YES

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


The system was reversed.

After renaming modulo { 0->0, 2->1, 1->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> ,
  0 0 -> 0 1 2 0 2 0 ,
  2 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 ,
  0 0 0 -> 0 1 6 8 2 8 0 ,
  0 0 1 -> 0 1 6 8 2 8 1 ,
  0 0 2 -> 0 1 6 8 2 8 2 ,
  0 0 3 -> 0 1 6 8 2 8 3 ,
  4 0 0 -> 4 1 6 8 2 8 0 ,
  4 0 1 -> 4 1 6 8 2 8 1 ,
  4 0 2 -> 4 1 6 8 2 8 2 ,
  4 0 3 -> 4 1 6 8 2 8 3 ,
  8 0 0 -> 8 1 6 8 2 8 0 ,
  8 0 1 -> 8 1 6 8 2 8 1 ,
  8 0 2 -> 8 1 6 8 2 8 2 ,
  8 0 3 -> 8 1 6 8 2 8 3 ,
  12 0 0 -> 12 1 6 8 2 8 0 ,
  12 0 1 -> 12 1 6 8 2 8 1 ,
  12 0 2 -> 12 1 6 8 2 8 2 ,
  12 0 3 -> 12 1 6 8 2 8 3 ,
  2 9 4 -> 0 0 ,
  2 9 5 -> 0 1 ,
  2 9 6 -> 0 2 ,
  2 9 7 -> 0 3 ,
  6 9 4 -> 4 0 ,
  6 9 5 -> 4 1 ,
  6 9 6 -> 4 2 ,
  6 9 7 -> 4 3 ,
  10 9 4 -> 8 0 ,
  10 9 5 -> 8 1 ,
  10 9 6 -> 8 2 ,
  10 9 7 -> 8 3 ,
  14 9 4 -> 12 0 ,
  14 9 5 -> 12 1 ,
  14 9 6 -> 12 2 ,
  14 9 7 -> 12 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 2 |
| 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 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 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 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, 1->1, 9->2, 2->3, 10->4, 0->5, 6->6, 3->7, 4->8, 12->9 }, 
it remains to prove termination of the 22-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  5 5 5 -> 5 1 6 0 3 0 5 ,
  5 5 1 -> 5 1 6 0 3 0 1 ,
  5 5 3 -> 5 1 6 0 3 0 3 ,
  5 5 7 -> 5 1 6 0 3 0 7 ,
  8 5 5 -> 8 1 6 0 3 0 5 ,
  8 5 1 -> 8 1 6 0 3 0 1 ,
  8 5 3 -> 8 1 6 0 3 0 3 ,
  8 5 7 -> 8 1 6 0 3 0 7 ,
  0 5 5 -> 0 1 6 0 3 0 5 ,
  0 5 1 -> 0 1 6 0 3 0 1 ,
  0 5 3 -> 0 1 6 0 3 0 3 ,
  0 5 7 -> 0 1 6 0 3 0 7 ,
  9 5 5 -> 9 1 6 0 3 0 5 ,
  9 5 1 -> 9 1 6 0 3 0 1 ,
  9 5 3 -> 9 1 6 0 3 0 3 ,
  9 5 7 -> 9 1 6 0 3 0 7 ,
  3 2 8 -> 5 5 ,
  3 2 6 -> 5 3 ,
  6 2 8 -> 8 5 ,
  6 2 6 -> 8 3 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


Applying the dependency pairs transformation.

After renaming modulo { (5,true)->0, (5,false)->1, (1,false)->2, (6,false)->3, (0,false)->4, (3,false)->5, (6,true)->6, (0,true)->7, (3,true)->8, (7,false)->9, (8,true)->10, (9,true)->11, (2,false)->12, (8,false)->13, (4,false)->14, (9,false)->15 },
it remains to prove termination of the 112-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 1 -> 6 4 5 4 1 ,
  0 1 1 -> 7 5 4 1 ,
  0 1 1 -> 8 4 1 ,
  0 1 1 -> 7 1 ,
  0 1 1 -> 0 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 2 -> 6 4 5 4 2 ,
  0 1 2 -> 7 5 4 2 ,
  0 1 2 -> 8 4 2 ,
  0 1 2 -> 7 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  0 1 5 -> 6 4 5 4 5 ,
  0 1 5 -> 7 5 4 5 ,
  0 1 5 -> 8 4 5 ,
  0 1 5 -> 7 5 ,
  0 1 5 -> 8 ,
  0 1 9 -> 0 2 3 4 5 4 9 ,
  0 1 9 -> 6 4 5 4 9 ,
  0 1 9 -> 7 5 4 9 ,
  0 1 9 -> 8 4 9 ,
  0 1 9 -> 7 9 ,
  10 1 1 -> 10 2 3 4 5 4 1 ,
  10 1 1 -> 6 4 5 4 1 ,
  10 1 1 -> 7 5 4 1 ,
  10 1 1 -> 8 4 1 ,
  10 1 1 -> 7 1 ,
  10 1 1 -> 0 ,
  10 1 2 -> 10 2 3 4 5 4 2 ,
  10 1 2 -> 6 4 5 4 2 ,
  10 1 2 -> 7 5 4 2 ,
  10 1 2 -> 8 4 2 ,
  10 1 2 -> 7 2 ,
  10 1 5 -> 10 2 3 4 5 4 5 ,
  10 1 5 -> 6 4 5 4 5 ,
  10 1 5 -> 7 5 4 5 ,
  10 1 5 -> 8 4 5 ,
  10 1 5 -> 7 5 ,
  10 1 5 -> 8 ,
  10 1 9 -> 10 2 3 4 5 4 9 ,
  10 1 9 -> 6 4 5 4 9 ,
  10 1 9 -> 7 5 4 9 ,
  10 1 9 -> 8 4 9 ,
  10 1 9 -> 7 9 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 1 -> 6 4 5 4 1 ,
  7 1 1 -> 7 5 4 1 ,
  7 1 1 -> 8 4 1 ,
  7 1 1 -> 7 1 ,
  7 1 1 -> 0 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 2 -> 6 4 5 4 2 ,
  7 1 2 -> 7 5 4 2 ,
  7 1 2 -> 8 4 2 ,
  7 1 2 -> 7 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  7 1 5 -> 6 4 5 4 5 ,
  7 1 5 -> 7 5 4 5 ,
  7 1 5 -> 8 4 5 ,
  7 1 5 -> 7 5 ,
  7 1 5 -> 8 ,
  7 1 9 -> 7 2 3 4 5 4 9 ,
  7 1 9 -> 6 4 5 4 9 ,
  7 1 9 -> 7 5 4 9 ,
  7 1 9 -> 8 4 9 ,
  7 1 9 -> 7 9 ,
  11 1 1 -> 11 2 3 4 5 4 1 ,
  11 1 1 -> 6 4 5 4 1 ,
  11 1 1 -> 7 5 4 1 ,
  11 1 1 -> 8 4 1 ,
  11 1 1 -> 7 1 ,
  11 1 1 -> 0 ,
  11 1 2 -> 11 2 3 4 5 4 2 ,
  11 1 2 -> 6 4 5 4 2 ,
  11 1 2 -> 7 5 4 2 ,
  11 1 2 -> 8 4 2 ,
  11 1 2 -> 7 2 ,
  11 1 5 -> 11 2 3 4 5 4 5 ,
  11 1 5 -> 6 4 5 4 5 ,
  11 1 5 -> 7 5 4 5 ,
  11 1 5 -> 8 4 5 ,
  11 1 5 -> 7 5 ,
  11 1 5 -> 8 ,
  8 12 13 -> 0 1 ,
  8 12 13 -> 0 ,
  8 12 3 -> 0 5 ,
  8 12 3 -> 8 ,
  6 12 13 -> 10 1 ,
  6 12 13 -> 0 ,
  6 12 3 -> 10 5 ,
  6 12 3 -> 8 ,
  4 2 ->= 12 ,
  4 5 ->= 14 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 9 ->= 1 2 3 4 5 4 9 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  13 1 9 ->= 13 2 3 4 5 4 9 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 9 ->= 4 2 3 4 5 4 9 ,
  15 1 1 ->= 15 2 3 4 5 4 1 ,
  15 1 2 ->= 15 2 3 4 5 4 2 ,
  15 1 5 ->= 15 2 3 4 5 4 5 ,
  5 12 13 ->= 1 1 ,
  5 12 3 ->= 1 5 ,
  3 12 13 ->= 13 1 ,
  3 12 3 ->= 13 5 }


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 1 |
| 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 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 }, 
it remains to prove termination of the 98-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 1 -> 6 4 5 4 1 ,
  0 1 1 -> 7 5 4 1 ,
  0 1 1 -> 8 4 1 ,
  0 1 1 -> 7 1 ,
  0 1 1 -> 0 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 2 -> 6 4 5 4 2 ,
  0 1 2 -> 7 5 4 2 ,
  0 1 2 -> 8 4 2 ,
  0 1 2 -> 7 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  0 1 5 -> 6 4 5 4 5 ,
  0 1 5 -> 7 5 4 5 ,
  0 1 5 -> 8 4 5 ,
  0 1 5 -> 7 5 ,
  0 1 5 -> 8 ,
  0 1 9 -> 0 2 3 4 5 4 9 ,
  0 1 9 -> 6 4 5 4 9 ,
  0 1 9 -> 7 5 4 9 ,
  0 1 9 -> 8 4 9 ,
  0 1 9 -> 7 9 ,
  10 1 1 -> 10 2 3 4 5 4 1 ,
  10 1 1 -> 6 4 5 4 1 ,
  10 1 1 -> 7 5 4 1 ,
  10 1 1 -> 8 4 1 ,
  10 1 1 -> 7 1 ,
  10 1 1 -> 0 ,
  10 1 2 -> 10 2 3 4 5 4 2 ,
  10 1 2 -> 6 4 5 4 2 ,
  10 1 2 -> 7 5 4 2 ,
  10 1 2 -> 8 4 2 ,
  10 1 2 -> 7 2 ,
  10 1 5 -> 10 2 3 4 5 4 5 ,
  10 1 5 -> 6 4 5 4 5 ,
  10 1 5 -> 7 5 4 5 ,
  10 1 5 -> 8 4 5 ,
  10 1 5 -> 7 5 ,
  10 1 5 -> 8 ,
  10 1 9 -> 10 2 3 4 5 4 9 ,
  10 1 9 -> 6 4 5 4 9 ,
  10 1 9 -> 7 5 4 9 ,
  10 1 9 -> 8 4 9 ,
  10 1 9 -> 7 9 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 1 -> 6 4 5 4 1 ,
  7 1 1 -> 7 5 4 1 ,
  7 1 1 -> 8 4 1 ,
  7 1 1 -> 7 1 ,
  7 1 1 -> 0 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 2 -> 6 4 5 4 2 ,
  7 1 2 -> 7 5 4 2 ,
  7 1 2 -> 8 4 2 ,
  7 1 2 -> 7 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  7 1 5 -> 6 4 5 4 5 ,
  7 1 5 -> 7 5 4 5 ,
  7 1 5 -> 8 4 5 ,
  7 1 5 -> 7 5 ,
  7 1 5 -> 8 ,
  7 1 9 -> 7 2 3 4 5 4 9 ,
  7 1 9 -> 6 4 5 4 9 ,
  7 1 9 -> 7 5 4 9 ,
  7 1 9 -> 8 4 9 ,
  7 1 9 -> 7 9 ,
  11 1 1 -> 11 2 3 4 5 4 1 ,
  11 1 2 -> 11 2 3 4 5 4 2 ,
  11 1 5 -> 11 2 3 4 5 4 5 ,
  8 12 13 -> 0 1 ,
  8 12 13 -> 0 ,
  8 12 3 -> 0 5 ,
  8 12 3 -> 8 ,
  6 12 13 -> 10 1 ,
  6 12 13 -> 0 ,
  6 12 3 -> 10 5 ,
  6 12 3 -> 8 ,
  4 2 ->= 12 ,
  4 5 ->= 14 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 9 ->= 1 2 3 4 5 4 9 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  13 1 9 ->= 13 2 3 4 5 4 9 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 9 ->= 4 2 3 4 5 4 9 ,
  15 1 1 ->= 15 2 3 4 5 4 1 ,
  15 1 2 ->= 15 2 3 4 5 4 2 ,
  15 1 5 ->= 15 2 3 4 5 4 5 ,
  5 12 13 ->= 1 1 ,
  5 12 3 ->= 1 5 ,
  3 12 13 ->= 13 1 ,
  3 12 3 ->= 13 5 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 9->6, 10->7, 7->8, 11->9, 12->10, 14->11, 13->12, 15->13 }, 
it remains to prove termination of the 36-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  0 1 6 -> 0 2 3 4 5 4 6 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  7 1 6 -> 7 2 3 4 5 4 6 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  8 1 6 -> 8 2 3 4 5 4 6 ,
  9 1 1 -> 9 2 3 4 5 4 1 ,
  9 1 2 -> 9 2 3 4 5 4 2 ,
  9 1 5 -> 9 2 3 4 5 4 5 ,
  4 2 ->= 10 ,
  4 5 ->= 11 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 6 ->= 1 2 3 4 5 4 6 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 6 ->= 12 2 3 4 5 4 6 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 6 ->= 4 2 3 4 5 4 6 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 10 12 ->= 1 1 ,
  5 10 3 ->= 1 5 ,
  3 10 12 ->= 12 1 ,
  3 10 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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, 7->6, 6->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13 }, 
it remains to prove termination of the 35-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  6 1 5 -> 6 2 3 4 5 4 5 ,
  6 1 7 -> 6 2 3 4 5 4 7 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  8 1 7 -> 8 2 3 4 5 4 7 ,
  9 1 1 -> 9 2 3 4 5 4 1 ,
  9 1 2 -> 9 2 3 4 5 4 2 ,
  9 1 5 -> 9 2 3 4 5 4 5 ,
  4 2 ->= 10 ,
  4 5 ->= 11 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 7 ->= 1 2 3 4 5 4 7 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 7 ->= 12 2 3 4 5 4 7 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 7 ->= 4 2 3 4 5 4 7 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 10 12 ->= 1 1 ,
  5 10 3 ->= 1 5 ,
  3 10 12 ->= 12 1 ,
  3 10 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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 34-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  6 1 5 -> 6 2 3 4 5 4 5 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  7 1 8 -> 7 2 3 4 5 4 8 ,
  9 1 1 -> 9 2 3 4 5 4 1 ,
  9 1 2 -> 9 2 3 4 5 4 2 ,
  9 1 5 -> 9 2 3 4 5 4 5 ,
  4 2 ->= 10 ,
  4 5 ->= 11 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 8 ->= 1 2 3 4 5 4 8 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 8 ->= 12 2 3 4 5 4 8 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 8 ->= 4 2 3 4 5 4 8 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 10 12 ->= 1 1 ,
  5 10 3 ->= 1 5 ,
  3 10 12 ->= 12 1 ,
  3 10 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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, 10->9, 11->10, 8->11, 12->12, 13->13 }, 
it remains to prove termination of the 33-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  0 1 5 -> 0 2 3 4 5 4 5 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  6 1 5 -> 6 2 3 4 5 4 5 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  4 2 ->= 9 ,
  4 5 ->= 10 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 11 ->= 1 2 3 4 5 4 11 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 11 ->= 12 2 3 4 5 4 11 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 11 ->= 4 2 3 4 5 4 11 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 9 12 ->= 1 1 ,
  5 9 3 ->= 1 5 ,
  3 9 12 ->= 12 1 ,
  3 9 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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 32-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  6 1 5 -> 6 2 3 4 5 4 5 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  4 2 ->= 9 ,
  4 5 ->= 10 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 11 ->= 1 2 3 4 5 4 11 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 11 ->= 12 2 3 4 5 4 11 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 11 ->= 4 2 3 4 5 4 11 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 9 12 ->= 1 1 ,
  5 9 3 ->= 1 5 ,
  3 9 12 ->= 12 1 ,
  3 9 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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 31-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  7 1 5 -> 7 2 3 4 5 4 5 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  4 2 ->= 9 ,
  4 5 ->= 10 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 11 ->= 1 2 3 4 5 4 11 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 11 ->= 12 2 3 4 5 4 11 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 11 ->= 4 2 3 4 5 4 11 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 9 12 ->= 1 1 ,
  5 9 3 ->= 1 5 ,
  3 9 12 ->= 12 1 ,
  3 9 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 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 30-rule system
{ 0 1 1 -> 0 2 3 4 5 4 1 ,
  0 1 2 -> 0 2 3 4 5 4 2 ,
  6 1 1 -> 6 2 3 4 5 4 1 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  7 1 1 -> 7 2 3 4 5 4 1 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  8 1 1 -> 8 2 3 4 5 4 1 ,
  8 1 2 -> 8 2 3 4 5 4 2 ,
  8 1 5 -> 8 2 3 4 5 4 5 ,
  4 2 ->= 9 ,
  4 5 ->= 10 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  1 1 11 ->= 1 2 3 4 5 4 11 ,
  12 1 1 ->= 12 2 3 4 5 4 1 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  12 1 5 ->= 12 2 3 4 5 4 5 ,
  12 1 11 ->= 12 2 3 4 5 4 11 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 11 ->= 4 2 3 4 5 4 11 ,
  13 1 1 ->= 13 2 3 4 5 4 1 ,
  13 1 2 ->= 13 2 3 4 5 4 2 ,
  13 1 5 ->= 13 2 3 4 5 4 5 ,
  5 9 12 ->= 1 1 ,
  5 9 3 ->= 1 5 ,
  3 9 12 ->= 12 1 ,
  3 9 3 ->= 12 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

After renaming modulo { 6->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12 }, 
it remains to prove termination of the 20-rule system
{ 0 1 2 -> 0 2 3 4 5 4 2 ,
  6 1 2 -> 6 2 3 4 5 4 2 ,
  7 1 2 -> 7 2 3 4 5 4 2 ,
  4 2 ->= 8 ,
  4 5 ->= 9 ,
  1 1 1 ->= 1 2 3 4 5 4 1 ,
  1 1 2 ->= 1 2 3 4 5 4 2 ,
  1 1 5 ->= 1 2 3 4 5 4 5 ,
  10 1 1 ->= 10 2 3 4 5 4 1 ,
  10 1 2 ->= 10 2 3 4 5 4 2 ,
  10 1 5 ->= 10 2 3 4 5 4 5 ,
  4 1 1 ->= 4 2 3 4 5 4 1 ,
  4 1 2 ->= 4 2 3 4 5 4 2 ,
  4 1 5 ->= 4 2 3 4 5 4 5 ,
  4 1 11 ->= 4 2 3 4 5 4 11 ,
  12 1 2 ->= 12 2 3 4 5 4 2 ,
  5 8 10 ->= 1 1 ,
  5 8 3 ->= 1 5 ,
  3 8 10 ->= 10 1 ,
  3 8 3 ->= 10 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 1 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

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

The system is trivially terminating.