YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 5-rule system
{ 0 -> ,
  0 0 -> 1 ,
  1 -> 2 ,
  1 2 -> 2 1 0 ,
  2 -> }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2 }, 
it remains to prove termination of the 5-rule system
{ 0 -> ,
  0 0 -> 1 ,
  1 -> 2 ,
  2 1 -> 0 1 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 80-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 0 0 -> 1 4 ,
  0 0 1 -> 1 5 ,
  0 0 2 -> 1 6 ,
  0 0 3 -> 1 7 ,
  4 0 0 -> 5 4 ,
  4 0 1 -> 5 5 ,
  4 0 2 -> 5 6 ,
  4 0 3 -> 5 7 ,
  8 0 0 -> 9 4 ,
  8 0 1 -> 9 5 ,
  8 0 2 -> 9 6 ,
  8 0 3 -> 9 7 ,
  12 0 0 -> 13 4 ,
  12 0 1 -> 13 5 ,
  12 0 2 -> 13 6 ,
  12 0 3 -> 13 7 ,
  1 4 -> 2 8 ,
  1 5 -> 2 9 ,
  1 6 -> 2 10 ,
  1 7 -> 2 11 ,
  5 4 -> 6 8 ,
  5 5 -> 6 9 ,
  5 6 -> 6 10 ,
  5 7 -> 6 11 ,
  9 4 -> 10 8 ,
  9 5 -> 10 9 ,
  9 6 -> 10 10 ,
  9 7 -> 10 11 ,
  13 4 -> 14 8 ,
  13 5 -> 14 9 ,
  13 6 -> 14 10 ,
  13 7 -> 14 11 ,
  2 9 4 -> 0 1 6 8 ,
  2 9 5 -> 0 1 6 9 ,
  2 9 6 -> 0 1 6 10 ,
  2 9 7 -> 0 1 6 11 ,
  6 9 4 -> 4 1 6 8 ,
  6 9 5 -> 4 1 6 9 ,
  6 9 6 -> 4 1 6 10 ,
  6 9 7 -> 4 1 6 11 ,
  10 9 4 -> 8 1 6 8 ,
  10 9 5 -> 8 1 6 9 ,
  10 9 6 -> 8 1 6 10 ,
  10 9 7 -> 8 1 6 11 ,
  14 9 4 -> 12 1 6 8 ,
  14 9 5 -> 12 1 6 9 ,
  14 9 6 -> 12 1 6 10 ,
  14 9 7 -> 12 1 6 11 ,
  2 8 -> 0 ,
  2 9 -> 1 ,
  2 10 -> 2 ,
  2 11 -> 3 ,
  6 8 -> 4 ,
  6 9 -> 5 ,
  6 10 -> 6 ,
  6 11 -> 7 ,
  10 8 -> 8 ,
  10 9 -> 9 ,
  10 10 -> 10 ,
  10 11 -> 11 ,
  14 8 -> 12 ,
  14 9 -> 13 ,
  14 10 -> 14 ,
  14 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 3 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 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 3 |
| 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 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (1,true)->0, (0,false)->1, (6,true)->2, (3,false)->3, (3,true)->4, (2,false)->5, (4,false)->6, (7,false)->7, (8,false)->8, (8,true)->9, (9,false)->10, (10,false)->11, (7,true)->12, (0,true)->13, (1,false)->14, (11,true)->15, (5,false)->16, (6,false)->17, (11,false)->18 },
it remains to prove termination of the 81-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 4 ,
  0 5 -> 2 6 ,
  0 7 -> 2 8 ,
  0 7 -> 9 ,
  0 10 -> 2 11 ,
  2 6 1 -> 0 7 3 ,
  2 6 1 -> 12 3 ,
  2 6 1 -> 4 ,
  2 6 5 -> 0 7 6 ,
  2 6 5 -> 12 6 ,
  2 6 7 -> 0 7 8 ,
  2 6 7 -> 12 8 ,
  2 6 7 -> 9 ,
  2 6 10 -> 0 7 11 ,
  2 6 10 -> 12 11 ,
  12 6 1 -> 13 14 7 3 ,
  12 6 1 -> 0 7 3 ,
  12 6 1 -> 12 3 ,
  12 6 1 -> 4 ,
  12 6 5 -> 13 14 7 6 ,
  12 6 5 -> 0 7 6 ,
  12 6 5 -> 12 6 ,
  12 6 7 -> 13 14 7 8 ,
  12 6 7 -> 0 7 8 ,
  12 6 7 -> 12 8 ,
  12 6 7 -> 9 ,
  12 6 10 -> 13 14 7 11 ,
  12 6 10 -> 0 7 11 ,
  12 6 10 -> 12 11 ,
  9 6 1 -> 4 14 7 3 ,
  9 6 1 -> 0 7 3 ,
  9 6 1 -> 12 3 ,
  9 6 1 -> 4 ,
  9 6 5 -> 4 14 7 6 ,
  9 6 5 -> 0 7 6 ,
  9 6 5 -> 12 6 ,
  9 6 7 -> 4 14 7 8 ,
  9 6 7 -> 0 7 8 ,
  9 6 7 -> 12 8 ,
  9 6 7 -> 9 ,
  9 6 10 -> 4 14 7 11 ,
  9 6 10 -> 0 7 11 ,
  9 6 10 -> 12 11 ,
  2 8 -> 2 ,
  12 3 -> 13 ,
  12 8 -> 12 ,
  9 3 -> 4 ,
  9 8 -> 9 ,
  15 8 -> 15 ,
  1 14 ->= 5 ,
  3 14 ->= 6 ,
  1 16 14 ->= 5 5 ,
  3 16 14 ->= 6 5 ,
  14 1 ->= 17 3 ,
  14 5 ->= 17 6 ,
  14 7 ->= 17 8 ,
  14 10 ->= 17 11 ,
  17 6 1 ->= 16 14 7 3 ,
  17 6 5 ->= 16 14 7 6 ,
  17 6 7 ->= 16 14 7 8 ,
  17 6 10 ->= 16 14 7 11 ,
  7 6 1 ->= 1 14 7 3 ,
  7 6 5 ->= 1 14 7 6 ,
  7 6 7 ->= 1 14 7 8 ,
  7 6 10 ->= 1 14 7 11 ,
  8 6 1 ->= 3 14 7 3 ,
  8 6 5 ->= 3 14 7 6 ,
  8 6 7 ->= 3 14 7 8 ,
  8 6 10 ->= 3 14 7 11 ,
  17 3 ->= 16 ,
  17 8 ->= 17 ,
  7 3 ->= 1 ,
  7 6 ->= 5 ,
  7 8 ->= 7 ,
  7 11 ->= 10 ,
  8 3 ->= 3 ,
  8 6 ->= 6 ,
  8 8 ->= 8 ,
  8 11 ->= 11 ,
  18 8 ->= 18 }


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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 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 |
 \   /
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 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 2->0, 8->1, 12->2, 9->3, 15->4, 1->5, 14->6, 5->7, 3->8, 6->9, 16->10, 17->11, 7->12, 10->13, 11->14, 18->15 }, 
it remains to prove termination of the 35-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 ->= 7 ,
  8 6 ->= 9 ,
  5 10 6 ->= 7 7 ,
  8 10 6 ->= 9 7 ,
  6 5 ->= 11 8 ,
  6 7 ->= 11 9 ,
  6 12 ->= 11 1 ,
  6 13 ->= 11 14 ,
  11 9 5 ->= 10 6 12 8 ,
  11 9 7 ->= 10 6 12 9 ,
  11 9 12 ->= 10 6 12 1 ,
  11 9 13 ->= 10 6 12 14 ,
  12 9 5 ->= 5 6 12 8 ,
  12 9 7 ->= 5 6 12 9 ,
  12 9 12 ->= 5 6 12 1 ,
  12 9 13 ->= 5 6 12 14 ,
  1 9 5 ->= 8 6 12 8 ,
  1 9 7 ->= 8 6 12 9 ,
  1 9 12 ->= 8 6 12 1 ,
  1 9 13 ->= 8 6 12 14 ,
  11 8 ->= 10 ,
  11 1 ->= 11 ,
  12 8 ->= 5 ,
  12 9 ->= 7 ,
  12 1 ->= 12 ,
  12 14 ->= 13 ,
  1 8 ->= 8 ,
  1 9 ->= 9 ,
  1 1 ->= 1 ,
  1 14 ->= 14 ,
  15 1 ->= 15 }


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 34-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 ->= 6 ,
  7 5 ->= 8 ,
  4 9 5 ->= 6 6 ,
  7 9 5 ->= 8 6 ,
  5 4 ->= 10 7 ,
  5 6 ->= 10 8 ,
  5 11 ->= 10 1 ,
  5 12 ->= 10 13 ,
  10 8 4 ->= 9 5 11 7 ,
  10 8 6 ->= 9 5 11 8 ,
  10 8 11 ->= 9 5 11 1 ,
  10 8 12 ->= 9 5 11 13 ,
  11 8 4 ->= 4 5 11 7 ,
  11 8 6 ->= 4 5 11 8 ,
  11 8 11 ->= 4 5 11 1 ,
  11 8 12 ->= 4 5 11 13 ,
  1 8 4 ->= 7 5 11 7 ,
  1 8 6 ->= 7 5 11 8 ,
  1 8 11 ->= 7 5 11 1 ,
  1 8 12 ->= 7 5 11 13 ,
  10 7 ->= 9 ,
  10 1 ->= 10 ,
  11 7 ->= 4 ,
  11 8 ->= 6 ,
  11 1 ->= 11 ,
  11 13 ->= 12 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  1 1 ->= 1 ,
  1 13 ->= 13 ,
  14 1 ->= 14 }


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 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 ->= 5 ,
  6 4 ->= 7 ,
  3 8 4 ->= 5 5 ,
  6 8 4 ->= 7 5 ,
  4 3 ->= 9 6 ,
  4 5 ->= 9 7 ,
  4 10 ->= 9 1 ,
  4 11 ->= 9 12 ,
  9 7 3 ->= 8 4 10 6 ,
  9 7 5 ->= 8 4 10 7 ,
  9 7 10 ->= 8 4 10 1 ,
  9 7 11 ->= 8 4 10 12 ,
  10 7 3 ->= 3 4 10 6 ,
  10 7 5 ->= 3 4 10 7 ,
  10 7 10 ->= 3 4 10 1 ,
  10 7 11 ->= 3 4 10 12 ,
  1 7 3 ->= 6 4 10 6 ,
  1 7 5 ->= 6 4 10 7 ,
  1 7 10 ->= 6 4 10 1 ,
  1 7 11 ->= 6 4 10 12 ,
  9 6 ->= 8 ,
  9 1 ->= 9 ,
  10 6 ->= 3 ,
  10 7 ->= 5 ,
  10 1 ->= 10 ,
  10 12 ->= 11 ,
  1 6 ->= 6 ,
  1 7 ->= 7 ,
  1 1 ->= 1 ,
  1 12 ->= 12 ,
  13 1 ->= 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 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 32-rule system
{ 0 1 -> 0 ,
  2 3 ->= 4 ,
  5 3 ->= 6 ,
  2 7 3 ->= 4 4 ,
  5 7 3 ->= 6 4 ,
  3 2 ->= 8 5 ,
  3 4 ->= 8 6 ,
  3 9 ->= 8 1 ,
  3 10 ->= 8 11 ,
  8 6 2 ->= 7 3 9 5 ,
  8 6 4 ->= 7 3 9 6 ,
  8 6 9 ->= 7 3 9 1 ,
  8 6 10 ->= 7 3 9 11 ,
  9 6 2 ->= 2 3 9 5 ,
  9 6 4 ->= 2 3 9 6 ,
  9 6 9 ->= 2 3 9 1 ,
  9 6 10 ->= 2 3 9 11 ,
  1 6 2 ->= 5 3 9 5 ,
  1 6 4 ->= 5 3 9 6 ,
  1 6 9 ->= 5 3 9 1 ,
  1 6 10 ->= 5 3 9 11 ,
  8 5 ->= 7 ,
  8 1 ->= 8 ,
  9 5 ->= 2 ,
  9 6 ->= 4 ,
  9 1 ->= 9 ,
  9 11 ->= 10 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  1 1 ->= 1 ,
  1 11 ->= 11 ,
  12 1 ->= 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 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 { 2->0, 3->1, 4->2, 5->3, 6->4, 7->5, 8->6, 9->7, 1->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 31-rule system
{ 0 1 ->= 2 ,
  3 1 ->= 4 ,
  0 5 1 ->= 2 2 ,
  3 5 1 ->= 4 2 ,
  1 0 ->= 6 3 ,
  1 2 ->= 6 4 ,
  1 7 ->= 6 8 ,
  1 9 ->= 6 10 ,
  6 4 0 ->= 5 1 7 3 ,
  6 4 2 ->= 5 1 7 4 ,
  6 4 7 ->= 5 1 7 8 ,
  6 4 9 ->= 5 1 7 10 ,
  7 4 0 ->= 0 1 7 3 ,
  7 4 2 ->= 0 1 7 4 ,
  7 4 7 ->= 0 1 7 8 ,
  7 4 9 ->= 0 1 7 10 ,
  8 4 0 ->= 3 1 7 3 ,
  8 4 2 ->= 3 1 7 4 ,
  8 4 7 ->= 3 1 7 8 ,
  8 4 9 ->= 3 1 7 10 ,
  6 3 ->= 5 ,
  6 8 ->= 6 ,
  7 3 ->= 0 ,
  7 4 ->= 2 ,
  7 8 ->= 7 ,
  7 10 ->= 9 ,
  8 3 ->= 3 ,
  8 4 ->= 4 ,
  8 8 ->= 8 ,
  8 10 ->= 10 ,
  11 8 ->= 11 }

The system is trivially terminating.