YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> 1 2 ,
  1 0 1 -> ,
  2 2 -> 0 0 0 1 }


The system was reversed.

After renaming modulo { 0->0, 2->1, 1->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> 1 2 ,
  2 0 2 -> ,
  1 1 -> 2 0 0 0 }


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

After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,0)->3, (2,1)->4, (0,2)->5, (2,2)->6, (0,4)->7, (2,4)->8, (1,0)->9, (1,1)->10, (3,0)->11, (3,1)->12, (1,4)->13, (3,2)->14, (3,4)->15 },
it remains to prove termination of the 48-rule system
{ 0 0 -> 1 2 3 ,
  0 1 -> 1 2 4 ,
  0 5 -> 1 2 6 ,
  0 7 -> 1 2 8 ,
  9 0 -> 10 2 3 ,
  9 1 -> 10 2 4 ,
  9 5 -> 10 2 6 ,
  9 7 -> 10 2 8 ,
  3 0 -> 4 2 3 ,
  3 1 -> 4 2 4 ,
  3 5 -> 4 2 6 ,
  3 7 -> 4 2 8 ,
  11 0 -> 12 2 3 ,
  11 1 -> 12 2 4 ,
  11 5 -> 12 2 6 ,
  11 7 -> 12 2 8 ,
  5 3 5 3 -> 0 ,
  5 3 5 4 -> 1 ,
  5 3 5 6 -> 5 ,
  5 3 5 8 -> 7 ,
  2 3 5 3 -> 9 ,
  2 3 5 4 -> 10 ,
  2 3 5 6 -> 2 ,
  2 3 5 8 -> 13 ,
  6 3 5 3 -> 3 ,
  6 3 5 4 -> 4 ,
  6 3 5 6 -> 6 ,
  6 3 5 8 -> 8 ,
  14 3 5 3 -> 11 ,
  14 3 5 4 -> 12 ,
  14 3 5 6 -> 14 ,
  14 3 5 8 -> 15 ,
  1 10 9 -> 5 3 0 0 0 ,
  1 10 10 -> 5 3 0 0 1 ,
  1 10 2 -> 5 3 0 0 5 ,
  1 10 13 -> 5 3 0 0 7 ,
  10 10 9 -> 2 3 0 0 0 ,
  10 10 10 -> 2 3 0 0 1 ,
  10 10 2 -> 2 3 0 0 5 ,
  10 10 13 -> 2 3 0 0 7 ,
  4 10 9 -> 6 3 0 0 0 ,
  4 10 10 -> 6 3 0 0 1 ,
  4 10 2 -> 6 3 0 0 5 ,
  4 10 13 -> 6 3 0 0 7 ,
  12 10 9 -> 14 3 0 0 0 ,
  12 10 10 -> 14 3 0 0 1 ,
  12 10 2 -> 14 3 0 0 5 ,
  12 10 13 -> 14 3 0 0 7 }


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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,true)->2, (2,false)->3, (3,false)->4, (2,true)->5, (3,true)->6, (1,false)->7, (4,false)->8, (4,true)->9, (5,false)->10, (6,false)->11, (7,true)->12, (8,false)->13, (7,false)->14 },
it remains to prove termination of the 41-rule system
{ 0 1 -> 2 3 4 ,
  0 1 -> 5 4 ,
  0 1 -> 6 ,
  0 7 -> 2 3 8 ,
  0 7 -> 5 8 ,
  0 7 -> 9 ,
  0 10 -> 2 3 11 ,
  0 10 -> 5 11 ,
  12 1 -> 5 4 ,
  12 1 -> 6 ,
  12 7 -> 5 8 ,
  12 7 -> 9 ,
  12 10 -> 5 11 ,
  6 1 -> 9 3 4 ,
  6 1 -> 5 4 ,
  6 1 -> 6 ,
  6 7 -> 9 3 8 ,
  6 7 -> 5 8 ,
  6 7 -> 9 ,
  6 10 -> 9 3 11 ,
  6 10 -> 5 11 ,
  5 4 10 4 -> 12 ,
  2 13 3 -> 6 1 1 10 ,
  2 13 3 -> 0 1 10 ,
  2 13 3 -> 0 10 ,
  9 13 3 -> 6 1 1 10 ,
  9 13 3 -> 0 1 10 ,
  9 13 3 -> 0 10 ,
  1 1 ->= 7 3 4 ,
  1 7 ->= 7 3 8 ,
  1 10 ->= 7 3 11 ,
  14 1 ->= 13 3 4 ,
  14 7 ->= 13 3 8 ,
  14 10 ->= 13 3 11 ,
  4 1 ->= 8 3 4 ,
  4 7 ->= 8 3 8 ,
  4 10 ->= 8 3 11 ,
  3 4 10 4 ->= 14 ,
  3 4 10 8 ->= 13 ,
  7 13 3 ->= 10 4 1 1 10 ,
  8 13 3 ->= 11 4 1 1 10 }


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

After renaming modulo { 6->0, 1->1, 9->2, 3->3, 4->4, 7->5, 8->6, 10->7, 11->8, 13->9, 14->10 }, 
it remains to prove termination of the 17-rule system
{ 0 1 -> 2 3 4 ,
  0 5 -> 2 3 6 ,
  0 7 -> 2 3 8 ,
  2 9 3 -> 0 1 1 7 ,
  1 1 ->= 5 3 4 ,
  1 5 ->= 5 3 6 ,
  1 7 ->= 5 3 8 ,
  10 1 ->= 9 3 4 ,
  10 5 ->= 9 3 6 ,
  10 7 ->= 9 3 8 ,
  4 1 ->= 6 3 4 ,
  4 5 ->= 6 3 6 ,
  4 7 ->= 6 3 8 ,
  3 4 7 4 ->= 10 ,
  3 4 7 6 ->= 9 ,
  5 9 3 ->= 7 4 1 1 7 ,
  6 9 3 ->= 8 4 1 1 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

0 is interpreted by
 /               \
| 1 0 0 0 0 0 0 1 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
1 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 1 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 1 0 0 |
 \               /
2 is interpreted by
 /               \
| 1 0 1 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
3 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 1 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
4 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 1 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
5 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 1 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
6 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 1 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
7 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 1 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
8 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
9 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 1 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /
10 is interpreted by
 /               \
| 1 0 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 1 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
| 0 0 0 0 0 0 0 0 |
 \               /

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


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 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 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 0 |
| 0 1 |
 \   /

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

The system is trivially terminating.