YES

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


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

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


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 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 1 |
| 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 1 |
| 0 1 |
 \   /

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


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 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 1 |
| 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 1 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


Applying the dependency pairs transformation.

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


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

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


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 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 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 1 |
| 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 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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

The system is trivially terminating.