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 ,
  1 -> 0 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 1 5 -> 2 9 6 9 5 ,
  0 1 6 -> 2 9 6 9 6 ,
  0 1 7 -> 2 9 6 9 7 ,
  4 1 4 -> 6 9 6 9 4 ,
  4 1 5 -> 6 9 6 9 5 ,
  4 1 6 -> 6 9 6 9 6 ,
  4 1 7 -> 6 9 6 9 7 ,
  8 1 4 -> 10 9 6 9 4 ,
  8 1 5 -> 10 9 6 9 5 ,
  8 1 6 -> 10 9 6 9 6 ,
  8 1 7 -> 10 9 6 9 7 ,
  12 1 4 -> 14 9 6 9 4 ,
  12 1 5 -> 14 9 6 9 5 ,
  12 1 6 -> 14 9 6 9 6 ,
  12 1 7 -> 14 9 6 9 7 ,
  1 4 -> 0 0 0 ,
  1 5 -> 0 0 1 ,
  1 6 -> 0 0 2 ,
  1 7 -> 0 0 3 ,
  5 4 -> 4 0 0 ,
  5 5 -> 4 0 1 ,
  5 6 -> 4 0 2 ,
  5 7 -> 4 0 3 ,
  9 4 -> 8 0 0 ,
  9 5 -> 8 0 1 ,
  9 6 -> 8 0 2 ,
  9 7 -> 8 0 3 ,
  13 4 -> 12 0 0 ,
  13 5 -> 12 0 1 ,
  13 6 -> 12 0 2 ,
  13 7 -> 12 0 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 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 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, 8->5, 10->6, 12->7, 9->8, 6->9, 5->10, 7->11 }, 
it remains to prove termination of the 20-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  5 0 -> 5 ,
  5 2 -> 6 ,
  7 0 -> 7 ,
  0 1 4 -> 2 8 9 8 4 ,
  0 1 10 -> 2 8 9 8 10 ,
  0 1 9 -> 2 8 9 8 9 ,
  0 1 11 -> 2 8 9 8 11 ,
  5 1 4 -> 6 8 9 8 4 ,
  5 1 10 -> 6 8 9 8 10 ,
  5 1 9 -> 6 8 9 8 9 ,
  5 1 11 -> 6 8 9 8 11 ,
  8 10 -> 5 0 1 ,
  8 9 -> 5 0 2 ,
  2 6 8 -> 1 ,
  9 6 8 -> 10 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 19-rule system
{ 0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  5 0 -> 5 ,
  5 2 -> 6 ,
  7 0 -> 7 ,
  0 1 4 -> 2 8 9 8 4 ,
  0 1 10 -> 2 8 9 8 10 ,
  0 1 9 -> 2 8 9 8 9 ,
  0 1 11 -> 2 8 9 8 11 ,
  5 1 4 -> 6 8 9 8 4 ,
  5 1 10 -> 6 8 9 8 10 ,
  5 1 9 -> 6 8 9 8 9 ,
  5 1 11 -> 6 8 9 8 11 ,
  8 10 -> 5 0 1 ,
  8 9 -> 5 0 2 ,
  2 6 8 -> 1 ,
  9 6 8 -> 10 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (2,false)->1, (2,true)->2, (4,true)->3, (0,false)->4, (5,true)->5, (7,true)->6, (1,false)->7, (4,false)->8, (8,false)->9, (9,false)->10, (8,true)->11, (9,true)->12, (10,false)->13, (11,false)->14, (3,false)->15, (5,false)->16, (6,false)->17, (7,false)->18 },
it remains to prove termination of the 60-rule system
{ 0 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  0 7 8 -> 2 9 10 9 8 ,
  0 7 8 -> 11 10 9 8 ,
  0 7 8 -> 12 9 8 ,
  0 7 8 -> 11 8 ,
  0 7 8 -> 3 ,
  0 7 13 -> 2 9 10 9 13 ,
  0 7 13 -> 11 10 9 13 ,
  0 7 13 -> 12 9 13 ,
  0 7 13 -> 11 13 ,
  0 7 10 -> 2 9 10 9 10 ,
  0 7 10 -> 11 10 9 10 ,
  0 7 10 -> 12 9 10 ,
  0 7 10 -> 11 10 ,
  0 7 10 -> 12 ,
  0 7 14 -> 2 9 10 9 14 ,
  0 7 14 -> 11 10 9 14 ,
  0 7 14 -> 12 9 14 ,
  0 7 14 -> 11 14 ,
  5 7 8 -> 11 10 9 8 ,
  5 7 8 -> 12 9 8 ,
  5 7 8 -> 11 8 ,
  5 7 8 -> 3 ,
  5 7 13 -> 11 10 9 13 ,
  5 7 13 -> 12 9 13 ,
  5 7 13 -> 11 13 ,
  5 7 10 -> 11 10 9 10 ,
  5 7 10 -> 12 9 10 ,
  5 7 10 -> 11 10 ,
  5 7 10 -> 12 ,
  5 7 14 -> 11 10 9 14 ,
  5 7 14 -> 12 9 14 ,
  5 7 14 -> 11 14 ,
  11 13 -> 5 4 7 ,
  11 13 -> 0 7 ,
  11 10 -> 5 4 1 ,
  11 10 -> 0 1 ,
  11 10 -> 2 ,
  4 7 ->= 7 ,
  4 1 ->= 1 ,
  4 15 ->= 15 ,
  8 4 ->= 8 ,
  16 4 ->= 16 ,
  16 1 ->= 17 ,
  18 4 ->= 18 ,
  4 7 8 ->= 1 9 10 9 8 ,
  4 7 13 ->= 1 9 10 9 13 ,
  4 7 10 ->= 1 9 10 9 10 ,
  4 7 14 ->= 1 9 10 9 14 ,
  16 7 8 ->= 17 9 10 9 8 ,
  16 7 13 ->= 17 9 10 9 13 ,
  16 7 10 ->= 17 9 10 9 10 ,
  16 7 14 ->= 17 9 10 9 14 ,
  9 13 ->= 16 4 7 ,
  9 10 ->= 16 4 1 ,
  1 17 9 ->= 7 ,
  10 17 9 ->= 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 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 0 |
| 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 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 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, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 58-rule system
{ 0 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  0 7 8 -> 2 9 10 9 8 ,
  0 7 8 -> 11 10 9 8 ,
  0 7 8 -> 12 9 8 ,
  0 7 8 -> 11 8 ,
  0 7 13 -> 2 9 10 9 13 ,
  0 7 13 -> 11 10 9 13 ,
  0 7 13 -> 12 9 13 ,
  0 7 13 -> 11 13 ,
  0 7 10 -> 2 9 10 9 10 ,
  0 7 10 -> 11 10 9 10 ,
  0 7 10 -> 12 9 10 ,
  0 7 10 -> 11 10 ,
  0 7 10 -> 12 ,
  0 7 14 -> 2 9 10 9 14 ,
  0 7 14 -> 11 10 9 14 ,
  0 7 14 -> 12 9 14 ,
  0 7 14 -> 11 14 ,
  5 7 8 -> 11 10 9 8 ,
  5 7 8 -> 12 9 8 ,
  5 7 8 -> 11 8 ,
  5 7 13 -> 11 10 9 13 ,
  5 7 13 -> 12 9 13 ,
  5 7 13 -> 11 13 ,
  5 7 10 -> 11 10 9 10 ,
  5 7 10 -> 12 9 10 ,
  5 7 10 -> 11 10 ,
  5 7 10 -> 12 ,
  5 7 14 -> 11 10 9 14 ,
  5 7 14 -> 12 9 14 ,
  5 7 14 -> 11 14 ,
  11 13 -> 5 4 7 ,
  11 13 -> 0 7 ,
  11 10 -> 5 4 1 ,
  11 10 -> 0 1 ,
  11 10 -> 2 ,
  4 7 ->= 7 ,
  4 1 ->= 1 ,
  4 15 ->= 15 ,
  8 4 ->= 8 ,
  16 4 ->= 16 ,
  16 1 ->= 17 ,
  18 4 ->= 18 ,
  4 7 8 ->= 1 9 10 9 8 ,
  4 7 13 ->= 1 9 10 9 13 ,
  4 7 10 ->= 1 9 10 9 10 ,
  4 7 14 ->= 1 9 10 9 14 ,
  16 7 8 ->= 17 9 10 9 8 ,
  16 7 13 ->= 17 9 10 9 13 ,
  16 7 10 ->= 17 9 10 9 10 ,
  16 7 14 ->= 17 9 10 9 14 ,
  9 13 ->= 16 4 7 ,
  9 10 ->= 16 4 1 ,
  1 17 9 ->= 7 ,
  10 17 9 ->= 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 2 |
| 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 4 |
| 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 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 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 { 3->0, 4->1, 5->2, 6->3, 7->4, 1->5, 15->6, 8->7, 16->8, 17->9, 18->10, 9->11, 10->12, 13->13, 14->14 }, 
it remains to prove termination of the 22-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  7 1 ->= 7 ,
  8 1 ->= 8 ,
  8 5 ->= 9 ,
  10 1 ->= 10 ,
  1 4 7 ->= 5 11 12 11 7 ,
  1 4 13 ->= 5 11 12 11 13 ,
  1 4 12 ->= 5 11 12 11 12 ,
  1 4 14 ->= 5 11 12 11 14 ,
  8 4 7 ->= 9 11 12 11 7 ,
  8 4 13 ->= 9 11 12 11 13 ,
  8 4 12 ->= 9 11 12 11 12 ,
  8 4 14 ->= 9 11 12 11 14 ,
  11 13 ->= 8 1 4 ,
  11 12 ->= 8 1 5 ,
  5 9 11 ->= 4 ,
  12 9 11 ->= 13 }


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 21-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 3 ->= 3 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  6 1 ->= 6 ,
  7 1 ->= 7 ,
  7 4 ->= 8 ,
  9 1 ->= 9 ,
  1 3 6 ->= 4 10 11 10 6 ,
  1 3 12 ->= 4 10 11 10 12 ,
  1 3 11 ->= 4 10 11 10 11 ,
  1 3 13 ->= 4 10 11 10 13 ,
  7 3 6 ->= 8 10 11 10 6 ,
  7 3 12 ->= 8 10 11 10 12 ,
  7 3 11 ->= 8 10 11 10 11 ,
  7 3 13 ->= 8 10 11 10 13 ,
  10 12 ->= 7 1 3 ,
  10 11 ->= 7 1 4 ,
  4 8 10 ->= 3 ,
  11 8 10 ->= 12 }


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 20-rule system
{ 0 1 -> 0 ,
  1 2 ->= 2 ,
  1 3 ->= 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  6 1 ->= 6 ,
  6 3 ->= 7 ,
  8 1 ->= 8 ,
  1 2 5 ->= 3 9 10 9 5 ,
  1 2 11 ->= 3 9 10 9 11 ,
  1 2 10 ->= 3 9 10 9 10 ,
  1 2 12 ->= 3 9 10 9 12 ,
  6 2 5 ->= 7 9 10 9 5 ,
  6 2 11 ->= 7 9 10 9 11 ,
  6 2 10 ->= 7 9 10 9 10 ,
  6 2 12 ->= 7 9 10 9 12 ,
  9 11 ->= 6 1 2 ,
  9 10 ->= 6 1 3 ,
  3 7 9 ->= 2 ,
  10 7 9 ->= 11 }


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 19-rule system
{ 0 1 ->= 1 ,
  0 2 ->= 2 ,
  0 3 ->= 3 ,
  4 0 ->= 4 ,
  5 0 ->= 5 ,
  5 2 ->= 6 ,
  7 0 ->= 7 ,
  0 1 4 ->= 2 8 9 8 4 ,
  0 1 10 ->= 2 8 9 8 10 ,
  0 1 9 ->= 2 8 9 8 9 ,
  0 1 11 ->= 2 8 9 8 11 ,
  5 1 4 ->= 6 8 9 8 4 ,
  5 1 10 ->= 6 8 9 8 10 ,
  5 1 9 ->= 6 8 9 8 9 ,
  5 1 11 ->= 6 8 9 8 11 ,
  8 10 ->= 5 0 1 ,
  8 9 ->= 5 0 2 ,
  2 6 8 ->= 1 ,
  9 6 8 ->= 10 }

The system is trivially terminating.