YES

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 12->10 }, 
it remains to prove termination of the 29-rule system
{ 0 0 -> 1 2 ,
  0 1 -> 1 3 ,
  0 4 -> 1 5 ,
  0 6 -> 1 7 ,
  2 0 -> 3 2 ,
  2 1 -> 3 3 ,
  2 4 -> 3 5 ,
  2 6 -> 3 7 ,
  8 0 -> 9 2 ,
  8 1 -> 9 3 ,
  8 4 -> 9 5 ,
  8 6 -> 9 7 ,
  0 1 2 -> 1 2 4 8 0 ,
  0 1 3 -> 1 2 4 8 1 ,
  0 1 5 -> 1 2 4 8 4 ,
  0 1 7 -> 1 2 4 8 6 ,
  2 1 2 -> 3 2 4 8 0 ,
  2 1 3 -> 3 2 4 8 1 ,
  2 1 5 -> 3 2 4 8 4 ,
  2 1 7 -> 3 2 4 8 6 ,
  8 1 2 -> 9 2 4 8 0 ,
  8 1 3 -> 9 2 4 8 1 ,
  8 1 5 -> 9 2 4 8 4 ,
  8 1 7 -> 9 2 4 8 6 ,
  9 3 5 -> 10 ,
  4 10 8 -> 0 ,
  4 10 9 -> 1 ,
  5 10 8 -> 2 ,
  5 10 9 -> 3 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (2,true)->2, (4,false)->3, (5,true)->4, (8,true)->5, (9,true)->6, (2,false)->7, (1,false)->8, (3,false)->9, (5,false)->10, (6,false)->11, (7,false)->12, (8,false)->13, (4,true)->14, (10,false)->15, (9,false)->16 },
it remains to prove termination of the 87-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  2 1 -> 2 ,
  2 3 -> 4 ,
  5 1 -> 6 7 ,
  5 1 -> 2 ,
  5 8 -> 6 9 ,
  5 3 -> 6 10 ,
  5 3 -> 4 ,
  5 11 -> 6 12 ,
  0 8 7 -> 2 3 13 1 ,
  0 8 7 -> 14 13 1 ,
  0 8 7 -> 5 1 ,
  0 8 7 -> 0 ,
  0 8 9 -> 2 3 13 8 ,
  0 8 9 -> 14 13 8 ,
  0 8 9 -> 5 8 ,
  0 8 10 -> 2 3 13 3 ,
  0 8 10 -> 14 13 3 ,
  0 8 10 -> 5 3 ,
  0 8 10 -> 14 ,
  0 8 12 -> 2 3 13 11 ,
  0 8 12 -> 14 13 11 ,
  0 8 12 -> 5 11 ,
  2 8 7 -> 2 3 13 1 ,
  2 8 7 -> 14 13 1 ,
  2 8 7 -> 5 1 ,
  2 8 7 -> 0 ,
  2 8 9 -> 2 3 13 8 ,
  2 8 9 -> 14 13 8 ,
  2 8 9 -> 5 8 ,
  2 8 10 -> 2 3 13 3 ,
  2 8 10 -> 14 13 3 ,
  2 8 10 -> 5 3 ,
  2 8 10 -> 14 ,
  2 8 12 -> 2 3 13 11 ,
  2 8 12 -> 14 13 11 ,
  2 8 12 -> 5 11 ,
  5 8 7 -> 6 7 3 13 1 ,
  5 8 7 -> 2 3 13 1 ,
  5 8 7 -> 14 13 1 ,
  5 8 7 -> 5 1 ,
  5 8 7 -> 0 ,
  5 8 9 -> 6 7 3 13 8 ,
  5 8 9 -> 2 3 13 8 ,
  5 8 9 -> 14 13 8 ,
  5 8 9 -> 5 8 ,
  5 8 10 -> 6 7 3 13 3 ,
  5 8 10 -> 2 3 13 3 ,
  5 8 10 -> 14 13 3 ,
  5 8 10 -> 5 3 ,
  5 8 10 -> 14 ,
  5 8 12 -> 6 7 3 13 11 ,
  5 8 12 -> 2 3 13 11 ,
  5 8 12 -> 14 13 11 ,
  5 8 12 -> 5 11 ,
  14 15 13 -> 0 ,
  4 15 13 -> 2 ,
  1 1 ->= 8 7 ,
  1 8 ->= 8 9 ,
  1 3 ->= 8 10 ,
  1 11 ->= 8 12 ,
  7 1 ->= 9 7 ,
  7 8 ->= 9 9 ,
  7 3 ->= 9 10 ,
  7 11 ->= 9 12 ,
  13 1 ->= 16 7 ,
  13 8 ->= 16 9 ,
  13 3 ->= 16 10 ,
  13 11 ->= 16 12 ,
  1 8 7 ->= 8 7 3 13 1 ,
  1 8 9 ->= 8 7 3 13 8 ,
  1 8 10 ->= 8 7 3 13 3 ,
  1 8 12 ->= 8 7 3 13 11 ,
  7 8 7 ->= 9 7 3 13 1 ,
  7 8 9 ->= 9 7 3 13 8 ,
  7 8 10 ->= 9 7 3 13 3 ,
  7 8 12 ->= 9 7 3 13 11 ,
  13 8 7 ->= 16 7 3 13 1 ,
  13 8 9 ->= 16 7 3 13 8 ,
  13 8 10 ->= 16 7 3 13 3 ,
  13 8 12 ->= 16 7 3 13 11 ,
  16 9 10 ->= 15 ,
  3 15 13 ->= 1 ,
  3 15 16 ->= 8 ,
  10 15 13 ->= 7 ,
  10 15 16 ->= 9 }


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 1 |
| 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 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 2 |
| 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 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 1->0, 8->1, 7->2, 9->3, 3->4, 10->5, 11->6, 12->7, 13->8, 16->9, 15->10 }, 
it remains to prove termination of the 29-rule system
{ 0 0 ->= 1 2 ,
  0 1 ->= 1 3 ,
  0 4 ->= 1 5 ,
  0 6 ->= 1 7 ,
  2 0 ->= 3 2 ,
  2 1 ->= 3 3 ,
  2 4 ->= 3 5 ,
  2 6 ->= 3 7 ,
  8 0 ->= 9 2 ,
  8 1 ->= 9 3 ,
  8 4 ->= 9 5 ,
  8 6 ->= 9 7 ,
  0 1 2 ->= 1 2 4 8 0 ,
  0 1 3 ->= 1 2 4 8 1 ,
  0 1 5 ->= 1 2 4 8 4 ,
  0 1 7 ->= 1 2 4 8 6 ,
  2 1 2 ->= 3 2 4 8 0 ,
  2 1 3 ->= 3 2 4 8 1 ,
  2 1 5 ->= 3 2 4 8 4 ,
  2 1 7 ->= 3 2 4 8 6 ,
  8 1 2 ->= 9 2 4 8 0 ,
  8 1 3 ->= 9 2 4 8 1 ,
  8 1 5 ->= 9 2 4 8 4 ,
  8 1 7 ->= 9 2 4 8 6 ,
  9 3 5 ->= 10 ,
  4 10 8 ->= 0 ,
  4 10 9 ->= 1 ,
  5 10 8 ->= 2 ,
  5 10 9 ->= 3 }

The system is trivially terminating.