YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 1 -> 1 2 0 ,
  2 -> 1 ,
  2 2 -> 0 2 }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  1 0 -> 0 2 1 ,
  2 -> 1 ,
  2 2 -> 2 0 }


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

After renaming modulo { 8->0, 2->1, 10->2, 1->3, 4->4, 0->5, 9->6, 5->7, 6->8, 14->9 }, 
it remains to prove termination of the 22-rule system
{ 0 1 -> 2 ,
  3 4 5 -> 5 1 6 4 ,
  3 4 3 -> 5 1 6 7 ,
  3 4 1 -> 5 1 6 8 ,
  7 4 5 -> 4 1 6 4 ,
  7 4 3 -> 4 1 6 7 ,
  7 4 1 -> 4 1 6 8 ,
  6 4 5 -> 0 1 6 4 ,
  6 4 3 -> 0 1 6 7 ,
  6 4 1 -> 0 1 6 8 ,
  1 0 -> 3 4 ,
  1 6 -> 3 7 ,
  8 0 -> 7 4 ,
  8 6 -> 7 7 ,
  1 2 0 -> 1 0 5 ,
  1 2 6 -> 1 0 3 ,
  8 2 0 -> 8 0 5 ,
  8 2 6 -> 8 0 3 ,
  2 2 0 -> 2 0 5 ,
  2 2 6 -> 2 0 3 ,
  9 2 0 -> 9 0 5 ,
  9 2 6 -> 9 0 3 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (3,true)->3, (4,false)->4, (5,false)->5, (1,true)->6, (6,false)->7, (6,true)->8, (3,false)->9, (7,false)->10, (7,true)->11, (8,false)->12, (8,true)->13, (0,false)->14, (2,false)->15, (9,true)->16, (9,false)->17 },
it remains to prove termination of the 76-rule system
{ 0 1 -> 2 ,
  3 4 5 -> 6 7 4 ,
  3 4 5 -> 8 4 ,
  3 4 9 -> 6 7 10 ,
  3 4 9 -> 8 10 ,
  3 4 9 -> 11 ,
  3 4 1 -> 6 7 12 ,
  3 4 1 -> 8 12 ,
  3 4 1 -> 13 ,
  11 4 5 -> 6 7 4 ,
  11 4 5 -> 8 4 ,
  11 4 9 -> 6 7 10 ,
  11 4 9 -> 8 10 ,
  11 4 9 -> 11 ,
  11 4 1 -> 6 7 12 ,
  11 4 1 -> 8 12 ,
  11 4 1 -> 13 ,
  8 4 5 -> 0 1 7 4 ,
  8 4 5 -> 6 7 4 ,
  8 4 5 -> 8 4 ,
  8 4 9 -> 0 1 7 10 ,
  8 4 9 -> 6 7 10 ,
  8 4 9 -> 8 10 ,
  8 4 9 -> 11 ,
  8 4 1 -> 0 1 7 12 ,
  8 4 1 -> 6 7 12 ,
  8 4 1 -> 8 12 ,
  8 4 1 -> 13 ,
  6 14 -> 3 4 ,
  6 7 -> 3 10 ,
  6 7 -> 11 ,
  13 14 -> 11 4 ,
  13 7 -> 11 10 ,
  13 7 -> 11 ,
  6 15 14 -> 6 14 5 ,
  6 15 14 -> 0 5 ,
  6 15 7 -> 6 14 9 ,
  6 15 7 -> 0 9 ,
  6 15 7 -> 3 ,
  13 15 14 -> 13 14 5 ,
  13 15 14 -> 0 5 ,
  13 15 7 -> 13 14 9 ,
  13 15 7 -> 0 9 ,
  13 15 7 -> 3 ,
  2 15 14 -> 2 14 5 ,
  2 15 14 -> 0 5 ,
  2 15 7 -> 2 14 9 ,
  2 15 7 -> 0 9 ,
  2 15 7 -> 3 ,
  16 15 14 -> 16 14 5 ,
  16 15 14 -> 0 5 ,
  16 15 7 -> 16 14 9 ,
  16 15 7 -> 0 9 ,
  16 15 7 -> 3 ,
  14 1 ->= 15 ,
  9 4 5 ->= 5 1 7 4 ,
  9 4 9 ->= 5 1 7 10 ,
  9 4 1 ->= 5 1 7 12 ,
  10 4 5 ->= 4 1 7 4 ,
  10 4 9 ->= 4 1 7 10 ,
  10 4 1 ->= 4 1 7 12 ,
  7 4 5 ->= 14 1 7 4 ,
  7 4 9 ->= 14 1 7 10 ,
  7 4 1 ->= 14 1 7 12 ,
  1 14 ->= 9 4 ,
  1 7 ->= 9 10 ,
  12 14 ->= 10 4 ,
  12 7 ->= 10 10 ,
  1 15 14 ->= 1 14 5 ,
  1 15 7 ->= 1 14 9 ,
  12 15 14 ->= 12 14 5 ,
  12 15 7 ->= 12 14 9 ,
  15 15 14 ->= 15 14 5 ,
  15 15 7 ->= 15 14 9 ,
  17 15 14 ->= 17 14 5 ,
  17 15 7 ->= 17 14 9 }


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 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 1 |
| 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 73-rule system
{ 0 1 -> 2 ,
  3 4 5 -> 6 7 4 ,
  3 4 5 -> 8 4 ,
  3 4 9 -> 6 7 10 ,
  3 4 9 -> 8 10 ,
  3 4 9 -> 11 ,
  3 4 1 -> 6 7 12 ,
  3 4 1 -> 8 12 ,
  3 4 1 -> 13 ,
  11 4 5 -> 6 7 4 ,
  11 4 5 -> 8 4 ,
  11 4 9 -> 6 7 10 ,
  11 4 9 -> 8 10 ,
  11 4 9 -> 11 ,
  11 4 1 -> 6 7 12 ,
  11 4 1 -> 8 12 ,
  11 4 1 -> 13 ,
  8 4 5 -> 0 1 7 4 ,
  8 4 5 -> 6 7 4 ,
  8 4 5 -> 8 4 ,
  8 4 9 -> 0 1 7 10 ,
  8 4 9 -> 6 7 10 ,
  8 4 9 -> 8 10 ,
  8 4 9 -> 11 ,
  8 4 1 -> 0 1 7 12 ,
  8 4 1 -> 6 7 12 ,
  8 4 1 -> 8 12 ,
  8 4 1 -> 13 ,
  6 14 -> 3 4 ,
  6 7 -> 3 10 ,
  6 7 -> 11 ,
  13 14 -> 11 4 ,
  13 7 -> 11 10 ,
  13 7 -> 11 ,
  6 15 14 -> 6 14 5 ,
  6 15 14 -> 0 5 ,
  6 15 7 -> 6 14 9 ,
  6 15 7 -> 0 9 ,
  6 15 7 -> 3 ,
  13 15 14 -> 13 14 5 ,
  13 15 14 -> 0 5 ,
  13 15 7 -> 13 14 9 ,
  13 15 7 -> 0 9 ,
  13 15 7 -> 3 ,
  2 15 14 -> 2 14 5 ,
  2 15 14 -> 0 5 ,
  2 15 7 -> 2 14 9 ,
  2 15 7 -> 0 9 ,
  2 15 7 -> 3 ,
  16 15 14 -> 16 14 5 ,
  16 15 7 -> 16 14 9 ,
  14 1 ->= 15 ,
  9 4 5 ->= 5 1 7 4 ,
  9 4 9 ->= 5 1 7 10 ,
  9 4 1 ->= 5 1 7 12 ,
  10 4 5 ->= 4 1 7 4 ,
  10 4 9 ->= 4 1 7 10 ,
  10 4 1 ->= 4 1 7 12 ,
  7 4 5 ->= 14 1 7 4 ,
  7 4 9 ->= 14 1 7 10 ,
  7 4 1 ->= 14 1 7 12 ,
  1 14 ->= 9 4 ,
  1 7 ->= 9 10 ,
  12 14 ->= 10 4 ,
  12 7 ->= 10 10 ,
  1 15 14 ->= 1 14 5 ,
  1 15 7 ->= 1 14 9 ,
  12 15 14 ->= 12 14 5 ,
  12 15 7 ->= 12 14 9 ,
  15 15 14 ->= 15 14 5 ,
  15 15 7 ->= 15 14 9 ,
  17 15 14 ->= 17 14 5 ,
  17 15 7 ->= 17 14 9 }


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

After renaming modulo { 6->0, 15->1, 14->2, 5->3, 7->4, 9->5, 13->6, 2->7, 16->8, 1->9, 4->10, 10->11, 12->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 ,
  2 9 ->= 1 ,
  5 10 3 ->= 3 9 4 10 ,
  5 10 5 ->= 3 9 4 11 ,
  5 10 9 ->= 3 9 4 12 ,
  11 10 3 ->= 10 9 4 10 ,
  11 10 5 ->= 10 9 4 11 ,
  11 10 9 ->= 10 9 4 12 ,
  4 10 3 ->= 2 9 4 10 ,
  4 10 5 ->= 2 9 4 11 ,
  4 10 9 ->= 2 9 4 12 ,
  9 2 ->= 5 10 ,
  9 4 ->= 5 11 ,
  12 2 ->= 11 10 ,
  12 4 ->= 11 11 ,
  9 1 2 ->= 9 2 3 ,
  9 1 4 ->= 9 2 5 ,
  12 1 2 ->= 12 2 3 ,
  12 1 4 ->= 12 2 5 ,
  1 1 2 ->= 1 2 3 ,
  1 1 4 ->= 1 2 5 ,
  13 1 2 ->= 13 2 3 ,
  13 1 4 ->= 13 2 5 }


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, 4->5, 5->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 ,
  4 1 2 -> 4 2 3 ,
  4 1 5 -> 4 2 6 ,
  7 1 2 -> 7 2 3 ,
  7 1 5 -> 7 2 6 ,
  8 1 2 -> 8 2 3 ,
  8 1 5 -> 8 2 6 ,
  2 9 ->= 1 ,
  6 10 3 ->= 3 9 5 10 ,
  6 10 6 ->= 3 9 5 11 ,
  6 10 9 ->= 3 9 5 12 ,
  11 10 3 ->= 10 9 5 10 ,
  11 10 6 ->= 10 9 5 11 ,
  11 10 9 ->= 10 9 5 12 ,
  5 10 3 ->= 2 9 5 10 ,
  5 10 6 ->= 2 9 5 11 ,
  5 10 9 ->= 2 9 5 12 ,
  9 2 ->= 6 10 ,
  9 5 ->= 6 11 ,
  12 2 ->= 11 10 ,
  12 5 ->= 11 11 ,
  9 1 2 ->= 9 2 3 ,
  9 1 5 ->= 9 2 6 ,
  12 1 2 ->= 12 2 3 ,
  12 1 5 ->= 12 2 6 ,
  1 1 2 ->= 1 2 3 ,
  1 1 5 ->= 1 2 6 ,
  13 1 2 ->= 13 2 3 ,
  13 1 5 ->= 13 2 6 }


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


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


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 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 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 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, 7->5, 5->6, 6->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 ,
  2 9 ->= 1 ,
  7 10 3 ->= 3 9 6 10 ,
  7 10 7 ->= 3 9 6 11 ,
  7 10 9 ->= 3 9 6 12 ,
  11 10 3 ->= 10 9 6 10 ,
  11 10 7 ->= 10 9 6 11 ,
  11 10 9 ->= 10 9 6 12 ,
  6 10 3 ->= 2 9 6 10 ,
  6 10 7 ->= 2 9 6 11 ,
  6 10 9 ->= 2 9 6 12 ,
  9 2 ->= 7 10 ,
  9 6 ->= 7 11 ,
  12 2 ->= 11 10 ,
  12 6 ->= 11 11 ,
  9 1 2 ->= 9 2 3 ,
  9 1 6 ->= 9 2 7 ,
  12 1 2 ->= 12 2 3 ,
  12 1 6 ->= 12 2 7 ,
  1 1 2 ->= 1 2 3 ,
  1 1 6 ->= 1 2 7 ,
  13 1 2 ->= 13 2 3 }


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, 7->8, 10->9, 6->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 ,
  2 7 ->= 1 ,
  8 9 3 ->= 3 7 10 9 ,
  8 9 8 ->= 3 7 10 11 ,
  8 9 7 ->= 3 7 10 12 ,
  11 9 3 ->= 9 7 10 9 ,
  11 9 8 ->= 9 7 10 11 ,
  11 9 7 ->= 9 7 10 12 ,
  10 9 3 ->= 2 7 10 9 ,
  10 9 8 ->= 2 7 10 11 ,
  10 9 7 ->= 2 7 10 12 ,
  7 2 ->= 8 9 ,
  7 10 ->= 8 11 ,
  12 2 ->= 11 9 ,
  12 10 ->= 11 11 ,
  7 1 2 ->= 7 2 3 ,
  7 1 10 ->= 7 2 8 ,
  12 1 2 ->= 12 2 3 ,
  12 1 10 ->= 12 2 8 ,
  1 1 2 ->= 1 2 3 ,
  1 1 10 ->= 1 2 8 ,
  13 1 2 ->= 13 2 3 }


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 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 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 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 1 0 0 0 |
| 0 1 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, 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 ,
  2 6 ->= 1 ,
  7 8 3 ->= 3 6 9 8 ,
  7 8 7 ->= 3 6 9 10 ,
  7 8 6 ->= 3 6 9 11 ,
  10 8 3 ->= 8 6 9 8 ,
  10 8 7 ->= 8 6 9 10 ,
  10 8 6 ->= 8 6 9 11 ,
  9 8 3 ->= 2 6 9 8 ,
  9 8 7 ->= 2 6 9 10 ,
  9 8 6 ->= 2 6 9 11 ,
  6 2 ->= 7 8 ,
  6 9 ->= 7 10 ,
  11 2 ->= 10 8 ,
  11 9 ->= 10 10 ,
  6 1 2 ->= 6 2 3 ,
  6 1 9 ->= 6 2 7 ,
  11 1 2 ->= 11 2 3 ,
  11 1 9 ->= 11 2 7 ,
  1 1 2 ->= 1 2 3 ,
  1 1 9 ->= 1 2 7 ,
  12 1 2 ->= 12 2 3 }


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 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 1 0 0 0 |
| 0 1 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 ,
  2 5 ->= 1 ,
  6 7 3 ->= 3 5 8 7 ,
  6 7 6 ->= 3 5 8 9 ,
  6 7 5 ->= 3 5 8 10 ,
  9 7 3 ->= 7 5 8 7 ,
  9 7 6 ->= 7 5 8 9 ,
  9 7 5 ->= 7 5 8 10 ,
  8 7 3 ->= 2 5 8 7 ,
  8 7 6 ->= 2 5 8 9 ,
  8 7 5 ->= 2 5 8 10 ,
  5 2 ->= 6 7 ,
  5 8 ->= 6 9 ,
  10 2 ->= 9 7 ,
  10 8 ->= 9 9 ,
  5 1 2 ->= 5 2 3 ,
  5 1 8 ->= 5 2 6 ,
  10 1 2 ->= 10 2 3 ,
  10 1 8 ->= 10 2 6 ,
  1 1 2 ->= 1 2 3 ,
  1 1 8 ->= 1 2 6 ,
  11 1 2 ->= 11 2 3 }


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 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 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 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 ,
  2 5 ->= 1 ,
  6 7 3 ->= 3 5 8 7 ,
  6 7 6 ->= 3 5 8 9 ,
  6 7 5 ->= 3 5 8 10 ,
  9 7 3 ->= 7 5 8 7 ,
  9 7 6 ->= 7 5 8 9 ,
  9 7 5 ->= 7 5 8 10 ,
  8 7 3 ->= 2 5 8 7 ,
  8 7 6 ->= 2 5 8 9 ,
  8 7 5 ->= 2 5 8 10 ,
  5 2 ->= 6 7 ,
  5 8 ->= 6 9 ,
  10 2 ->= 9 7 ,
  10 8 ->= 9 9 ,
  5 1 2 ->= 5 2 3 ,
  5 1 8 ->= 5 2 6 ,
  10 1 2 ->= 10 2 3 ,
  10 1 8 ->= 10 2 6 ,
  1 1 2 ->= 1 2 3 ,
  1 1 8 ->= 1 2 6 }


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 1 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 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 |
 \         /

After renaming modulo { 0->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 ,
  2 4 ->= 1 ,
  5 6 3 ->= 3 4 7 6 ,
  5 6 5 ->= 3 4 7 8 ,
  5 6 4 ->= 3 4 7 9 ,
  8 6 3 ->= 6 4 7 6 ,
  8 6 5 ->= 6 4 7 8 ,
  8 6 4 ->= 6 4 7 9 ,
  7 6 3 ->= 2 4 7 6 ,
  7 6 5 ->= 2 4 7 8 ,
  7 6 4 ->= 2 4 7 9 ,
  4 2 ->= 5 6 ,
  4 7 ->= 5 8 ,
  9 2 ->= 8 6 ,
  9 7 ->= 8 8 ,
  4 1 2 ->= 4 2 3 ,
  4 1 7 ->= 4 2 5 ,
  9 1 2 ->= 9 2 3 ,
  9 1 7 ->= 9 2 5 ,
  1 1 2 ->= 1 2 3 ,
  1 1 7 ->= 1 2 5 }


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 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 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 |
 \         /

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

The system is trivially terminating.