YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> ,
  0 1 -> 1 2 0 ,
  2 2 0 -> 0 1 0 }


The system was reversed.

After renaming modulo { 0->0, 1->1, 2->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> ,
  1 0 -> 0 2 1 ,
  0 2 2 -> 0 1 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 48-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 ,
  0 2 10 8 -> 0 1 4 0 ,
  0 2 10 9 -> 0 1 4 1 ,
  0 2 10 10 -> 0 1 4 2 ,
  0 2 10 11 -> 0 1 4 3 ,
  4 2 10 8 -> 4 1 4 0 ,
  4 2 10 9 -> 4 1 4 1 ,
  4 2 10 10 -> 4 1 4 2 ,
  4 2 10 11 -> 4 1 4 3 ,
  8 2 10 8 -> 8 1 4 0 ,
  8 2 10 9 -> 8 1 4 1 ,
  8 2 10 10 -> 8 1 4 2 ,
  8 2 10 11 -> 8 1 4 3 ,
  12 2 10 8 -> 12 1 4 0 ,
  12 2 10 9 -> 12 1 4 1 ,
  12 2 10 10 -> 12 1 4 2 ,
  12 2 10 11 -> 12 1 4 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 2 |
| 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 2 |
| 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 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 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 |
 \   /

After renaming modulo { 8->0, 2->1, 10->2, 1->3, 4->4, 0->5, 9->6, 5->7, 6->8, 12->9 }, 
it remains to prove termination of the 18-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 ,
  5 1 2 0 -> 5 3 4 5 ,
  5 1 2 6 -> 5 3 4 3 ,
  4 1 2 0 -> 4 3 4 5 ,
  4 1 2 6 -> 4 3 4 3 ,
  0 1 2 0 -> 0 3 4 5 ,
  0 1 2 6 -> 0 3 4 3 ,
  9 1 2 0 -> 9 3 4 5 ,
  9 1 2 6 -> 9 3 4 3 }


Applying the dependency pairs transformation.

After renaming modulo { (3,true)->0, (4,false)->1, (5,false)->2, (5,true)->3, (1,false)->4, (6,false)->5, (6,true)->6, (4,true)->7, (3,false)->8, (7,false)->9, (7,true)->10, (8,false)->11, (0,true)->12, (2,false)->13, (0,false)->14, (9,true)->15, (9,false)->16 },
it remains to prove termination of the 74-rule system
{ 0 1 2 -> 3 4 5 1 ,
  0 1 2 -> 6 1 ,
  0 1 2 -> 7 ,
  0 1 8 -> 3 4 5 9 ,
  0 1 8 -> 6 9 ,
  0 1 8 -> 10 ,
  0 1 4 -> 3 4 5 11 ,
  0 1 4 -> 6 11 ,
  10 1 2 -> 7 4 5 1 ,
  10 1 2 -> 6 1 ,
  10 1 2 -> 7 ,
  10 1 8 -> 7 4 5 9 ,
  10 1 8 -> 6 9 ,
  10 1 8 -> 10 ,
  10 1 4 -> 7 4 5 11 ,
  10 1 4 -> 6 11 ,
  6 1 2 -> 12 4 5 1 ,
  6 1 2 -> 6 1 ,
  6 1 2 -> 7 ,
  6 1 8 -> 12 4 5 9 ,
  6 1 8 -> 6 9 ,
  6 1 8 -> 10 ,
  6 1 4 -> 12 4 5 11 ,
  6 1 4 -> 6 11 ,
  3 4 13 14 -> 3 8 1 2 ,
  3 4 13 14 -> 0 1 2 ,
  3 4 13 14 -> 7 2 ,
  3 4 13 14 -> 3 ,
  3 4 13 5 -> 3 8 1 8 ,
  3 4 13 5 -> 0 1 8 ,
  3 4 13 5 -> 7 8 ,
  3 4 13 5 -> 0 ,
  7 4 13 14 -> 7 8 1 2 ,
  7 4 13 14 -> 0 1 2 ,
  7 4 13 14 -> 7 2 ,
  7 4 13 14 -> 3 ,
  7 4 13 5 -> 7 8 1 8 ,
  7 4 13 5 -> 0 1 8 ,
  7 4 13 5 -> 7 8 ,
  7 4 13 5 -> 0 ,
  12 4 13 14 -> 12 8 1 2 ,
  12 4 13 14 -> 0 1 2 ,
  12 4 13 14 -> 7 2 ,
  12 4 13 14 -> 3 ,
  12 4 13 5 -> 12 8 1 8 ,
  12 4 13 5 -> 0 1 8 ,
  12 4 13 5 -> 7 8 ,
  12 4 13 5 -> 0 ,
  15 4 13 14 -> 15 8 1 2 ,
  15 4 13 14 -> 0 1 2 ,
  15 4 13 14 -> 7 2 ,
  15 4 13 14 -> 3 ,
  15 4 13 5 -> 15 8 1 8 ,
  15 4 13 5 -> 0 1 8 ,
  15 4 13 5 -> 7 8 ,
  15 4 13 5 -> 0 ,
  14 4 ->= 13 ,
  8 1 2 ->= 2 4 5 1 ,
  8 1 8 ->= 2 4 5 9 ,
  8 1 4 ->= 2 4 5 11 ,
  9 1 2 ->= 1 4 5 1 ,
  9 1 8 ->= 1 4 5 9 ,
  9 1 4 ->= 1 4 5 11 ,
  5 1 2 ->= 14 4 5 1 ,
  5 1 8 ->= 14 4 5 9 ,
  5 1 4 ->= 14 4 5 11 ,
  2 4 13 14 ->= 2 8 1 2 ,
  2 4 13 5 ->= 2 8 1 8 ,
  1 4 13 14 ->= 1 8 1 2 ,
  1 4 13 5 ->= 1 8 1 8 ,
  14 4 13 14 ->= 14 8 1 2 ,
  14 4 13 5 ->= 14 8 1 8 ,
  16 4 13 14 ->= 16 8 1 2 ,
  16 4 13 5 ->= 16 8 1 8 }


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 1 |
| 0 1 |
 \   /
16 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 }, 
it remains to prove termination of the 68-rule system
{ 0 1 2 -> 3 4 5 1 ,
  0 1 2 -> 6 1 ,
  0 1 2 -> 7 ,
  0 1 8 -> 3 4 5 9 ,
  0 1 8 -> 6 9 ,
  0 1 8 -> 10 ,
  0 1 4 -> 3 4 5 11 ,
  0 1 4 -> 6 11 ,
  10 1 2 -> 7 4 5 1 ,
  10 1 2 -> 6 1 ,
  10 1 2 -> 7 ,
  10 1 8 -> 7 4 5 9 ,
  10 1 8 -> 6 9 ,
  10 1 8 -> 10 ,
  10 1 4 -> 7 4 5 11 ,
  10 1 4 -> 6 11 ,
  6 1 2 -> 12 4 5 1 ,
  6 1 2 -> 6 1 ,
  6 1 2 -> 7 ,
  6 1 8 -> 12 4 5 9 ,
  6 1 8 -> 6 9 ,
  6 1 8 -> 10 ,
  6 1 4 -> 12 4 5 11 ,
  6 1 4 -> 6 11 ,
  3 4 13 14 -> 3 8 1 2 ,
  3 4 13 14 -> 0 1 2 ,
  3 4 13 14 -> 7 2 ,
  3 4 13 14 -> 3 ,
  3 4 13 5 -> 3 8 1 8 ,
  3 4 13 5 -> 0 1 8 ,
  3 4 13 5 -> 7 8 ,
  3 4 13 5 -> 0 ,
  7 4 13 14 -> 7 8 1 2 ,
  7 4 13 14 -> 0 1 2 ,
  7 4 13 14 -> 7 2 ,
  7 4 13 14 -> 3 ,
  7 4 13 5 -> 7 8 1 8 ,
  7 4 13 5 -> 0 1 8 ,
  7 4 13 5 -> 7 8 ,
  7 4 13 5 -> 0 ,
  12 4 13 14 -> 12 8 1 2 ,
  12 4 13 14 -> 0 1 2 ,
  12 4 13 14 -> 7 2 ,
  12 4 13 14 -> 3 ,
  12 4 13 5 -> 12 8 1 8 ,
  12 4 13 5 -> 0 1 8 ,
  12 4 13 5 -> 7 8 ,
  12 4 13 5 -> 0 ,
  15 4 13 14 -> 15 8 1 2 ,
  15 4 13 5 -> 15 8 1 8 ,
  14 4 ->= 13 ,
  8 1 2 ->= 2 4 5 1 ,
  8 1 8 ->= 2 4 5 9 ,
  8 1 4 ->= 2 4 5 11 ,
  9 1 2 ->= 1 4 5 1 ,
  9 1 8 ->= 1 4 5 9 ,
  9 1 4 ->= 1 4 5 11 ,
  5 1 2 ->= 14 4 5 1 ,
  5 1 8 ->= 14 4 5 9 ,
  5 1 4 ->= 14 4 5 11 ,
  2 4 13 14 ->= 2 8 1 2 ,
  2 4 13 5 ->= 2 8 1 8 ,
  1 4 13 14 ->= 1 8 1 2 ,
  1 4 13 5 ->= 1 8 1 8 ,
  14 4 13 14 ->= 14 8 1 2 ,
  14 4 13 5 ->= 14 8 1 8 ,
  16 4 13 14 ->= 16 8 1 2 ,
  16 4 13 5 ->= 16 8 1 8 }


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 2 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 2 |
| 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 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 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 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 3->0, 4->1, 13->2, 14->3, 8->4, 1->5, 2->6, 5->7, 7->8, 12->9, 15->10, 9->11, 11->12, 16->13 }, 
it remains to prove termination of the 26-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  0 1 2 7 -> 0 4 5 4 ,
  8 1 2 3 -> 8 4 5 6 ,
  8 1 2 7 -> 8 4 5 4 ,
  9 1 2 3 -> 9 4 5 6 ,
  9 1 2 7 -> 9 4 5 4 ,
  10 1 2 3 -> 10 4 5 6 ,
  10 1 2 7 -> 10 4 5 4 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 7 5 ,
  4 5 4 ->= 6 1 7 11 ,
  4 5 1 ->= 6 1 7 12 ,
  11 5 6 ->= 5 1 7 5 ,
  11 5 4 ->= 5 1 7 11 ,
  11 5 1 ->= 5 1 7 12 ,
  7 5 6 ->= 3 1 7 5 ,
  7 5 4 ->= 3 1 7 11 ,
  7 5 1 ->= 3 1 7 12 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 7 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 7 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 7 ->= 3 4 5 4 ,
  13 1 2 3 ->= 13 4 5 6 ,
  13 1 2 7 ->= 13 4 5 4 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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, 9->8, 8->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 23-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  7 1 2 3 -> 7 4 5 6 ,
  8 1 2 3 -> 8 4 5 6 ,
  8 1 2 9 -> 8 4 5 4 ,
  10 1 2 3 -> 10 4 5 6 ,
  10 1 2 9 -> 10 4 5 4 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 9 5 ,
  4 5 4 ->= 6 1 9 11 ,
  4 5 1 ->= 6 1 9 12 ,
  11 5 6 ->= 5 1 9 5 ,
  11 5 4 ->= 5 1 9 11 ,
  11 5 1 ->= 5 1 9 12 ,
  9 5 6 ->= 3 1 9 5 ,
  9 5 4 ->= 3 1 9 11 ,
  9 5 1 ->= 3 1 9 12 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 9 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 9 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 9 ->= 3 4 5 4 ,
  13 1 2 3 ->= 13 4 5 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
10 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 22-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  7 1 2 3 -> 7 4 5 6 ,
  8 1 2 3 -> 8 4 5 6 ,
  8 1 2 9 -> 8 4 5 4 ,
  10 1 2 3 -> 10 4 5 6 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 9 5 ,
  4 5 4 ->= 6 1 9 11 ,
  4 5 1 ->= 6 1 9 12 ,
  11 5 6 ->= 5 1 9 5 ,
  11 5 4 ->= 5 1 9 11 ,
  11 5 1 ->= 5 1 9 12 ,
  9 5 6 ->= 3 1 9 5 ,
  9 5 4 ->= 3 1 9 11 ,
  9 5 1 ->= 3 1 9 12 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 9 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 9 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 9 ->= 3 4 5 4 ,
  13 1 2 3 ->= 13 4 5 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
10 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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, 10->9, 9->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  7 1 2 3 -> 7 4 5 6 ,
  8 1 2 3 -> 8 4 5 6 ,
  9 1 2 3 -> 9 4 5 6 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 10 5 ,
  4 5 4 ->= 6 1 10 11 ,
  4 5 1 ->= 6 1 10 12 ,
  11 5 6 ->= 5 1 10 5 ,
  11 5 4 ->= 5 1 10 11 ,
  11 5 1 ->= 5 1 10 12 ,
  10 5 6 ->= 3 1 10 5 ,
  10 5 4 ->= 3 1 10 11 ,
  10 5 1 ->= 3 1 10 12 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 10 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 10 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 10 ->= 3 4 5 4 ,
  13 1 2 3 ->= 13 4 5 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
11 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 19-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  7 1 2 3 -> 7 4 5 6 ,
  8 1 2 3 -> 8 4 5 6 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 9 5 ,
  4 5 4 ->= 6 1 9 10 ,
  4 5 1 ->= 6 1 9 11 ,
  10 5 6 ->= 5 1 9 5 ,
  10 5 4 ->= 5 1 9 10 ,
  10 5 1 ->= 5 1 9 11 ,
  9 5 6 ->= 3 1 9 5 ,
  9 5 4 ->= 3 1 9 10 ,
  9 5 1 ->= 3 1 9 11 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 9 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 9 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 9 ->= 3 4 5 4 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
7 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
10 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 18-rule system
{ 0 1 2 3 -> 0 4 5 6 ,
  7 1 2 3 -> 7 4 5 6 ,
  3 1 ->= 2 ,
  4 5 6 ->= 6 1 8 5 ,
  4 5 4 ->= 6 1 8 9 ,
  4 5 1 ->= 6 1 8 10 ,
  9 5 6 ->= 5 1 8 5 ,
  9 5 4 ->= 5 1 8 9 ,
  9 5 1 ->= 5 1 8 10 ,
  8 5 6 ->= 3 1 8 5 ,
  8 5 4 ->= 3 1 8 9 ,
  8 5 1 ->= 3 1 8 10 ,
  6 1 2 3 ->= 6 4 5 6 ,
  6 1 2 8 ->= 6 4 5 4 ,
  5 1 2 3 ->= 5 4 5 6 ,
  5 1 2 8 ->= 5 4 5 4 ,
  3 1 2 3 ->= 3 4 5 6 ,
  3 1 2 8 ->= 3 4 5 4 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
9 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

0 is interpreted by
 /           \
| 1 0 1 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 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 0 |
 \           /
2 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 1 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
3 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 1 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
4 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /
8 is interpreted by
 /           \
| 1 0 0 0 0 0 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 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 |
| 0 1 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
 \           /

After renaming modulo { 3->0, 1->1, 2->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8 }, 
it remains to prove termination of the 16-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 ,
  5 1 2 0 ->= 5 3 4 5 ,
  5 1 2 6 ->= 5 3 4 3 ,
  4 1 2 0 ->= 4 3 4 5 ,
  4 1 2 6 ->= 4 3 4 3 ,
  0 1 2 0 ->= 0 3 4 5 ,
  0 1 2 6 ->= 0 3 4 3 }

The system is trivially terminating.