YES

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


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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 2 |
| 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 1 |
| 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 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 4->0, 1->1, 5->2, 2->3, 6->4, 8->5, 9->6, 10->7, 0->8, 12->9 }, 
it remains to prove termination of the 22-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  5 1 -> 6 ,
  5 3 -> 7 ,
  8 8 1 -> 8 1 2 ,
  8 8 3 -> 8 1 4 ,
  0 8 1 -> 0 1 2 ,
  0 8 3 -> 0 1 4 ,
  5 8 1 -> 5 1 2 ,
  5 8 3 -> 5 1 4 ,
  9 8 1 -> 9 1 2 ,
  9 8 3 -> 9 1 4 ,
  1 0 -> 8 ,
  3 6 0 -> 1 0 3 7 5 ,
  3 6 2 -> 1 0 3 7 6 ,
  3 6 4 -> 1 0 3 7 7 ,
  4 6 0 -> 2 0 3 7 5 ,
  4 6 2 -> 2 0 3 7 6 ,
  4 6 4 -> 2 0 3 7 7 ,
  7 6 0 -> 6 0 3 7 5 ,
  7 6 2 -> 6 0 3 7 6 ,
  7 6 4 -> 6 0 3 7 7 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (3,false)->1, (4,true)->2, (5,true)->3, (7,true)->4, (8,true)->5, (8,false)->6, (1,false)->7, (2,false)->8, (1,true)->9, (4,false)->10, (9,true)->11, (0,false)->12, (3,true)->13, (6,false)->14, (7,false)->15, (5,false)->16, (9,false)->17 },
it remains to prove termination of the 81-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  5 6 7 -> 5 7 8 ,
  5 6 7 -> 9 8 ,
  5 6 1 -> 5 7 10 ,
  5 6 1 -> 9 10 ,
  5 6 1 -> 2 ,
  0 6 7 -> 0 7 8 ,
  0 6 7 -> 9 8 ,
  0 6 1 -> 0 7 10 ,
  0 6 1 -> 9 10 ,
  0 6 1 -> 2 ,
  3 6 7 -> 3 7 8 ,
  3 6 7 -> 9 8 ,
  3 6 1 -> 3 7 10 ,
  3 6 1 -> 9 10 ,
  3 6 1 -> 2 ,
  11 6 7 -> 11 7 8 ,
  11 6 7 -> 9 8 ,
  11 6 1 -> 11 7 10 ,
  11 6 1 -> 9 10 ,
  11 6 1 -> 2 ,
  9 12 -> 5 ,
  13 14 12 -> 9 12 1 15 16 ,
  13 14 12 -> 0 1 15 16 ,
  13 14 12 -> 13 15 16 ,
  13 14 12 -> 4 16 ,
  13 14 12 -> 3 ,
  13 14 8 -> 9 12 1 15 14 ,
  13 14 8 -> 0 1 15 14 ,
  13 14 8 -> 13 15 14 ,
  13 14 8 -> 4 14 ,
  13 14 10 -> 9 12 1 15 15 ,
  13 14 10 -> 0 1 15 15 ,
  13 14 10 -> 13 15 15 ,
  13 14 10 -> 4 15 ,
  13 14 10 -> 4 ,
  2 14 12 -> 0 1 15 16 ,
  2 14 12 -> 13 15 16 ,
  2 14 12 -> 4 16 ,
  2 14 12 -> 3 ,
  2 14 8 -> 0 1 15 14 ,
  2 14 8 -> 13 15 14 ,
  2 14 8 -> 4 14 ,
  2 14 10 -> 0 1 15 15 ,
  2 14 10 -> 13 15 15 ,
  2 14 10 -> 4 15 ,
  2 14 10 -> 4 ,
  4 14 12 -> 0 1 15 16 ,
  4 14 12 -> 13 15 16 ,
  4 14 12 -> 4 16 ,
  4 14 12 -> 3 ,
  4 14 8 -> 0 1 15 14 ,
  4 14 8 -> 13 15 14 ,
  4 14 8 -> 4 14 ,
  4 14 10 -> 0 1 15 15 ,
  4 14 10 -> 13 15 15 ,
  4 14 10 -> 4 15 ,
  4 14 10 -> 4 ,
  12 7 ->= 8 ,
  12 1 ->= 10 ,
  16 7 ->= 14 ,
  16 1 ->= 15 ,
  6 6 7 ->= 6 7 8 ,
  6 6 1 ->= 6 7 10 ,
  12 6 7 ->= 12 7 8 ,
  12 6 1 ->= 12 7 10 ,
  16 6 7 ->= 16 7 8 ,
  16 6 1 ->= 16 7 10 ,
  17 6 7 ->= 17 7 8 ,
  17 6 1 ->= 17 7 10 ,
  7 12 ->= 6 ,
  1 14 12 ->= 7 12 1 15 16 ,
  1 14 8 ->= 7 12 1 15 14 ,
  1 14 10 ->= 7 12 1 15 15 ,
  10 14 12 ->= 8 12 1 15 16 ,
  10 14 8 ->= 8 12 1 15 14 ,
  10 14 10 ->= 8 12 1 15 15 ,
  15 14 12 ->= 14 12 1 15 16 ,
  15 14 8 ->= 14 12 1 15 14 ,
  15 14 10 ->= 14 12 1 15 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 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 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 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 0 |
| 0 1 |
 \   /
17 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 }, 
it remains to prove termination of the 78-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  5 6 7 -> 5 7 8 ,
  5 6 7 -> 9 8 ,
  5 6 1 -> 5 7 10 ,
  5 6 1 -> 9 10 ,
  5 6 1 -> 2 ,
  0 6 7 -> 0 7 8 ,
  0 6 7 -> 9 8 ,
  0 6 1 -> 0 7 10 ,
  0 6 1 -> 9 10 ,
  0 6 1 -> 2 ,
  3 6 7 -> 3 7 8 ,
  3 6 7 -> 9 8 ,
  3 6 1 -> 3 7 10 ,
  3 6 1 -> 9 10 ,
  3 6 1 -> 2 ,
  11 6 7 -> 11 7 8 ,
  11 6 1 -> 11 7 10 ,
  9 12 -> 5 ,
  13 14 12 -> 9 12 1 15 16 ,
  13 14 12 -> 0 1 15 16 ,
  13 14 12 -> 13 15 16 ,
  13 14 12 -> 4 16 ,
  13 14 12 -> 3 ,
  13 14 8 -> 9 12 1 15 14 ,
  13 14 8 -> 0 1 15 14 ,
  13 14 8 -> 13 15 14 ,
  13 14 8 -> 4 14 ,
  13 14 10 -> 9 12 1 15 15 ,
  13 14 10 -> 0 1 15 15 ,
  13 14 10 -> 13 15 15 ,
  13 14 10 -> 4 15 ,
  13 14 10 -> 4 ,
  2 14 12 -> 0 1 15 16 ,
  2 14 12 -> 13 15 16 ,
  2 14 12 -> 4 16 ,
  2 14 12 -> 3 ,
  2 14 8 -> 0 1 15 14 ,
  2 14 8 -> 13 15 14 ,
  2 14 8 -> 4 14 ,
  2 14 10 -> 0 1 15 15 ,
  2 14 10 -> 13 15 15 ,
  2 14 10 -> 4 15 ,
  2 14 10 -> 4 ,
  4 14 12 -> 0 1 15 16 ,
  4 14 12 -> 13 15 16 ,
  4 14 12 -> 4 16 ,
  4 14 12 -> 3 ,
  4 14 8 -> 0 1 15 14 ,
  4 14 8 -> 13 15 14 ,
  4 14 8 -> 4 14 ,
  4 14 10 -> 0 1 15 15 ,
  4 14 10 -> 13 15 15 ,
  4 14 10 -> 4 15 ,
  4 14 10 -> 4 ,
  12 7 ->= 8 ,
  12 1 ->= 10 ,
  16 7 ->= 14 ,
  16 1 ->= 15 ,
  6 6 7 ->= 6 7 8 ,
  6 6 1 ->= 6 7 10 ,
  12 6 7 ->= 12 7 8 ,
  12 6 1 ->= 12 7 10 ,
  16 6 7 ->= 16 7 8 ,
  16 6 1 ->= 16 7 10 ,
  17 6 7 ->= 17 7 8 ,
  17 6 1 ->= 17 7 10 ,
  7 12 ->= 6 ,
  1 14 12 ->= 7 12 1 15 16 ,
  1 14 8 ->= 7 12 1 15 14 ,
  1 14 10 ->= 7 12 1 15 15 ,
  10 14 12 ->= 8 12 1 15 16 ,
  10 14 8 ->= 8 12 1 15 14 ,
  10 14 10 ->= 8 12 1 15 15 ,
  15 14 12 ->= 14 12 1 15 16 ,
  15 14 8 ->= 14 12 1 15 14 ,
  15 14 10 ->= 14 12 1 15 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 1 |
| 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 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 2 |
| 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 1 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 6->1, 7->2, 8->3, 1->4, 10->5, 0->6, 3->7, 11->8, 12->9, 16->10, 14->11, 15->12, 17->13 }, 
it remains to prove termination of the 30-rule system
{ 0 1 2 -> 0 2 3 ,
  0 1 4 -> 0 2 5 ,
  6 1 2 -> 6 2 3 ,
  6 1 4 -> 6 2 5 ,
  7 1 2 -> 7 2 3 ,
  7 1 4 -> 7 2 5 ,
  8 1 2 -> 8 2 3 ,
  8 1 4 -> 8 2 5 ,
  9 2 ->= 3 ,
  9 4 ->= 5 ,
  10 2 ->= 11 ,
  10 4 ->= 12 ,
  1 1 2 ->= 1 2 3 ,
  1 1 4 ->= 1 2 5 ,
  9 1 2 ->= 9 2 3 ,
  9 1 4 ->= 9 2 5 ,
  10 1 2 ->= 10 2 3 ,
  10 1 4 ->= 10 2 5 ,
  13 1 2 ->= 13 2 3 ,
  13 1 4 ->= 13 2 5 ,
  2 9 ->= 1 ,
  4 11 9 ->= 2 9 4 12 10 ,
  4 11 3 ->= 2 9 4 12 11 ,
  4 11 5 ->= 2 9 4 12 12 ,
  5 11 9 ->= 3 9 4 12 10 ,
  5 11 3 ->= 3 9 4 12 11 ,
  5 11 5 ->= 3 9 4 12 12 ,
  12 11 9 ->= 11 9 4 12 10 ,
  12 11 3 ->= 11 9 4 12 11 ,
  12 11 5 ->= 11 9 4 12 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
8 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
10 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
13 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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, 9->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 28-rule system
{ 0 1 2 -> 0 2 3 ,
  0 1 4 -> 0 2 5 ,
  6 1 2 -> 6 2 3 ,
  7 1 2 -> 7 2 3 ,
  7 1 4 -> 7 2 5 ,
  8 1 2 -> 8 2 3 ,
  9 2 ->= 3 ,
  9 4 ->= 5 ,
  10 2 ->= 11 ,
  10 4 ->= 12 ,
  1 1 2 ->= 1 2 3 ,
  1 1 4 ->= 1 2 5 ,
  9 1 2 ->= 9 2 3 ,
  9 1 4 ->= 9 2 5 ,
  10 1 2 ->= 10 2 3 ,
  10 1 4 ->= 10 2 5 ,
  13 1 2 ->= 13 2 3 ,
  13 1 4 ->= 13 2 5 ,
  2 9 ->= 1 ,
  4 11 9 ->= 2 9 4 12 10 ,
  4 11 3 ->= 2 9 4 12 11 ,
  4 11 5 ->= 2 9 4 12 12 ,
  5 11 9 ->= 3 9 4 12 10 ,
  5 11 3 ->= 3 9 4 12 11 ,
  5 11 5 ->= 3 9 4 12 12 ,
  12 11 9 ->= 11 9 4 12 10 ,
  12 11 3 ->= 11 9 4 12 11 ,
  12 11 5 ->= 11 9 4 12 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 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 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
10 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
13 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 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, 9->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 27-rule system
{ 0 1 2 -> 0 2 3 ,
  0 1 4 -> 0 2 5 ,
  6 1 2 -> 6 2 3 ,
  7 1 2 -> 7 2 3 ,
  7 1 4 -> 7 2 5 ,
  8 1 2 -> 8 2 3 ,
  9 2 ->= 3 ,
  9 4 ->= 5 ,
  10 2 ->= 11 ,
  10 4 ->= 12 ,
  1 1 2 ->= 1 2 3 ,
  1 1 4 ->= 1 2 5 ,
  9 1 2 ->= 9 2 3 ,
  9 1 4 ->= 9 2 5 ,
  10 1 2 ->= 10 2 3 ,
  10 1 4 ->= 10 2 5 ,
  13 1 2 ->= 13 2 3 ,
  2 9 ->= 1 ,
  4 11 9 ->= 2 9 4 12 10 ,
  4 11 3 ->= 2 9 4 12 11 ,
  4 11 5 ->= 2 9 4 12 12 ,
  5 11 9 ->= 3 9 4 12 10 ,
  5 11 3 ->= 3 9 4 12 11 ,
  5 11 5 ->= 3 9 4 12 12 ,
  12 11 9 ->= 11 9 4 12 10 ,
  12 11 3 ->= 11 9 4 12 11 ,
  12 11 5 ->= 11 9 4 12 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 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 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
10 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
13 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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, 6->4, 7->5, 4->6, 5->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 26-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 1 2 -> 5 2 3 ,
  5 1 6 -> 5 2 7 ,
  8 1 2 -> 8 2 3 ,
  9 2 ->= 3 ,
  9 6 ->= 7 ,
  10 2 ->= 11 ,
  10 6 ->= 12 ,
  1 1 2 ->= 1 2 3 ,
  1 1 6 ->= 1 2 7 ,
  9 1 2 ->= 9 2 3 ,
  9 1 6 ->= 9 2 7 ,
  10 1 2 ->= 10 2 3 ,
  10 1 6 ->= 10 2 7 ,
  13 1 2 ->= 13 2 3 ,
  2 9 ->= 1 ,
  6 11 9 ->= 2 9 6 12 10 ,
  6 11 3 ->= 2 9 6 12 11 ,
  6 11 7 ->= 2 9 6 12 12 ,
  7 11 9 ->= 3 9 6 12 10 ,
  7 11 3 ->= 3 9 6 12 11 ,
  7 11 7 ->= 3 9 6 12 12 ,
  12 11 9 ->= 11 9 6 12 10 ,
  12 11 3 ->= 11 9 6 12 11 ,
  12 11 7 ->= 11 9 6 12 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 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 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 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 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
10 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
13 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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, 8->6, 9->7, 6->8, 7->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 25-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 1 2 -> 5 2 3 ,
  6 1 2 -> 6 2 3 ,
  7 2 ->= 3 ,
  7 8 ->= 9 ,
  10 2 ->= 11 ,
  10 8 ->= 12 ,
  1 1 2 ->= 1 2 3 ,
  1 1 8 ->= 1 2 9 ,
  7 1 2 ->= 7 2 3 ,
  7 1 8 ->= 7 2 9 ,
  10 1 2 ->= 10 2 3 ,
  10 1 8 ->= 10 2 9 ,
  13 1 2 ->= 13 2 3 ,
  2 7 ->= 1 ,
  8 11 7 ->= 2 7 8 12 10 ,
  8 11 3 ->= 2 7 8 12 11 ,
  8 11 9 ->= 2 7 8 12 12 ,
  9 11 7 ->= 3 7 8 12 10 ,
  9 11 3 ->= 3 7 8 12 11 ,
  9 11 9 ->= 3 7 8 12 12 ,
  12 11 7 ->= 11 7 8 12 10 ,
  12 11 3 ->= 11 7 8 12 11 ,
  12 11 9 ->= 11 7 8 12 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
8 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
9 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
13 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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, 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 24-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 1 2 -> 5 2 3 ,
  6 2 ->= 3 ,
  6 7 ->= 8 ,
  9 2 ->= 10 ,
  9 7 ->= 11 ,
  1 1 2 ->= 1 2 3 ,
  1 1 7 ->= 1 2 8 ,
  6 1 2 ->= 6 2 3 ,
  6 1 7 ->= 6 2 8 ,
  9 1 2 ->= 9 2 3 ,
  9 1 7 ->= 9 2 8 ,
  12 1 2 ->= 12 2 3 ,
  2 6 ->= 1 ,
  7 10 6 ->= 2 6 7 11 9 ,
  7 10 3 ->= 2 6 7 11 10 ,
  7 10 8 ->= 2 6 7 11 11 ,
  8 10 6 ->= 3 6 7 11 9 ,
  8 10 3 ->= 3 6 7 11 10 ,
  8 10 8 ->= 3 6 7 11 11 ,
  11 10 6 ->= 10 6 7 11 9 ,
  11 10 3 ->= 10 6 7 11 10 ,
  11 10 8 ->= 10 6 7 11 11 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
4 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
8 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
12 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 23-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 2 ->= 3 ,
  5 6 ->= 7 ,
  8 2 ->= 9 ,
  8 6 ->= 10 ,
  1 1 2 ->= 1 2 3 ,
  1 1 6 ->= 1 2 7 ,
  5 1 2 ->= 5 2 3 ,
  5 1 6 ->= 5 2 7 ,
  8 1 2 ->= 8 2 3 ,
  8 1 6 ->= 8 2 7 ,
  11 1 2 ->= 11 2 3 ,
  2 5 ->= 1 ,
  6 9 5 ->= 2 5 6 10 8 ,
  6 9 3 ->= 2 5 6 10 9 ,
  6 9 7 ->= 2 5 6 10 10 ,
  7 9 5 ->= 3 5 6 10 8 ,
  7 9 3 ->= 3 5 6 10 9 ,
  7 9 7 ->= 3 5 6 10 10 ,
  10 9 5 ->= 9 5 6 10 8 ,
  10 9 3 ->= 9 5 6 10 9 ,
  10 9 7 ->= 9 5 6 10 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 1 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 1 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
3 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
5 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 0 |
 \         /
6 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
 \         /
7 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 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 1 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 1 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 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
11 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 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, 9->9, 10->10 }, 
it remains to prove termination of the 22-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 2 ->= 3 ,
  5 6 ->= 7 ,
  8 2 ->= 9 ,
  8 6 ->= 10 ,
  1 1 2 ->= 1 2 3 ,
  1 1 6 ->= 1 2 7 ,
  5 1 2 ->= 5 2 3 ,
  5 1 6 ->= 5 2 7 ,
  8 1 2 ->= 8 2 3 ,
  8 1 6 ->= 8 2 7 ,
  2 5 ->= 1 ,
  6 9 5 ->= 2 5 6 10 8 ,
  6 9 3 ->= 2 5 6 10 9 ,
  6 9 7 ->= 2 5 6 10 10 ,
  7 9 5 ->= 3 5 6 10 8 ,
  7 9 3 ->= 3 5 6 10 9 ,
  7 9 7 ->= 3 5 6 10 10 ,
  10 9 5 ->= 9 5 6 10 8 ,
  10 9 3 ->= 9 5 6 10 9 ,
  10 9 7 ->= 9 5 6 10 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 4->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 -> 0 2 3 ,
  4 2 ->= 3 ,
  4 5 ->= 6 ,
  7 2 ->= 8 ,
  7 5 ->= 9 ,
  1 1 2 ->= 1 2 3 ,
  1 1 5 ->= 1 2 6 ,
  4 1 2 ->= 4 2 3 ,
  4 1 5 ->= 4 2 6 ,
  7 1 2 ->= 7 2 3 ,
  7 1 5 ->= 7 2 6 ,
  2 4 ->= 1 ,
  5 8 4 ->= 2 4 5 9 7 ,
  5 8 3 ->= 2 4 5 9 8 ,
  5 8 6 ->= 2 4 5 9 9 ,
  6 8 4 ->= 3 4 5 9 7 ,
  6 8 3 ->= 3 4 5 9 8 ,
  6 8 6 ->= 3 4 5 9 9 ,
  9 8 4 ->= 8 4 5 9 7 ,
  9 8 3 ->= 8 4 5 9 8 ,
  9 8 6 ->= 8 4 5 9 9 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 4->0, 2->1, 3->2, 5->3, 6->4, 7->5, 8->6, 9->7, 1->8 }, 
it remains to prove termination of the 20-rule system
{ 0 1 ->= 2 ,
  0 3 ->= 4 ,
  5 1 ->= 6 ,
  5 3 ->= 7 ,
  8 8 1 ->= 8 1 2 ,
  8 8 3 ->= 8 1 4 ,
  0 8 1 ->= 0 1 2 ,
  0 8 3 ->= 0 1 4 ,
  5 8 1 ->= 5 1 2 ,
  5 8 3 ->= 5 1 4 ,
  1 0 ->= 8 ,
  3 6 0 ->= 1 0 3 7 5 ,
  3 6 2 ->= 1 0 3 7 6 ,
  3 6 4 ->= 1 0 3 7 7 ,
  4 6 0 ->= 2 0 3 7 5 ,
  4 6 2 ->= 2 0 3 7 6 ,
  4 6 4 ->= 2 0 3 7 7 ,
  7 6 0 ->= 6 0 3 7 5 ,
  7 6 2 ->= 6 0 3 7 6 ,
  7 6 4 ->= 6 0 3 7 7 }

The system is trivially terminating.