YES

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

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (1,true)->3, (4,true)->4, (5,true)->5, (6,true)->6, (7,true)->7, (10,true)->8, (11,true)->9, (4,false)->10, (2,false)->11, (7,false)->12, (12,false)->13, (6,false)->14, (12,true)->15, (8,false)->16, (3,false)->17, (9,false)->18, (5,false)->19, (10,false)->20, (11,false)->21 },
it remains to prove termination of the 134-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  6 2 -> 7 ,
  8 1 -> 8 ,
  8 2 -> 9 ,
  3 10 1 -> 0 11 12 13 12 13 14 ,
  3 10 1 -> 7 13 12 13 14 ,
  3 10 1 -> 15 12 13 14 ,
  3 10 1 -> 7 13 14 ,
  3 10 1 -> 15 14 ,
  3 10 1 -> 6 ,
  3 10 2 -> 0 11 12 13 12 13 12 ,
  3 10 2 -> 7 13 12 13 12 ,
  3 10 2 -> 15 12 13 12 ,
  3 10 2 -> 7 13 12 ,
  3 10 2 -> 15 12 ,
  3 10 2 -> 7 ,
  3 10 11 -> 0 11 12 13 12 13 16 ,
  3 10 11 -> 7 13 12 13 16 ,
  3 10 11 -> 15 12 13 16 ,
  3 10 11 -> 7 13 16 ,
  3 10 11 -> 15 16 ,
  3 10 17 -> 0 11 12 13 12 13 18 ,
  3 10 17 -> 7 13 12 13 18 ,
  3 10 17 -> 15 12 13 18 ,
  3 10 17 -> 7 13 18 ,
  3 10 17 -> 15 18 ,
  5 10 1 -> 4 11 12 13 12 13 14 ,
  5 10 1 -> 7 13 12 13 14 ,
  5 10 1 -> 15 12 13 14 ,
  5 10 1 -> 7 13 14 ,
  5 10 1 -> 15 14 ,
  5 10 1 -> 6 ,
  5 10 2 -> 4 11 12 13 12 13 12 ,
  5 10 2 -> 7 13 12 13 12 ,
  5 10 2 -> 15 12 13 12 ,
  5 10 2 -> 7 13 12 ,
  5 10 2 -> 15 12 ,
  5 10 2 -> 7 ,
  5 10 11 -> 4 11 12 13 12 13 16 ,
  5 10 11 -> 7 13 12 13 16 ,
  5 10 11 -> 15 12 13 16 ,
  5 10 11 -> 7 13 16 ,
  5 10 11 -> 15 16 ,
  5 10 17 -> 4 11 12 13 12 13 18 ,
  5 10 17 -> 7 13 12 13 18 ,
  5 10 17 -> 15 12 13 18 ,
  5 10 17 -> 7 13 18 ,
  5 10 17 -> 15 18 ,
  7 10 1 -> 6 11 12 13 12 13 14 ,
  7 10 1 -> 7 13 12 13 14 ,
  7 10 1 -> 15 12 13 14 ,
  7 10 1 -> 7 13 14 ,
  7 10 1 -> 15 14 ,
  7 10 1 -> 6 ,
  7 10 2 -> 6 11 12 13 12 13 12 ,
  7 10 2 -> 7 13 12 13 12 ,
  7 10 2 -> 15 12 13 12 ,
  7 10 2 -> 7 13 12 ,
  7 10 2 -> 15 12 ,
  7 10 2 -> 7 ,
  7 10 11 -> 6 11 12 13 12 13 16 ,
  7 10 11 -> 7 13 12 13 16 ,
  7 10 11 -> 15 12 13 16 ,
  7 10 11 -> 7 13 16 ,
  7 10 11 -> 15 16 ,
  7 10 17 -> 6 11 12 13 12 13 18 ,
  7 10 17 -> 7 13 12 13 18 ,
  7 10 17 -> 15 12 13 18 ,
  7 10 17 -> 7 13 18 ,
  7 10 17 -> 15 18 ,
  9 10 1 -> 8 11 12 13 12 13 14 ,
  9 10 1 -> 7 13 12 13 14 ,
  9 10 1 -> 15 12 13 14 ,
  9 10 1 -> 7 13 14 ,
  9 10 1 -> 15 14 ,
  9 10 1 -> 6 ,
  9 10 2 -> 8 11 12 13 12 13 12 ,
  9 10 2 -> 7 13 12 13 12 ,
  9 10 2 -> 15 12 13 12 ,
  9 10 2 -> 7 13 12 ,
  9 10 2 -> 15 12 ,
  9 10 2 -> 7 ,
  9 10 11 -> 8 11 12 13 12 13 16 ,
  9 10 11 -> 7 13 12 13 16 ,
  9 10 11 -> 15 12 13 16 ,
  9 10 11 -> 7 13 16 ,
  9 10 11 -> 15 16 ,
  9 10 17 -> 8 11 12 13 12 13 18 ,
  9 10 17 -> 7 13 12 13 18 ,
  9 10 17 -> 15 12 13 18 ,
  9 10 17 -> 7 13 18 ,
  9 10 17 -> 15 18 ,
  15 16 14 -> 4 1 ,
  15 16 14 -> 0 ,
  15 16 12 -> 4 2 ,
  15 16 12 -> 3 ,
  15 16 16 -> 4 11 ,
  15 16 18 -> 4 17 ,
  1 1 ->= 1 ,
  1 2 ->= 2 ,
  1 11 ->= 11 ,
  1 17 ->= 17 ,
  10 1 ->= 10 ,
  10 2 ->= 19 ,
  14 1 ->= 14 ,
  14 2 ->= 12 ,
  14 11 ->= 16 ,
  14 17 ->= 18 ,
  20 1 ->= 20 ,
  20 2 ->= 21 ,
  2 10 1 ->= 1 11 12 13 12 13 14 ,
  2 10 2 ->= 1 11 12 13 12 13 12 ,
  2 10 11 ->= 1 11 12 13 12 13 16 ,
  2 10 17 ->= 1 11 12 13 12 13 18 ,
  19 10 1 ->= 10 11 12 13 12 13 14 ,
  19 10 2 ->= 10 11 12 13 12 13 12 ,
  19 10 11 ->= 10 11 12 13 12 13 16 ,
  19 10 17 ->= 10 11 12 13 12 13 18 ,
  12 10 1 ->= 14 11 12 13 12 13 14 ,
  12 10 2 ->= 14 11 12 13 12 13 12 ,
  12 10 11 ->= 14 11 12 13 12 13 16 ,
  12 10 17 ->= 14 11 12 13 12 13 18 ,
  21 10 1 ->= 20 11 12 13 12 13 14 ,
  21 10 2 ->= 20 11 12 13 12 13 12 ,
  21 10 11 ->= 20 11 12 13 12 13 16 ,
  21 10 17 ->= 20 11 12 13 12 13 18 ,
  13 16 14 ->= 10 1 ,
  13 16 12 ->= 10 2 ,
  13 16 16 ->= 10 11 ,
  13 16 18 ->= 10 17 }


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 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
19 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
20 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
21 is interpreted by
 /   \
| 1 0 |
| 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, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20 }, 
it remains to prove termination of the 56-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  6 2 -> 7 ,
  8 1 -> 8 ,
  8 2 -> 9 ,
  3 10 1 -> 0 11 12 13 12 13 14 ,
  3 10 2 -> 0 11 12 13 12 13 12 ,
  3 10 11 -> 0 11 12 13 12 13 15 ,
  3 10 16 -> 0 11 12 13 12 13 17 ,
  5 10 1 -> 4 11 12 13 12 13 14 ,
  5 10 2 -> 4 11 12 13 12 13 12 ,
  5 10 11 -> 4 11 12 13 12 13 15 ,
  5 10 16 -> 4 11 12 13 12 13 17 ,
  7 10 1 -> 6 11 12 13 12 13 14 ,
  7 10 2 -> 6 11 12 13 12 13 12 ,
  7 10 11 -> 6 11 12 13 12 13 15 ,
  7 10 16 -> 6 11 12 13 12 13 17 ,
  9 10 1 -> 8 11 12 13 12 13 14 ,
  9 10 2 -> 8 11 12 13 12 13 12 ,
  9 10 11 -> 8 11 12 13 12 13 15 ,
  9 10 16 -> 8 11 12 13 12 13 17 ,
  1 1 ->= 1 ,
  1 2 ->= 2 ,
  1 11 ->= 11 ,
  1 16 ->= 16 ,
  10 1 ->= 10 ,
  10 2 ->= 18 ,
  14 1 ->= 14 ,
  14 2 ->= 12 ,
  14 11 ->= 15 ,
  14 16 ->= 17 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  2 10 1 ->= 1 11 12 13 12 13 14 ,
  2 10 2 ->= 1 11 12 13 12 13 12 ,
  2 10 11 ->= 1 11 12 13 12 13 15 ,
  2 10 16 ->= 1 11 12 13 12 13 17 ,
  18 10 1 ->= 10 11 12 13 12 13 14 ,
  18 10 2 ->= 10 11 12 13 12 13 12 ,
  18 10 11 ->= 10 11 12 13 12 13 15 ,
  18 10 16 ->= 10 11 12 13 12 13 17 ,
  12 10 1 ->= 14 11 12 13 12 13 14 ,
  12 10 2 ->= 14 11 12 13 12 13 12 ,
  12 10 11 ->= 14 11 12 13 12 13 15 ,
  12 10 16 ->= 14 11 12 13 12 13 17 ,
  20 10 1 ->= 19 11 12 13 12 13 14 ,
  20 10 2 ->= 19 11 12 13 12 13 12 ,
  20 10 11 ->= 19 11 12 13 12 13 15 ,
  20 10 16 ->= 19 11 12 13 12 13 17 ,
  13 15 14 ->= 10 1 ,
  13 15 12 ->= 10 2 ,
  13 15 15 ->= 10 11 ,
  13 15 17 ->= 10 16 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
17 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
18 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
19 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
20 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

After renaming modulo { 0->0, 1->1, 4->2, 2->3, 5->4, 6->5, 7->6, 8->7, 9->8, 3->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 55-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  2 3 -> 4 ,
  5 1 -> 5 ,
  5 3 -> 6 ,
  7 1 -> 7 ,
  7 3 -> 8 ,
  9 10 1 -> 0 11 12 13 12 13 14 ,
  9 10 3 -> 0 11 12 13 12 13 12 ,
  9 10 11 -> 0 11 12 13 12 13 15 ,
  9 10 16 -> 0 11 12 13 12 13 17 ,
  4 10 1 -> 2 11 12 13 12 13 14 ,
  4 10 3 -> 2 11 12 13 12 13 12 ,
  4 10 11 -> 2 11 12 13 12 13 15 ,
  4 10 16 -> 2 11 12 13 12 13 17 ,
  6 10 1 -> 5 11 12 13 12 13 14 ,
  6 10 3 -> 5 11 12 13 12 13 12 ,
  6 10 11 -> 5 11 12 13 12 13 15 ,
  6 10 16 -> 5 11 12 13 12 13 17 ,
  8 10 1 -> 7 11 12 13 12 13 14 ,
  8 10 3 -> 7 11 12 13 12 13 12 ,
  8 10 11 -> 7 11 12 13 12 13 15 ,
  8 10 16 -> 7 11 12 13 12 13 17 ,
  1 1 ->= 1 ,
  1 3 ->= 3 ,
  1 11 ->= 11 ,
  1 16 ->= 16 ,
  10 1 ->= 10 ,
  10 3 ->= 18 ,
  14 1 ->= 14 ,
  14 3 ->= 12 ,
  14 11 ->= 15 ,
  14 16 ->= 17 ,
  19 1 ->= 19 ,
  19 3 ->= 20 ,
  3 10 1 ->= 1 11 12 13 12 13 14 ,
  3 10 3 ->= 1 11 12 13 12 13 12 ,
  3 10 11 ->= 1 11 12 13 12 13 15 ,
  3 10 16 ->= 1 11 12 13 12 13 17 ,
  18 10 1 ->= 10 11 12 13 12 13 14 ,
  18 10 3 ->= 10 11 12 13 12 13 12 ,
  18 10 11 ->= 10 11 12 13 12 13 15 ,
  18 10 16 ->= 10 11 12 13 12 13 17 ,
  12 10 1 ->= 14 11 12 13 12 13 14 ,
  12 10 3 ->= 14 11 12 13 12 13 12 ,
  12 10 11 ->= 14 11 12 13 12 13 15 ,
  12 10 16 ->= 14 11 12 13 12 13 17 ,
  20 10 1 ->= 19 11 12 13 12 13 14 ,
  20 10 3 ->= 19 11 12 13 12 13 12 ,
  20 10 11 ->= 19 11 12 13 12 13 15 ,
  20 10 16 ->= 19 11 12 13 12 13 17 ,
  13 15 14 ->= 10 1 ,
  13 15 12 ->= 10 3 ,
  13 15 15 ->= 10 11 ,
  13 15 17 ->= 10 16 }


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 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 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
19 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
20 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19 }, 
it remains to prove termination of the 51-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  2 3 -> 4 ,
  5 1 -> 5 ,
  5 3 -> 6 ,
  7 1 -> 7 ,
  7 3 -> 8 ,
  4 9 1 -> 2 10 11 12 11 12 13 ,
  4 9 3 -> 2 10 11 12 11 12 11 ,
  4 9 10 -> 2 10 11 12 11 12 14 ,
  4 9 15 -> 2 10 11 12 11 12 16 ,
  6 9 1 -> 5 10 11 12 11 12 13 ,
  6 9 3 -> 5 10 11 12 11 12 11 ,
  6 9 10 -> 5 10 11 12 11 12 14 ,
  6 9 15 -> 5 10 11 12 11 12 16 ,
  8 9 1 -> 7 10 11 12 11 12 13 ,
  8 9 3 -> 7 10 11 12 11 12 11 ,
  8 9 10 -> 7 10 11 12 11 12 14 ,
  8 9 15 -> 7 10 11 12 11 12 16 ,
  1 1 ->= 1 ,
  1 3 ->= 3 ,
  1 10 ->= 10 ,
  1 15 ->= 15 ,
  9 1 ->= 9 ,
  9 3 ->= 17 ,
  13 1 ->= 13 ,
  13 3 ->= 11 ,
  13 10 ->= 14 ,
  13 15 ->= 16 ,
  18 1 ->= 18 ,
  18 3 ->= 19 ,
  3 9 1 ->= 1 10 11 12 11 12 13 ,
  3 9 3 ->= 1 10 11 12 11 12 11 ,
  3 9 10 ->= 1 10 11 12 11 12 14 ,
  3 9 15 ->= 1 10 11 12 11 12 16 ,
  17 9 1 ->= 9 10 11 12 11 12 13 ,
  17 9 3 ->= 9 10 11 12 11 12 11 ,
  17 9 10 ->= 9 10 11 12 11 12 14 ,
  17 9 15 ->= 9 10 11 12 11 12 16 ,
  11 9 1 ->= 13 10 11 12 11 12 13 ,
  11 9 3 ->= 13 10 11 12 11 12 11 ,
  11 9 10 ->= 13 10 11 12 11 12 14 ,
  11 9 15 ->= 13 10 11 12 11 12 16 ,
  19 9 1 ->= 18 10 11 12 11 12 13 ,
  19 9 3 ->= 18 10 11 12 11 12 11 ,
  19 9 10 ->= 18 10 11 12 11 12 14 ,
  19 9 15 ->= 18 10 11 12 11 12 16 ,
  12 14 13 ->= 9 1 ,
  12 14 11 ->= 9 3 ,
  12 14 14 ->= 9 10 ,
  12 14 16 ->= 9 15 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
17 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
18 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
19 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

After renaming modulo { 0->0, 1->1, 2->2, 5->3, 3->4, 6->5, 7->6, 8->7, 4->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19 }, 
it remains to prove termination of the 50-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  3 4 -> 5 ,
  6 1 -> 6 ,
  6 4 -> 7 ,
  8 9 1 -> 2 10 11 12 11 12 13 ,
  8 9 4 -> 2 10 11 12 11 12 11 ,
  8 9 10 -> 2 10 11 12 11 12 14 ,
  8 9 15 -> 2 10 11 12 11 12 16 ,
  5 9 1 -> 3 10 11 12 11 12 13 ,
  5 9 4 -> 3 10 11 12 11 12 11 ,
  5 9 10 -> 3 10 11 12 11 12 14 ,
  5 9 15 -> 3 10 11 12 11 12 16 ,
  7 9 1 -> 6 10 11 12 11 12 13 ,
  7 9 4 -> 6 10 11 12 11 12 11 ,
  7 9 10 -> 6 10 11 12 11 12 14 ,
  7 9 15 -> 6 10 11 12 11 12 16 ,
  1 1 ->= 1 ,
  1 4 ->= 4 ,
  1 10 ->= 10 ,
  1 15 ->= 15 ,
  9 1 ->= 9 ,
  9 4 ->= 17 ,
  13 1 ->= 13 ,
  13 4 ->= 11 ,
  13 10 ->= 14 ,
  13 15 ->= 16 ,
  18 1 ->= 18 ,
  18 4 ->= 19 ,
  4 9 1 ->= 1 10 11 12 11 12 13 ,
  4 9 4 ->= 1 10 11 12 11 12 11 ,
  4 9 10 ->= 1 10 11 12 11 12 14 ,
  4 9 15 ->= 1 10 11 12 11 12 16 ,
  17 9 1 ->= 9 10 11 12 11 12 13 ,
  17 9 4 ->= 9 10 11 12 11 12 11 ,
  17 9 10 ->= 9 10 11 12 11 12 14 ,
  17 9 15 ->= 9 10 11 12 11 12 16 ,
  11 9 1 ->= 13 10 11 12 11 12 13 ,
  11 9 4 ->= 13 10 11 12 11 12 11 ,
  11 9 10 ->= 13 10 11 12 11 12 14 ,
  11 9 15 ->= 13 10 11 12 11 12 16 ,
  19 9 1 ->= 18 10 11 12 11 12 13 ,
  19 9 4 ->= 18 10 11 12 11 12 11 ,
  19 9 10 ->= 18 10 11 12 11 12 14 ,
  19 9 15 ->= 18 10 11 12 11 12 16 ,
  12 14 13 ->= 9 1 ,
  12 14 11 ->= 9 4 ,
  12 14 14 ->= 9 10 ,
  12 14 16 ->= 9 15 }


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

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 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 1 |
| 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 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
19 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18 }, 
it remains to prove termination of the 46-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  3 4 -> 5 ,
  6 1 -> 6 ,
  6 4 -> 7 ,
  5 8 1 -> 3 9 10 11 10 11 12 ,
  5 8 4 -> 3 9 10 11 10 11 10 ,
  5 8 9 -> 3 9 10 11 10 11 13 ,
  5 8 14 -> 3 9 10 11 10 11 15 ,
  7 8 1 -> 6 9 10 11 10 11 12 ,
  7 8 4 -> 6 9 10 11 10 11 10 ,
  7 8 9 -> 6 9 10 11 10 11 13 ,
  7 8 14 -> 6 9 10 11 10 11 15 ,
  1 1 ->= 1 ,
  1 4 ->= 4 ,
  1 9 ->= 9 ,
  1 14 ->= 14 ,
  8 1 ->= 8 ,
  8 4 ->= 16 ,
  12 1 ->= 12 ,
  12 4 ->= 10 ,
  12 9 ->= 13 ,
  12 14 ->= 15 ,
  17 1 ->= 17 ,
  17 4 ->= 18 ,
  4 8 1 ->= 1 9 10 11 10 11 12 ,
  4 8 4 ->= 1 9 10 11 10 11 10 ,
  4 8 9 ->= 1 9 10 11 10 11 13 ,
  4 8 14 ->= 1 9 10 11 10 11 15 ,
  16 8 1 ->= 8 9 10 11 10 11 12 ,
  16 8 4 ->= 8 9 10 11 10 11 10 ,
  16 8 9 ->= 8 9 10 11 10 11 13 ,
  16 8 14 ->= 8 9 10 11 10 11 15 ,
  10 8 1 ->= 12 9 10 11 10 11 12 ,
  10 8 4 ->= 12 9 10 11 10 11 10 ,
  10 8 9 ->= 12 9 10 11 10 11 13 ,
  10 8 14 ->= 12 9 10 11 10 11 15 ,
  18 8 1 ->= 17 9 10 11 10 11 12 ,
  18 8 4 ->= 17 9 10 11 10 11 10 ,
  18 8 9 ->= 17 9 10 11 10 11 13 ,
  18 8 14 ->= 17 9 10 11 10 11 15 ,
  11 13 12 ->= 8 1 ,
  11 13 10 ->= 8 4 ,
  11 13 13 ->= 8 9 ,
  11 13 15 ->= 8 14 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 6->4, 4->5, 7->6, 5->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 45-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  4 5 -> 6 ,
  7 8 1 -> 3 9 10 11 10 11 12 ,
  7 8 5 -> 3 9 10 11 10 11 10 ,
  7 8 9 -> 3 9 10 11 10 11 13 ,
  7 8 14 -> 3 9 10 11 10 11 15 ,
  6 8 1 -> 4 9 10 11 10 11 12 ,
  6 8 5 -> 4 9 10 11 10 11 10 ,
  6 8 9 -> 4 9 10 11 10 11 13 ,
  6 8 14 -> 4 9 10 11 10 11 15 ,
  1 1 ->= 1 ,
  1 5 ->= 5 ,
  1 9 ->= 9 ,
  1 14 ->= 14 ,
  8 1 ->= 8 ,
  8 5 ->= 16 ,
  12 1 ->= 12 ,
  12 5 ->= 10 ,
  12 9 ->= 13 ,
  12 14 ->= 15 ,
  17 1 ->= 17 ,
  17 5 ->= 18 ,
  5 8 1 ->= 1 9 10 11 10 11 12 ,
  5 8 5 ->= 1 9 10 11 10 11 10 ,
  5 8 9 ->= 1 9 10 11 10 11 13 ,
  5 8 14 ->= 1 9 10 11 10 11 15 ,
  16 8 1 ->= 8 9 10 11 10 11 12 ,
  16 8 5 ->= 8 9 10 11 10 11 10 ,
  16 8 9 ->= 8 9 10 11 10 11 13 ,
  16 8 14 ->= 8 9 10 11 10 11 15 ,
  10 8 1 ->= 12 9 10 11 10 11 12 ,
  10 8 5 ->= 12 9 10 11 10 11 10 ,
  10 8 9 ->= 12 9 10 11 10 11 13 ,
  10 8 14 ->= 12 9 10 11 10 11 15 ,
  18 8 1 ->= 17 9 10 11 10 11 12 ,
  18 8 5 ->= 17 9 10 11 10 11 10 ,
  18 8 9 ->= 17 9 10 11 10 11 13 ,
  18 8 14 ->= 17 9 10 11 10 11 15 ,
  11 13 12 ->= 8 1 ,
  11 13 10 ->= 8 5 ,
  11 13 13 ->= 8 9 ,
  11 13 15 ->= 8 14 }


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 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 1 |
| 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 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17 }, 
it remains to prove termination of the 41-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  4 5 -> 6 ,
  6 7 1 -> 4 8 9 10 9 10 11 ,
  6 7 5 -> 4 8 9 10 9 10 9 ,
  6 7 8 -> 4 8 9 10 9 10 12 ,
  6 7 13 -> 4 8 9 10 9 10 14 ,
  1 1 ->= 1 ,
  1 5 ->= 5 ,
  1 8 ->= 8 ,
  1 13 ->= 13 ,
  7 1 ->= 7 ,
  7 5 ->= 15 ,
  11 1 ->= 11 ,
  11 5 ->= 9 ,
  11 8 ->= 12 ,
  11 13 ->= 14 ,
  16 1 ->= 16 ,
  16 5 ->= 17 ,
  5 7 1 ->= 1 8 9 10 9 10 11 ,
  5 7 5 ->= 1 8 9 10 9 10 9 ,
  5 7 8 ->= 1 8 9 10 9 10 12 ,
  5 7 13 ->= 1 8 9 10 9 10 14 ,
  15 7 1 ->= 7 8 9 10 9 10 11 ,
  15 7 5 ->= 7 8 9 10 9 10 9 ,
  15 7 8 ->= 7 8 9 10 9 10 12 ,
  15 7 13 ->= 7 8 9 10 9 10 14 ,
  9 7 1 ->= 11 8 9 10 9 10 11 ,
  9 7 5 ->= 11 8 9 10 9 10 9 ,
  9 7 8 ->= 11 8 9 10 9 10 12 ,
  9 7 13 ->= 11 8 9 10 9 10 14 ,
  17 7 1 ->= 16 8 9 10 9 10 11 ,
  17 7 5 ->= 16 8 9 10 9 10 9 ,
  17 7 8 ->= 16 8 9 10 9 10 12 ,
  17 7 13 ->= 16 8 9 10 9 10 14 ,
  10 12 11 ->= 7 1 ,
  10 12 9 ->= 7 5 ,
  10 12 12 ->= 7 8 ,
  10 12 14 ->= 7 13 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
17 is interpreted by
 /     \
| 1 0 0 |
| 0 1 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, 5->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 40-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 1 -> 4 7 8 9 8 9 10 ,
  5 6 11 -> 4 7 8 9 8 9 8 ,
  5 6 7 -> 4 7 8 9 8 9 12 ,
  5 6 13 -> 4 7 8 9 8 9 14 ,
  1 1 ->= 1 ,
  1 11 ->= 11 ,
  1 7 ->= 7 ,
  1 13 ->= 13 ,
  6 1 ->= 6 ,
  6 11 ->= 15 ,
  10 1 ->= 10 ,
  10 11 ->= 8 ,
  10 7 ->= 12 ,
  10 13 ->= 14 ,
  16 1 ->= 16 ,
  16 11 ->= 17 ,
  11 6 1 ->= 1 7 8 9 8 9 10 ,
  11 6 11 ->= 1 7 8 9 8 9 8 ,
  11 6 7 ->= 1 7 8 9 8 9 12 ,
  11 6 13 ->= 1 7 8 9 8 9 14 ,
  15 6 1 ->= 6 7 8 9 8 9 10 ,
  15 6 11 ->= 6 7 8 9 8 9 8 ,
  15 6 7 ->= 6 7 8 9 8 9 12 ,
  15 6 13 ->= 6 7 8 9 8 9 14 ,
  8 6 1 ->= 10 7 8 9 8 9 10 ,
  8 6 11 ->= 10 7 8 9 8 9 8 ,
  8 6 7 ->= 10 7 8 9 8 9 12 ,
  8 6 13 ->= 10 7 8 9 8 9 14 ,
  17 6 1 ->= 16 7 8 9 8 9 10 ,
  17 6 11 ->= 16 7 8 9 8 9 8 ,
  17 6 7 ->= 16 7 8 9 8 9 12 ,
  17 6 13 ->= 16 7 8 9 8 9 14 ,
  9 12 10 ->= 6 1 ,
  9 12 8 ->= 6 11 ,
  9 12 12 ->= 6 7 ,
  9 12 14 ->= 6 13 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 11->5, 7->6, 13->7, 6->8, 15->9, 10->10, 8->11, 12->12, 14->13, 16->14, 17->15, 9->16 }, 
it remains to prove termination of the 36-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  1 1 ->= 1 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  1 7 ->= 7 ,
  8 1 ->= 8 ,
  8 5 ->= 9 ,
  10 1 ->= 10 ,
  10 5 ->= 11 ,
  10 6 ->= 12 ,
  10 7 ->= 13 ,
  14 1 ->= 14 ,
  14 5 ->= 15 ,
  5 8 1 ->= 1 6 11 16 11 16 10 ,
  5 8 5 ->= 1 6 11 16 11 16 11 ,
  5 8 6 ->= 1 6 11 16 11 16 12 ,
  5 8 7 ->= 1 6 11 16 11 16 13 ,
  9 8 1 ->= 8 6 11 16 11 16 10 ,
  9 8 5 ->= 8 6 11 16 11 16 11 ,
  9 8 6 ->= 8 6 11 16 11 16 12 ,
  9 8 7 ->= 8 6 11 16 11 16 13 ,
  11 8 1 ->= 10 6 11 16 11 16 10 ,
  11 8 5 ->= 10 6 11 16 11 16 11 ,
  11 8 6 ->= 10 6 11 16 11 16 12 ,
  11 8 7 ->= 10 6 11 16 11 16 13 ,
  15 8 1 ->= 14 6 11 16 11 16 10 ,
  15 8 5 ->= 14 6 11 16 11 16 11 ,
  15 8 6 ->= 14 6 11 16 11 16 12 ,
  15 8 7 ->= 14 6 11 16 11 16 13 ,
  16 12 10 ->= 8 1 ,
  16 12 11 ->= 8 5 ,
  16 12 12 ->= 8 6 ,
  16 12 13 ->= 8 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 7->6, 8->7, 5->8, 9->9, 10->10, 12->11, 13->12, 14->13, 15->14, 11->15, 16->16 }, 
it remains to prove termination of the 32-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  7 1 ->= 7 ,
  7 8 ->= 9 ,
  10 5 ->= 11 ,
  10 6 ->= 12 ,
  13 1 ->= 13 ,
  13 8 ->= 14 ,
  8 7 1 ->= 1 5 15 16 15 16 10 ,
  8 7 8 ->= 1 5 15 16 15 16 15 ,
  8 7 5 ->= 1 5 15 16 15 16 11 ,
  8 7 6 ->= 1 5 15 16 15 16 12 ,
  9 7 1 ->= 7 5 15 16 15 16 10 ,
  9 7 8 ->= 7 5 15 16 15 16 15 ,
  9 7 5 ->= 7 5 15 16 15 16 11 ,
  9 7 6 ->= 7 5 15 16 15 16 12 ,
  15 7 1 ->= 10 5 15 16 15 16 10 ,
  15 7 8 ->= 10 5 15 16 15 16 15 ,
  15 7 5 ->= 10 5 15 16 15 16 11 ,
  15 7 6 ->= 10 5 15 16 15 16 12 ,
  14 7 1 ->= 13 5 15 16 15 16 10 ,
  14 7 8 ->= 13 5 15 16 15 16 15 ,
  14 7 5 ->= 13 5 15 16 15 16 11 ,
  14 7 6 ->= 13 5 15 16 15 16 12 ,
  16 11 10 ->= 7 1 ,
  16 11 15 ->= 7 8 ,
  16 11 11 ->= 7 5 ,
  16 11 12 ->= 7 6 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 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, 15->14, 16->15, 14->16 }, 
it remains to prove termination of the 31-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  7 1 ->= 7 ,
  7 8 ->= 9 ,
  10 5 ->= 11 ,
  10 6 ->= 12 ,
  13 1 ->= 13 ,
  8 7 1 ->= 1 5 14 15 14 15 10 ,
  8 7 8 ->= 1 5 14 15 14 15 14 ,
  8 7 5 ->= 1 5 14 15 14 15 11 ,
  8 7 6 ->= 1 5 14 15 14 15 12 ,
  9 7 1 ->= 7 5 14 15 14 15 10 ,
  9 7 8 ->= 7 5 14 15 14 15 14 ,
  9 7 5 ->= 7 5 14 15 14 15 11 ,
  9 7 6 ->= 7 5 14 15 14 15 12 ,
  14 7 1 ->= 10 5 14 15 14 15 10 ,
  14 7 8 ->= 10 5 14 15 14 15 14 ,
  14 7 5 ->= 10 5 14 15 14 15 11 ,
  14 7 6 ->= 10 5 14 15 14 15 12 ,
  16 7 1 ->= 13 5 14 15 14 15 10 ,
  16 7 8 ->= 13 5 14 15 14 15 14 ,
  16 7 5 ->= 13 5 14 15 14 15 11 ,
  16 7 6 ->= 13 5 14 15 14 15 12 ,
  15 11 10 ->= 7 1 ,
  15 11 14 ->= 7 8 ,
  15 11 11 ->= 7 5 ,
  15 11 12 ->= 7 6 }


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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 8->7, 9->8, 10->9, 11->10, 13->11, 14->12, 15->13, 6->14, 12->15 }, 
it remains to prove termination of the 25-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  1 5 ->= 5 ,
  6 1 ->= 6 ,
  6 7 ->= 8 ,
  9 5 ->= 10 ,
  11 1 ->= 11 ,
  7 6 1 ->= 1 5 12 13 12 13 9 ,
  7 6 7 ->= 1 5 12 13 12 13 12 ,
  7 6 5 ->= 1 5 12 13 12 13 10 ,
  7 6 14 ->= 1 5 12 13 12 13 15 ,
  8 6 1 ->= 6 5 12 13 12 13 9 ,
  8 6 7 ->= 6 5 12 13 12 13 12 ,
  8 6 5 ->= 6 5 12 13 12 13 10 ,
  8 6 14 ->= 6 5 12 13 12 13 15 ,
  12 6 1 ->= 9 5 12 13 12 13 9 ,
  12 6 7 ->= 9 5 12 13 12 13 12 ,
  12 6 5 ->= 9 5 12 13 12 13 10 ,
  12 6 14 ->= 9 5 12 13 12 13 15 ,
  13 10 9 ->= 6 1 ,
  13 10 12 ->= 6 7 ,
  13 10 10 ->= 6 5 ,
  13 10 15 ->= 6 14 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 24-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 6 ->= 7 ,
  8 4 ->= 9 ,
  10 1 ->= 10 ,
  6 5 1 ->= 1 4 11 12 11 12 8 ,
  6 5 6 ->= 1 4 11 12 11 12 11 ,
  6 5 4 ->= 1 4 11 12 11 12 9 ,
  6 5 13 ->= 1 4 11 12 11 12 14 ,
  7 5 1 ->= 5 4 11 12 11 12 8 ,
  7 5 6 ->= 5 4 11 12 11 12 11 ,
  7 5 4 ->= 5 4 11 12 11 12 9 ,
  7 5 13 ->= 5 4 11 12 11 12 14 ,
  11 5 1 ->= 8 4 11 12 11 12 8 ,
  11 5 6 ->= 8 4 11 12 11 12 11 ,
  11 5 4 ->= 8 4 11 12 11 12 9 ,
  11 5 13 ->= 8 4 11 12 11 12 14 ,
  12 9 8 ->= 5 1 ,
  12 9 11 ->= 5 6 ,
  12 9 9 ->= 5 4 ,
  12 9 14 ->= 5 13 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 11->10, 12->11, 13->12, 14->13 }, 
it remains to prove termination of the 23-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 6 ->= 7 ,
  8 4 ->= 9 ,
  6 5 1 ->= 1 4 10 11 10 11 8 ,
  6 5 6 ->= 1 4 10 11 10 11 10 ,
  6 5 4 ->= 1 4 10 11 10 11 9 ,
  6 5 12 ->= 1 4 10 11 10 11 13 ,
  7 5 1 ->= 5 4 10 11 10 11 8 ,
  7 5 6 ->= 5 4 10 11 10 11 10 ,
  7 5 4 ->= 5 4 10 11 10 11 9 ,
  7 5 12 ->= 5 4 10 11 10 11 13 ,
  10 5 1 ->= 8 4 10 11 10 11 8 ,
  10 5 6 ->= 8 4 10 11 10 11 10 ,
  10 5 4 ->= 8 4 10 11 10 11 9 ,
  10 5 12 ->= 8 4 10 11 10 11 13 ,
  11 9 8 ->= 5 1 ,
  11 9 10 ->= 5 6 ,
  11 9 9 ->= 5 4 ,
  11 9 13 ->= 5 12 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 0->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12 }, 
it remains to prove termination of the 22-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 3 ->= 3 ,
  4 1 ->= 4 ,
  4 5 ->= 6 ,
  7 3 ->= 8 ,
  5 4 1 ->= 1 3 9 10 9 10 7 ,
  5 4 5 ->= 1 3 9 10 9 10 9 ,
  5 4 3 ->= 1 3 9 10 9 10 8 ,
  5 4 11 ->= 1 3 9 10 9 10 12 ,
  6 4 1 ->= 4 3 9 10 9 10 7 ,
  6 4 5 ->= 4 3 9 10 9 10 9 ,
  6 4 3 ->= 4 3 9 10 9 10 8 ,
  6 4 11 ->= 4 3 9 10 9 10 12 ,
  9 4 1 ->= 7 3 9 10 9 10 7 ,
  9 4 5 ->= 7 3 9 10 9 10 9 ,
  9 4 3 ->= 7 3 9 10 9 10 8 ,
  9 4 11 ->= 7 3 9 10 9 10 12 ,
  10 8 7 ->= 4 1 ,
  10 8 9 ->= 4 5 ,
  10 8 8 ->= 4 3 ,
  10 8 12 ->= 4 11 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 21-rule system
{ 0 1 -> 0 ,
  1 2 ->= 2 ,
  3 1 ->= 3 ,
  3 4 ->= 5 ,
  6 2 ->= 7 ,
  4 3 1 ->= 1 2 8 9 8 9 6 ,
  4 3 4 ->= 1 2 8 9 8 9 8 ,
  4 3 2 ->= 1 2 8 9 8 9 7 ,
  4 3 10 ->= 1 2 8 9 8 9 11 ,
  5 3 1 ->= 3 2 8 9 8 9 6 ,
  5 3 4 ->= 3 2 8 9 8 9 8 ,
  5 3 2 ->= 3 2 8 9 8 9 7 ,
  5 3 10 ->= 3 2 8 9 8 9 11 ,
  8 3 1 ->= 6 2 8 9 8 9 6 ,
  8 3 4 ->= 6 2 8 9 8 9 8 ,
  8 3 2 ->= 6 2 8 9 8 9 7 ,
  8 3 10 ->= 6 2 8 9 8 9 11 ,
  9 7 6 ->= 3 1 ,
  9 7 8 ->= 3 4 ,
  9 7 7 ->= 3 2 ,
  9 7 11 ->= 3 10 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 3:

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

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

The system is trivially terminating.