 -> 12 7 1 8 14 ,
  9 4 13 -> 0 1 8 14 ,
  9 4 13 -> 3 8 14 ,
  9 4 13 -> 9 14 ,
  2 4 5 -> 0 1 8 4 ,
  2 4 5 -> 3 8 4 ,
  2 4 5 -> 9 4 ,
  2 4 1 -> 0 1 8 8 ,
  2 4 1 -> 3 8 8 ,
  2 4 1 -> 9 8 ,
  2 4 1 -> 9 ,
  2 4 10 -> 0 1 8 11 ,
  2 4 10 -> 3 8 11 ,
  2 4 10 -> 9 11 ,
  2 4 10 -> 12 ,
  2 4 13 -> 0 1 8 14 ,
  2 4 13 -> 3 8 14 ,
  2 4 13 -> 9 14 ,
  3 8 8 -> 3 ,
  3 8 11 -> 6 ,
  9 8 8 -> 3 ,
  9 8 11 -> 6 ,
  7 1 ->= 15 ,
  7 10 ->= 16 ,
  1 4 5 ->= 10 7 1 8 4 ,
  1 4 1 ->= 10 7 1 8 8 ,
  1 4 10 ->= 10 7 1 8 11 ,
  1 4 13 ->= 10 7 1 8 14 ,
  8 4 5 ->= 11 7 1 8 4 ,
  8 4 1 ->= 11 7 1 8 8 ,
  8 4 10 ->= 11 7 1 8 11 ,
  8 4 13 ->= 11 7 1 8 14 ,
  15 4 5 ->= 16 7 1 8 4 ,
  15 4 1 ->= 16 7 1 8 8 ,
  15 4 10 ->= 16 7 1 8 11 ,
  15 4 13 ->= 16 7 1 8 14 ,
  1 8 4 ->= 5 5 ,
  1 8 8 ->= 5 1 ,
  1 8 11 ->= 5 10 ,
  1 8 14 ->= 5 13 ,
  8 8 4 ->= 4 5 ,
  8 8 8 ->= 4 1 ,
  8 8 11 ->= 4 10 ,
  8 8 14 ->= 4 13 ,
  10 16 7 ->= 5 ,
  11 16 7 ->= 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 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

After renaming modulo { 7->0, 1->1, 15->2, 10->3, 16->4, 4->5, 5->6, 8->7, 11->8, 13->9, 14->10 }, 
it remains to prove termination of the 24-rule system
{ 0 1 ->= 2 ,
  0 3 ->= 4 ,
  1 5 6 ->= 3 0 1 7 5 ,
  1 5 1 ->= 3 0 1 7 7 ,
  1 5 3 ->= 3 0 1 7 8 ,
  1 5 9 ->= 3 0 1 7 10 ,
  7 5 6 ->= 8 0 1 7 5 ,
  7 5 1 ->= 8 0 1 7 7 ,
  7 5 3 ->= 8 0 1 7 8 ,
  7 5 9 ->= 8 0 1 7 10 ,
  2 5 6 ->= 4 0 1 7 5 ,
  2 5 1 ->= 4 0 1 7 7 ,
  2 5 3 ->= 4 0 1 7 8 ,
  2 5 9 ->= 4 0 1 7 10 ,
  1 7 5 ->= 6 6 ,
  1 7 7 ->= 6 1 ,
  1 7 8 ->= 6 3 ,
  1 7 10 ->= 6 9 ,
  7 7 5 ->= 5 6 ,
  7 7 7 ->= 5 1 ,
  7 7 8 ->= 5 3 ,
  7 7 10 ->= 5 9 ,
  3 4 0 ->= 6 ,
  8 4 0 ->= 5 }

The system is trivially terminating.