YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 1 -> 2 1 2 1 0 ,
  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 ,
  0 1 4 -> 2 9 6 9 4 0 ,
  0 1 5 -> 2 9 6 9 4 1 ,
  0 1 6 -> 2 9 6 9 4 2 ,
  0 1 7 -> 2 9 6 9 4 3 ,
  4 1 4 -> 6 9 6 9 4 0 ,
  4 1 5 -> 6 9 6 9 4 1 ,
  4 1 6 -> 6 9 6 9 4 2 ,
  4 1 7 -> 6 9 6 9 4 3 ,
  8 1 4 -> 10 9 6 9 4 0 ,
  8 1 5 -> 10 9 6 9 4 1 ,
  8 1 6 -> 10 9 6 9 4 2 ,
  8 1 7 -> 10 9 6 9 4 3 ,
  12 1 4 -> 14 9 6 9 4 0 ,
  12 1 5 -> 14 9 6 9 4 1 ,
  12 1 6 -> 14 9 6 9 4 2 ,
  12 1 7 -> 14 9 6 9 4 3 ,
  1 4 -> 0 0 ,
  1 5 -> 0 1 ,
  1 6 -> 0 2 ,
  1 7 -> 0 3 ,
  5 4 -> 4 0 ,
  5 5 -> 4 1 ,
  5 6 -> 4 2 ,
  5 7 -> 4 3 ,
  9 4 -> 8 0 ,
  9 5 -> 8 1 ,
  9 6 -> 8 2 ,
  9 7 -> 8 3 ,
  13 4 -> 12 0 ,
  13 5 -> 12 1 ,
  13 6 -> 12 2 ,
  13 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 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 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 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 10->9, 12->10, 9->11 }, 
it remains to prove termination of the 29-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 2 -> 9 ,
  10 0 -> 10 ,
  0 1 4 -> 2 11 6 11 4 0 ,
  0 1 5 -> 2 11 6 11 4 1 ,
  0 1 6 -> 2 11 6 11 4 2 ,
  0 1 7 -> 2 11 6 11 4 3 ,
  4 1 4 -> 6 11 6 11 4 0 ,
  4 1 5 -> 6 11 6 11 4 1 ,
  4 1 6 -> 6 11 6 11 4 2 ,
  4 1 7 -> 6 11 6 11 4 3 ,
  8 1 4 -> 9 11 6 11 4 0 ,
  8 1 5 -> 9 11 6 11 4 1 ,
  8 1 6 -> 9 11 6 11 4 2 ,
  8 1 7 -> 9 11 6 11 4 3 ,
  11 4 -> 8 0 ,
  11 5 -> 8 1 ,
  11 6 -> 8 2 ,
  11 7 -> 8 3 ,
  2 9 11 -> 1 ,
  6 9 11 -> 5 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (2,false)->2, (2,true)->3, (4,true)->4, (6,true)->5, (8,true)->6, (10,true)->7, (1,false)->8, (4,false)->9, (11,false)->10, (6,false)->11, (11,true)->12, (5,false)->13, (7,false)->14, (3,false)->15, (8,false)->16, (9,false)->17, (10,false)->18 },
it remains to prove termination of the 103-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  7 1 -> 7 ,
  0 8 9 -> 3 10 11 10 9 1 ,
  0 8 9 -> 12 11 10 9 1 ,
  0 8 9 -> 5 10 9 1 ,
  0 8 9 -> 12 9 1 ,
  0 8 9 -> 4 1 ,
  0 8 9 -> 0 ,
  0 8 13 -> 3 10 11 10 9 8 ,
  0 8 13 -> 12 11 10 9 8 ,
  0 8 13 -> 5 10 9 8 ,
  0 8 13 -> 12 9 8 ,
  0 8 13 -> 4 8 ,
  0 8 11 -> 3 10 11 10 9 2 ,
  0 8 11 -> 12 11 10 9 2 ,
  0 8 11 -> 5 10 9 2 ,
  0 8 11 -> 12 9 2 ,
  0 8 11 -> 4 2 ,
  0 8 11 -> 3 ,
  0 8 14 -> 3 10 11 10 9 15 ,
  0 8 14 -> 12 11 10 9 15 ,
  0 8 14 -> 5 10 9 15 ,
  0 8 14 -> 12 9 15 ,
  0 8 14 -> 4 15 ,
  4 8 9 -> 5 10 11 10 9 1 ,
  4 8 9 -> 12 11 10 9 1 ,
  4 8 9 -> 5 10 9 1 ,
  4 8 9 -> 12 9 1 ,
  4 8 9 -> 4 1 ,
  4 8 9 -> 0 ,
  4 8 13 -> 5 10 11 10 9 8 ,
  4 8 13 -> 12 11 10 9 8 ,
  4 8 13 -> 5 10 9 8 ,
  4 8 13 -> 12 9 8 ,
  4 8 13 -> 4 8 ,
  4 8 11 -> 5 10 11 10 9 2 ,
  4 8 11 -> 12 11 10 9 2 ,
  4 8 11 -> 5 10 9 2 ,
  4 8 11 -> 12 9 2 ,
  4 8 11 -> 4 2 ,
  4 8 11 -> 3 ,
  4 8 14 -> 5 10 11 10 9 15 ,
  4 8 14 -> 12 11 10 9 15 ,
  4 8 14 -> 5 10 9 15 ,
  4 8 14 -> 12 9 15 ,
  4 8 14 -> 4 15 ,
  6 8 9 -> 12 11 10 9 1 ,
  6 8 9 -> 5 10 9 1 ,
  6 8 9 -> 12 9 1 ,
  6 8 9 -> 4 1 ,
  6 8 9 -> 0 ,
  6 8 13 -> 12 11 10 9 8 ,
  6 8 13 -> 5 10 9 8 ,
  6 8 13 -> 12 9 8 ,
  6 8 13 -> 4 8 ,
  6 8 11 -> 12 11 10 9 2 ,
  6 8 11 -> 5 10 9 2 ,
  6 8 11 -> 12 9 2 ,
  6 8 11 -> 4 2 ,
  6 8 11 -> 3 ,
  6 8 14 -> 12 11 10 9 15 ,
  6 8 14 -> 5 10 9 15 ,
  6 8 14 -> 12 9 15 ,
  6 8 14 -> 4 15 ,
  12 9 -> 6 1 ,
  12 9 -> 0 ,
  12 13 -> 6 8 ,
  12 11 -> 6 2 ,
  12 11 -> 3 ,
  12 14 -> 6 15 ,
  1 1 ->= 1 ,
  1 8 ->= 8 ,
  1 2 ->= 2 ,
  1 15 ->= 15 ,
  9 1 ->= 9 ,
  9 8 ->= 13 ,
  9 2 ->= 11 ,
  9 15 ->= 14 ,
  16 1 ->= 16 ,
  16 2 ->= 17 ,
  18 1 ->= 18 ,
  1 8 9 ->= 2 10 11 10 9 1 ,
  1 8 13 ->= 2 10 11 10 9 8 ,
  1 8 11 ->= 2 10 11 10 9 2 ,
  1 8 14 ->= 2 10 11 10 9 15 ,
  9 8 9 ->= 11 10 11 10 9 1 ,
  9 8 13 ->= 11 10 11 10 9 8 ,
  9 8 11 ->= 11 10 11 10 9 2 ,
  9 8 14 ->= 11 10 11 10 9 15 ,
  16 8 9 ->= 17 10 11 10 9 1 ,
  16 8 13 ->= 17 10 11 10 9 8 ,
  16 8 11 ->= 17 10 11 10 9 2 ,
  16 8 14 ->= 17 10 11 10 9 15 ,
  10 9 ->= 16 1 ,
  10 13 ->= 16 8 ,
  10 11 ->= 16 2 ,
  10 14 ->= 16 15 ,
  2 17 10 ->= 8 ,
  11 17 10 ->= 13 }


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 2 |
| 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 4 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 4->2, 6->3, 7->4, 8->5, 2->6, 15->7, 9->8, 13->9, 11->10, 14->11, 16->12, 17->13, 18->14, 10->15 }, 
it remains to prove termination of the 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  1 1 ->= 1 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  1 7 ->= 7 ,
  8 1 ->= 8 ,
  8 5 ->= 9 ,
  8 6 ->= 10 ,
  8 7 ->= 11 ,
  12 1 ->= 12 ,
  12 6 ->= 13 ,
  14 1 ->= 14 ,
  1 5 8 ->= 6 15 10 15 8 1 ,
  1 5 9 ->= 6 15 10 15 8 5 ,
  1 5 10 ->= 6 15 10 15 8 6 ,
  1 5 11 ->= 6 15 10 15 8 7 ,
  8 5 8 ->= 10 15 10 15 8 1 ,
  8 5 9 ->= 10 15 10 15 8 5 ,
  8 5 10 ->= 10 15 10 15 8 6 ,
  8 5 11 ->= 10 15 10 15 8 7 ,
  12 5 8 ->= 13 15 10 15 8 1 ,
  12 5 9 ->= 13 15 10 15 8 5 ,
  12 5 10 ->= 13 15 10 15 8 6 ,
  12 5 11 ->= 13 15 10 15 8 7 ,
  15 8 ->= 12 1 ,
  15 9 ->= 12 5 ,
  15 10 ->= 12 6 ,
  15 11 ->= 12 7 ,
  6 13 15 ->= 5 ,
  10 13 15 ->= 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 32-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 1 ->= 1 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  7 1 ->= 7 ,
  7 4 ->= 8 ,
  7 5 ->= 9 ,
  7 6 ->= 10 ,
  11 1 ->= 11 ,
  11 5 ->= 12 ,
  13 1 ->= 13 ,
  1 4 7 ->= 5 14 9 14 7 1 ,
  1 4 8 ->= 5 14 9 14 7 4 ,
  1 4 9 ->= 5 14 9 14 7 5 ,
  1 4 10 ->= 5 14 9 14 7 6 ,
  7 4 7 ->= 9 14 9 14 7 1 ,
  7 4 8 ->= 9 14 9 14 7 4 ,
  7 4 9 ->= 9 14 9 14 7 5 ,
  7 4 10 ->= 9 14 9 14 7 6 ,
  11 4 7 ->= 12 14 9 14 7 1 ,
  11 4 8 ->= 12 14 9 14 7 4 ,
  11 4 9 ->= 12 14 9 14 7 5 ,
  11 4 10 ->= 12 14 9 14 7 6 ,
  14 7 ->= 11 1 ,
  14 8 ->= 11 4 ,
  14 9 ->= 11 5 ,
  14 10 ->= 11 6 ,
  5 12 14 ->= 4 ,
  9 12 14 ->= 8 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13 }, 
it remains to prove termination of the 31-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 1 ->= 1 ,
  1 3 ->= 3 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  6 1 ->= 6 ,
  6 3 ->= 7 ,
  6 4 ->= 8 ,
  6 5 ->= 9 ,
  10 1 ->= 10 ,
  10 4 ->= 11 ,
  12 1 ->= 12 ,
  1 3 6 ->= 4 13 8 13 6 1 ,
  1 3 7 ->= 4 13 8 13 6 3 ,
  1 3 8 ->= 4 13 8 13 6 4 ,
  1 3 9 ->= 4 13 8 13 6 5 ,
  6 3 6 ->= 8 13 8 13 6 1 ,
  6 3 7 ->= 8 13 8 13 6 3 ,
  6 3 8 ->= 8 13 8 13 6 4 ,
  6 3 9 ->= 8 13 8 13 6 5 ,
  10 3 6 ->= 11 13 8 13 6 1 ,
  10 3 7 ->= 11 13 8 13 6 3 ,
  10 3 8 ->= 11 13 8 13 6 4 ,
  10 3 9 ->= 11 13 8 13 6 5 ,
  13 6 ->= 10 1 ,
  13 7 ->= 10 3 ,
  13 8 ->= 10 4 ,
  13 9 ->= 10 5 ,
  4 11 13 ->= 3 ,
  8 11 13 ->= 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12 }, 
it remains to prove termination of the 30-rule system
{ 0 1 -> 0 ,
  1 1 ->= 1 ,
  1 2 ->= 2 ,
  1 3 ->= 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 2 ->= 6 ,
  5 3 ->= 7 ,
  5 4 ->= 8 ,
  9 1 ->= 9 ,
  9 3 ->= 10 ,
  11 1 ->= 11 ,
  1 2 5 ->= 3 12 7 12 5 1 ,
  1 2 6 ->= 3 12 7 12 5 2 ,
  1 2 7 ->= 3 12 7 12 5 3 ,
  1 2 8 ->= 3 12 7 12 5 4 ,
  5 2 5 ->= 7 12 7 12 5 1 ,
  5 2 6 ->= 7 12 7 12 5 2 ,
  5 2 7 ->= 7 12 7 12 5 3 ,
  5 2 8 ->= 7 12 7 12 5 4 ,
  9 2 5 ->= 10 12 7 12 5 1 ,
  9 2 6 ->= 10 12 7 12 5 2 ,
  9 2 7 ->= 10 12 7 12 5 3 ,
  9 2 8 ->= 10 12 7 12 5 4 ,
  12 5 ->= 9 1 ,
  12 6 ->= 9 2 ,
  12 7 ->= 9 3 ,
  12 8 ->= 9 4 ,
  3 10 12 ->= 2 ,
  7 10 12 ->= 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

The system is trivially terminating.