YES

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


The system was reversed.

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


Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019].

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (0,4)->3, (1,0)->4, (1,1)->5, (1,2)->6, (1,4)->7, (2,0)->8, (2,1)->9, (2,2)->10, (2,4)->11, (3,0)->12, (3,1)->13, (3,2)->14, (3,4)->15 },
it remains to prove termination of the 64-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  4 2 -> 6 ,
  4 3 -> 7 ,
  8 0 -> 8 ,
  8 1 -> 9 ,
  8 2 -> 10 ,
  8 3 -> 11 ,
  12 0 -> 12 ,
  12 1 -> 13 ,
  12 2 -> 14 ,
  12 3 -> 15 ,
  0 0 -> 1 4 ,
  0 1 -> 1 5 ,
  0 2 -> 1 6 ,
  0 3 -> 1 7 ,
  4 0 -> 5 4 ,
  4 1 -> 5 5 ,
  4 2 -> 5 6 ,
  4 3 -> 5 7 ,
  8 0 -> 9 4 ,
  8 1 -> 9 5 ,
  8 2 -> 9 6 ,
  8 3 -> 9 7 ,
  12 0 -> 13 4 ,
  12 1 -> 13 5 ,
  12 2 -> 13 6 ,
  12 3 -> 13 7 ,
  2 9 4 0 -> 0 1 4 2 10 8 ,
  2 9 4 1 -> 0 1 4 2 10 9 ,
  2 9 4 2 -> 0 1 4 2 10 10 ,
  2 9 4 3 -> 0 1 4 2 10 11 ,
  6 9 4 0 -> 4 1 4 2 10 8 ,
  6 9 4 1 -> 4 1 4 2 10 9 ,
  6 9 4 2 -> 4 1 4 2 10 10 ,
  6 9 4 3 -> 4 1 4 2 10 11 ,
  10 9 4 0 -> 8 1 4 2 10 8 ,
  10 9 4 1 -> 8 1 4 2 10 9 ,
  10 9 4 2 -> 8 1 4 2 10 10 ,
  10 9 4 3 -> 8 1 4 2 10 11 ,
  14 9 4 0 -> 12 1 4 2 10 8 ,
  14 9 4 1 -> 12 1 4 2 10 9 ,
  14 9 4 2 -> 12 1 4 2 10 10 ,
  14 9 4 3 -> 12 1 4 2 10 11 ,
  2 8 -> 0 ,
  2 9 -> 1 ,
  2 10 -> 2 ,
  2 11 -> 3 ,
  6 8 -> 4 ,
  6 9 -> 5 ,
  6 10 -> 6 ,
  6 11 -> 7 ,
  10 8 -> 8 ,
  10 9 -> 9 ,
  10 10 -> 10 ,
  10 11 -> 11 ,
  14 8 -> 12 ,
  14 9 -> 13 ,
  14 10 -> 14 ,
  14 11 -> 15 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9, 11->10, 12->11, 14->12 }, 
it remains to prove termination of the 51-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  4 2 -> 6 ,
  7 0 -> 7 ,
  7 1 -> 8 ,
  7 2 -> 9 ,
  7 3 -> 10 ,
  11 0 -> 11 ,
  11 2 -> 12 ,
  0 0 -> 1 4 ,
  0 1 -> 1 5 ,
  0 2 -> 1 6 ,
  4 0 -> 5 4 ,
  4 1 -> 5 5 ,
  4 2 -> 5 6 ,
  7 0 -> 8 4 ,
  7 1 -> 8 5 ,
  7 2 -> 8 6 ,
  2 8 4 0 -> 0 1 4 2 9 7 ,
  2 8 4 1 -> 0 1 4 2 9 8 ,
  2 8 4 2 -> 0 1 4 2 9 9 ,
  2 8 4 3 -> 0 1 4 2 9 10 ,
  6 8 4 0 -> 4 1 4 2 9 7 ,
  6 8 4 1 -> 4 1 4 2 9 8 ,
  6 8 4 2 -> 4 1 4 2 9 9 ,
  6 8 4 3 -> 4 1 4 2 9 10 ,
  9 8 4 0 -> 7 1 4 2 9 7 ,
  9 8 4 1 -> 7 1 4 2 9 8 ,
  9 8 4 2 -> 7 1 4 2 9 9 ,
  9 8 4 3 -> 7 1 4 2 9 10 ,
  12 8 4 0 -> 11 1 4 2 9 7 ,
  12 8 4 1 -> 11 1 4 2 9 8 ,
  12 8 4 2 -> 11 1 4 2 9 9 ,
  12 8 4 3 -> 11 1 4 2 9 10 ,
  2 7 -> 0 ,
  2 8 -> 1 ,
  2 9 -> 2 ,
  2 10 -> 3 ,
  6 7 -> 4 ,
  6 8 -> 5 ,
  6 9 -> 6 ,
  9 7 -> 7 ,
  9 8 -> 8 ,
  9 9 -> 9 ,
  9 10 -> 10 ,
  12 7 -> 11 ,
  12 9 -> 12 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (2,false)->2, (2,true)->3, (4,true)->4, (6,true)->5, (7,true)->6, (9,true)->7, (11,true)->8, (12,true)->9, (8,false)->10, (4,false)->11, (1,false)->12, (9,false)->13, (7,false)->14, (3,false)->15, (10,false)->16, (5,false)->17, (6,false)->18, (11,false)->19, (12,false)->20 },
it remains to prove termination of the 143-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 ,
  0 1 -> 4 ,
  0 2 -> 5 ,
  6 1 -> 4 ,
  6 2 -> 5 ,
  3 10 11 1 -> 0 12 11 2 13 14 ,
  3 10 11 1 -> 4 2 13 14 ,
  3 10 11 1 -> 3 13 14 ,
  3 10 11 1 -> 7 14 ,
  3 10 11 1 -> 6 ,
  3 10 11 12 -> 0 12 11 2 13 10 ,
  3 10 11 12 -> 4 2 13 10 ,
  3 10 11 12 -> 3 13 10 ,
  3 10 11 12 -> 7 10 ,
  3 10 11 2 -> 0 12 11 2 13 13 ,
  3 10 11 2 -> 4 2 13 13 ,
  3 10 11 2 -> 3 13 13 ,
  3 10 11 2 -> 7 13 ,
  3 10 11 2 -> 7 ,
  3 10 11 15 -> 0 12 11 2 13 16 ,
  3 10 11 15 -> 4 2 13 16 ,
  3 10 11 15 -> 3 13 16 ,
  3 10 11 15 -> 7 16 ,
  5 10 11 1 -> 4 12 11 2 13 14 ,
  5 10 11 1 -> 4 2 13 14 ,
  5 10 11 1 -> 3 13 14 ,
  5 10 11 1 -> 7 14 ,
  5 10 11 1 -> 6 ,
  5 10 11 12 -> 4 12 11 2 13 10 ,
  5 10 11 12 -> 4 2 13 10 ,
  5 10 11 12 -> 3 13 10 ,
  5 10 11 12 -> 7 10 ,
  5 10 11 2 -> 4 12 11 2 13 13 ,
  5 10 11 2 -> 4 2 13 13 ,
  5 10 11 2 -> 3 13 13 ,
  5 10 11 2 -> 7 13 ,
  5 10 11 2 -> 7 ,
  5 10 11 15 -> 4 12 11 2 13 16 ,
  5 10 11 15 -> 4 2 13 16 ,
  5 10 11 15 -> 3 13 16 ,
  5 10 11 15 -> 7 16 ,
  7 10 11 1 -> 6 12 11 2 13 14 ,
  7 10 11 1 -> 4 2 13 14 ,
  7 10 11 1 -> 3 13 14 ,
  7 10 11 1 -> 7 14 ,
  7 10 11 1 -> 6 ,
  7 10 11 12 -> 6 12 11 2 13 10 ,
  7 10 11 12 -> 4 2 13 10 ,
  7 10 11 12 -> 3 13 10 ,
  7 10 11 12 -> 7 10 ,
  7 10 11 2 -> 6 12 11 2 13 13 ,
  7 10 11 2 -> 4 2 13 13 ,
  7 10 11 2 -> 3 13 13 ,
  7 10 11 2 -> 7 13 ,
  7 10 11 2 -> 7 ,
  7 10 11 15 -> 6 12 11 2 13 16 ,
  7 10 11 15 -> 4 2 13 16 ,
  7 10 11 15 -> 3 13 16 ,
  7 10 11 15 -> 7 16 ,
  9 10 11 1 -> 8 12 11 2 13 14 ,
  9 10 11 1 -> 4 2 13 14 ,
  9 10 11 1 -> 3 13 14 ,
  9 10 11 1 -> 7 14 ,
  9 10 11 1 -> 6 ,
  9 10 11 12 -> 8 12 11 2 13 10 ,
  9 10 11 12 -> 4 2 13 10 ,
  9 10 11 12 -> 3 13 10 ,
  9 10 11 12 -> 7 10 ,
  9 10 11 2 -> 8 12 11 2 13 13 ,
  9 10 11 2 -> 4 2 13 13 ,
  9 10 11 2 -> 3 13 13 ,
  9 10 11 2 -> 7 13 ,
  9 10 11 2 -> 7 ,
  9 10 11 15 -> 8 12 11 2 13 16 ,
  9 10 11 15 -> 4 2 13 16 ,
  9 10 11 15 -> 3 13 16 ,
  9 10 11 15 -> 7 16 ,
  3 14 -> 0 ,
  3 13 -> 3 ,
  5 14 -> 4 ,
  5 13 -> 5 ,
  7 14 -> 6 ,
  7 13 -> 7 ,
  9 14 -> 8 ,
  9 13 -> 9 ,
  1 1 ->= 1 ,
  1 12 ->= 12 ,
  1 2 ->= 2 ,
  1 15 ->= 15 ,
  11 1 ->= 11 ,
  11 12 ->= 17 ,
  11 2 ->= 18 ,
  14 1 ->= 14 ,
  14 12 ->= 10 ,
  14 2 ->= 13 ,
  14 15 ->= 16 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  1 1 ->= 12 11 ,
  1 12 ->= 12 17 ,
  1 2 ->= 12 18 ,
  11 1 ->= 17 11 ,
  11 12 ->= 17 17 ,
  11 2 ->= 17 18 ,
  14 1 ->= 10 11 ,
  14 12 ->= 10 17 ,
  14 2 ->= 10 18 ,
  2 10 11 1 ->= 1 12 11 2 13 14 ,
  2 10 11 12 ->= 1 12 11 2 13 10 ,
  2 10 11 2 ->= 1 12 11 2 13 13 ,
  2 10 11 15 ->= 1 12 11 2 13 16 ,
  18 10 11 1 ->= 11 12 11 2 13 14 ,
  18 10 11 12 ->= 11 12 11 2 13 10 ,
  18 10 11 2 ->= 11 12 11 2 13 13 ,
  18 10 11 15 ->= 11 12 11 2 13 16 ,
  13 10 11 1 ->= 14 12 11 2 13 14 ,
  13 10 11 12 ->= 14 12 11 2 13 10 ,
  13 10 11 2 ->= 14 12 11 2 13 13 ,
  13 10 11 15 ->= 14 12 11 2 13 16 ,
  20 10 11 1 ->= 19 12 11 2 13 14 ,
  20 10 11 12 ->= 19 12 11 2 13 10 ,
  20 10 11 2 ->= 19 12 11 2 13 13 ,
  20 10 11 15 ->= 19 12 11 2 13 16 ,
  2 14 ->= 1 ,
  2 10 ->= 12 ,
  2 13 ->= 2 ,
  2 16 ->= 15 ,
  18 14 ->= 11 ,
  18 10 ->= 17 ,
  18 13 ->= 18 ,
  13 14 ->= 14 ,
  13 10 ->= 10 ,
  13 13 ->= 13 ,
  13 16 ->= 16 ,
  20 14 ->= 19 ,
  20 13 ->= 20 }


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 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 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, 9->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 129-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 ,
  0 1 -> 4 ,
  0 2 -> 5 ,
  6 1 -> 4 ,
  6 2 -> 5 ,
  3 10 11 1 -> 0 12 11 2 13 14 ,
  3 10 11 1 -> 4 2 13 14 ,
  3 10 11 1 -> 3 13 14 ,
  3 10 11 1 -> 7 14 ,
  3 10 11 1 -> 6 ,
  3 10 11 12 -> 0 12 11 2 13 10 ,
  3 10 11 12 -> 4 2 13 10 ,
  3 10 11 12 -> 3 13 10 ,
  3 10 11 12 -> 7 10 ,
  3 10 11 2 -> 0 12 11 2 13 13 ,
  3 10 11 2 -> 4 2 13 13 ,
  3 10 11 2 -> 3 13 13 ,
  3 10 11 2 -> 7 13 ,
  3 10 11 2 -> 7 ,
  3 10 11 15 -> 0 12 11 2 13 16 ,
  3 10 11 15 -> 4 2 13 16 ,
  3 10 11 15 -> 3 13 16 ,
  3 10 11 15 -> 7 16 ,
  5 10 11 1 -> 4 12 11 2 13 14 ,
  5 10 11 1 -> 4 2 13 14 ,
  5 10 11 1 -> 3 13 14 ,
  5 10 11 1 -> 7 14 ,
  5 10 11 1 -> 6 ,
  5 10 11 12 -> 4 12 11 2 13 10 ,
  5 10 11 12 -> 4 2 13 10 ,
  5 10 11 12 -> 3 13 10 ,
  5 10 11 12 -> 7 10 ,
  5 10 11 2 -> 4 12 11 2 13 13 ,
  5 10 11 2 -> 4 2 13 13 ,
  5 10 11 2 -> 3 13 13 ,
  5 10 11 2 -> 7 13 ,
  5 10 11 2 -> 7 ,
  5 10 11 15 -> 4 12 11 2 13 16 ,
  5 10 11 15 -> 4 2 13 16 ,
  5 10 11 15 -> 3 13 16 ,
  5 10 11 15 -> 7 16 ,
  7 10 11 1 -> 6 12 11 2 13 14 ,
  7 10 11 1 -> 4 2 13 14 ,
  7 10 11 1 -> 3 13 14 ,
  7 10 11 1 -> 7 14 ,
  7 10 11 1 -> 6 ,
  7 10 11 12 -> 6 12 11 2 13 10 ,
  7 10 11 12 -> 4 2 13 10 ,
  7 10 11 12 -> 3 13 10 ,
  7 10 11 12 -> 7 10 ,
  7 10 11 2 -> 6 12 11 2 13 13 ,
  7 10 11 2 -> 4 2 13 13 ,
  7 10 11 2 -> 3 13 13 ,
  7 10 11 2 -> 7 13 ,
  7 10 11 2 -> 7 ,
  7 10 11 15 -> 6 12 11 2 13 16 ,
  7 10 11 15 -> 4 2 13 16 ,
  7 10 11 15 -> 3 13 16 ,
  7 10 11 15 -> 7 16 ,
  9 10 11 1 -> 8 12 11 2 13 14 ,
  9 10 11 12 -> 8 12 11 2 13 10 ,
  9 10 11 2 -> 8 12 11 2 13 13 ,
  9 10 11 15 -> 8 12 11 2 13 16 ,
  3 14 -> 0 ,
  3 13 -> 3 ,
  5 14 -> 4 ,
  5 13 -> 5 ,
  7 14 -> 6 ,
  7 13 -> 7 ,
  9 14 -> 8 ,
  9 13 -> 9 ,
  1 1 ->= 1 ,
  1 12 ->= 12 ,
  1 2 ->= 2 ,
  1 15 ->= 15 ,
  11 1 ->= 11 ,
  11 12 ->= 17 ,
  11 2 ->= 18 ,
  14 1 ->= 14 ,
  14 12 ->= 10 ,
  14 2 ->= 13 ,
  14 15 ->= 16 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  1 1 ->= 12 11 ,
  1 12 ->= 12 17 ,
  1 2 ->= 12 18 ,
  11 1 ->= 17 11 ,
  11 12 ->= 17 17 ,
  11 2 ->= 17 18 ,
  14 1 ->= 10 11 ,
  14 12 ->= 10 17 ,
  14 2 ->= 10 18 ,
  2 10 11 1 ->= 1 12 11 2 13 14 ,
  2 10 11 12 ->= 1 12 11 2 13 10 ,
  2 10 11 2 ->= 1 12 11 2 13 13 ,
  2 10 11 15 ->= 1 12 11 2 13 16 ,
  18 10 11 1 ->= 11 12 11 2 13 14 ,
  18 10 11 12 ->= 11 12 11 2 13 10 ,
  18 10 11 2 ->= 11 12 11 2 13 13 ,
  18 10 11 15 ->= 11 12 11 2 13 16 ,
  13 10 11 1 ->= 14 12 11 2 13 14 ,
  13 10 11 12 ->= 14 12 11 2 13 10 ,
  13 10 11 2 ->= 14 12 11 2 13 13 ,
  13 10 11 15 ->= 14 12 11 2 13 16 ,
  20 10 11 1 ->= 19 12 11 2 13 14 ,
  20 10 11 12 ->= 19 12 11 2 13 10 ,
  20 10 11 2 ->= 19 12 11 2 13 13 ,
  20 10 11 15 ->= 19 12 11 2 13 16 ,
  2 14 ->= 1 ,
  2 10 ->= 12 ,
  2 13 ->= 2 ,
  2 16 ->= 15 ,
  18 14 ->= 11 ,
  18 10 ->= 17 ,
  18 13 ->= 18 ,
  13 14 ->= 14 ,
  13 10 ->= 10 ,
  13 13 ->= 13 ,
  13 16 ->= 16 ,
  20 14 ->= 19 ,
  20 13 ->= 20 }


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 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 1 |
| 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, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 121-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 ,
  0 1 -> 4 ,
  0 2 -> 5 ,
  6 1 -> 4 ,
  6 2 -> 5 ,
  3 10 11 1 -> 0 12 11 2 13 14 ,
  3 10 11 1 -> 4 2 13 14 ,
  3 10 11 1 -> 3 13 14 ,
  3 10 11 1 -> 7 14 ,
  3 10 11 1 -> 6 ,
  3 10 11 12 -> 0 12 11 2 13 10 ,
  3 10 11 12 -> 4 2 13 10 ,
  3 10 11 12 -> 3 13 10 ,
  3 10 11 12 -> 7 10 ,
  3 10 11 2 -> 0 12 11 2 13 13 ,
  3 10 11 2 -> 4 2 13 13 ,
  3 10 11 2 -> 3 13 13 ,
  3 10 11 2 -> 7 13 ,
  3 10 11 2 -> 7 ,
  3 10 11 15 -> 0 12 11 2 13 16 ,
  3 10 11 15 -> 4 2 13 16 ,
  3 10 11 15 -> 3 13 16 ,
  3 10 11 15 -> 7 16 ,
  5 10 11 1 -> 4 12 11 2 13 14 ,
  5 10 11 1 -> 4 2 13 14 ,
  5 10 11 1 -> 3 13 14 ,
  5 10 11 1 -> 7 14 ,
  5 10 11 1 -> 6 ,
  5 10 11 12 -> 4 12 11 2 13 10 ,
  5 10 11 12 -> 4 2 13 10 ,
  5 10 11 12 -> 3 13 10 ,
  5 10 11 12 -> 7 10 ,
  5 10 11 2 -> 4 12 11 2 13 13 ,
  5 10 11 2 -> 4 2 13 13 ,
  5 10 11 2 -> 3 13 13 ,
  5 10 11 2 -> 7 13 ,
  5 10 11 2 -> 7 ,
  5 10 11 15 -> 4 12 11 2 13 16 ,
  5 10 11 15 -> 4 2 13 16 ,
  5 10 11 15 -> 3 13 16 ,
  5 10 11 15 -> 7 16 ,
  7 10 11 1 -> 6 12 11 2 13 14 ,
  7 10 11 1 -> 4 2 13 14 ,
  7 10 11 1 -> 3 13 14 ,
  7 10 11 1 -> 7 14 ,
  7 10 11 1 -> 6 ,
  7 10 11 12 -> 6 12 11 2 13 10 ,
  7 10 11 12 -> 4 2 13 10 ,
  7 10 11 12 -> 3 13 10 ,
  7 10 11 12 -> 7 10 ,
  7 10 11 2 -> 6 12 11 2 13 13 ,
  7 10 11 2 -> 4 2 13 13 ,
  7 10 11 2 -> 3 13 13 ,
  7 10 11 2 -> 7 13 ,
  7 10 11 2 -> 7 ,
  7 10 11 15 -> 6 12 11 2 13 16 ,
  7 10 11 15 -> 4 2 13 16 ,
  7 10 11 15 -> 3 13 16 ,
  7 10 11 15 -> 7 16 ,
  9 10 11 1 -> 8 12 11 2 13 14 ,
  9 10 11 12 -> 8 12 11 2 13 10 ,
  9 10 11 2 -> 8 12 11 2 13 13 ,
  9 10 11 15 -> 8 12 11 2 13 16 ,
  3 14 -> 0 ,
  3 13 -> 3 ,
  5 14 -> 4 ,
  5 13 -> 5 ,
  7 14 -> 6 ,
  7 13 -> 7 ,
  9 14 -> 8 ,
  9 13 -> 9 ,
  1 12 ->= 12 ,
  1 15 ->= 15 ,
  11 1 ->= 11 ,
  11 12 ->= 17 ,
  11 2 ->= 18 ,
  14 12 ->= 10 ,
  14 15 ->= 16 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  1 12 ->= 12 17 ,
  11 1 ->= 17 11 ,
  11 12 ->= 17 17 ,
  11 2 ->= 17 18 ,
  14 12 ->= 10 17 ,
  2 10 11 1 ->= 1 12 11 2 13 14 ,
  2 10 11 12 ->= 1 12 11 2 13 10 ,
  2 10 11 2 ->= 1 12 11 2 13 13 ,
  2 10 11 15 ->= 1 12 11 2 13 16 ,
  18 10 11 1 ->= 11 12 11 2 13 14 ,
  18 10 11 12 ->= 11 12 11 2 13 10 ,
  18 10 11 2 ->= 11 12 11 2 13 13 ,
  18 10 11 15 ->= 11 12 11 2 13 16 ,
  13 10 11 1 ->= 14 12 11 2 13 14 ,
  13 10 11 12 ->= 14 12 11 2 13 10 ,
  13 10 11 2 ->= 14 12 11 2 13 13 ,
  13 10 11 15 ->= 14 12 11 2 13 16 ,
  20 10 11 1 ->= 19 12 11 2 13 14 ,
  20 10 11 12 ->= 19 12 11 2 13 10 ,
  20 10 11 2 ->= 19 12 11 2 13 13 ,
  20 10 11 15 ->= 19 12 11 2 13 16 ,
  2 14 ->= 1 ,
  2 10 ->= 12 ,
  2 13 ->= 2 ,
  2 16 ->= 15 ,
  18 14 ->= 11 ,
  18 10 ->= 17 ,
  18 13 ->= 18 ,
  13 14 ->= 14 ,
  13 10 ->= 10 ,
  13 13 ->= 13 ,
  13 16 ->= 16 ,
  20 14 ->= 19 ,
  20 13 ->= 20 }


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

0 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 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 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 2 |
| 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, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 18->17, 19->18, 20->19, 17->20 }, 
it remains to prove termination of the 72-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 11 1 -> 0 12 11 2 13 14 ,
  3 10 11 12 -> 0 12 11 2 13 10 ,
  3 10 11 2 -> 0 12 11 2 13 13 ,
  3 10 11 15 -> 0 12 11 2 13 16 ,
  5 10 11 1 -> 4 12 11 2 13 14 ,
  5 10 11 12 -> 4 12 11 2 13 10 ,
  5 10 11 2 -> 4 12 11 2 13 13 ,
  5 10 11 15 -> 4 12 11 2 13 16 ,
  7 10 11 1 -> 6 12 11 2 13 14 ,
  7 10 11 12 -> 6 12 11 2 13 10 ,
  7 10 11 2 -> 6 12 11 2 13 13 ,
  7 10 11 15 -> 6 12 11 2 13 16 ,
  9 10 11 1 -> 8 12 11 2 13 14 ,
  9 10 11 12 -> 8 12 11 2 13 10 ,
  9 10 11 2 -> 8 12 11 2 13 13 ,
  9 10 11 15 -> 8 12 11 2 13 16 ,
  3 14 -> 0 ,
  3 13 -> 3 ,
  5 14 -> 4 ,
  5 13 -> 5 ,
  7 14 -> 6 ,
  7 13 -> 7 ,
  9 14 -> 8 ,
  9 13 -> 9 ,
  1 12 ->= 12 ,
  1 15 ->= 15 ,
  11 1 ->= 11 ,
  11 2 ->= 17 ,
  14 12 ->= 10 ,
  14 15 ->= 16 ,
  18 1 ->= 18 ,
  18 2 ->= 19 ,
  1 12 ->= 12 20 ,
  11 1 ->= 20 11 ,
  11 2 ->= 20 17 ,
  14 12 ->= 10 20 ,
  2 10 11 1 ->= 1 12 11 2 13 14 ,
  2 10 11 12 ->= 1 12 11 2 13 10 ,
  2 10 11 2 ->= 1 12 11 2 13 13 ,
  2 10 11 15 ->= 1 12 11 2 13 16 ,
  17 10 11 1 ->= 11 12 11 2 13 14 ,
  17 10 11 12 ->= 11 12 11 2 13 10 ,
  17 10 11 2 ->= 11 12 11 2 13 13 ,
  17 10 11 15 ->= 11 12 11 2 13 16 ,
  13 10 11 1 ->= 14 12 11 2 13 14 ,
  13 10 11 12 ->= 14 12 11 2 13 10 ,
  13 10 11 2 ->= 14 12 11 2 13 13 ,
  13 10 11 15 ->= 14 12 11 2 13 16 ,
  19 10 11 1 ->= 18 12 11 2 13 14 ,
  19 10 11 12 ->= 18 12 11 2 13 10 ,
  19 10 11 2 ->= 18 12 11 2 13 13 ,
  19 10 11 15 ->= 18 12 11 2 13 16 ,
  2 14 ->= 1 ,
  2 10 ->= 12 ,
  2 13 ->= 2 ,
  2 16 ->= 15 ,
  17 14 ->= 11 ,
  17 13 ->= 17 ,
  13 14 ->= 14 ,
  13 10 ->= 10 ,
  13 13 ->= 13 ,
  13 16 ->= 16 ,
  19 14 ->= 18 ,
  19 13 ->= 19 }


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 0 |
 \     /
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 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 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 1 |
| 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, 2->2, 3->3, 4->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 5->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 71-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  7 2 -> 8 ,
  3 9 10 1 -> 0 11 10 2 12 13 ,
  3 9 10 11 -> 0 11 10 2 12 9 ,
  3 9 10 2 -> 0 11 10 2 12 12 ,
  3 9 10 14 -> 0 11 10 2 12 15 ,
  16 9 10 1 -> 4 11 10 2 12 13 ,
  16 9 10 11 -> 4 11 10 2 12 9 ,
  16 9 10 2 -> 4 11 10 2 12 12 ,
  16 9 10 14 -> 4 11 10 2 12 15 ,
  6 9 10 1 -> 5 11 10 2 12 13 ,
  6 9 10 11 -> 5 11 10 2 12 9 ,
  6 9 10 2 -> 5 11 10 2 12 12 ,
  6 9 10 14 -> 5 11 10 2 12 15 ,
  8 9 10 1 -> 7 11 10 2 12 13 ,
  8 9 10 11 -> 7 11 10 2 12 9 ,
  8 9 10 2 -> 7 11 10 2 12 12 ,
  8 9 10 14 -> 7 11 10 2 12 15 ,
  3 13 -> 0 ,
  3 12 -> 3 ,
  16 13 -> 4 ,
  16 12 -> 16 ,
  6 13 -> 5 ,
  6 12 -> 6 ,
  8 13 -> 7 ,
  8 12 -> 8 ,
  1 11 ->= 11 ,
  1 14 ->= 14 ,
  10 1 ->= 10 ,
  10 2 ->= 17 ,
  13 11 ->= 9 ,
  13 14 ->= 15 ,
  18 1 ->= 18 ,
  18 2 ->= 19 ,
  1 11 ->= 11 20 ,
  10 1 ->= 20 10 ,
  10 2 ->= 20 17 ,
  13 11 ->= 9 20 ,
  2 9 10 1 ->= 1 11 10 2 12 13 ,
  2 9 10 11 ->= 1 11 10 2 12 9 ,
  2 9 10 2 ->= 1 11 10 2 12 12 ,
  2 9 10 14 ->= 1 11 10 2 12 15 ,
  17 9 10 1 ->= 10 11 10 2 12 13 ,
  17 9 10 11 ->= 10 11 10 2 12 9 ,
  17 9 10 2 ->= 10 11 10 2 12 12 ,
  17 9 10 14 ->= 10 11 10 2 12 15 ,
  12 9 10 1 ->= 13 11 10 2 12 13 ,
  12 9 10 11 ->= 13 11 10 2 12 9 ,
  12 9 10 2 ->= 13 11 10 2 12 12 ,
  12 9 10 14 ->= 13 11 10 2 12 15 ,
  19 9 10 1 ->= 18 11 10 2 12 13 ,
  19 9 10 11 ->= 18 11 10 2 12 9 ,
  19 9 10 2 ->= 18 11 10 2 12 12 ,
  19 9 10 14 ->= 18 11 10 2 12 15 ,
  2 13 ->= 1 ,
  2 9 ->= 11 ,
  2 12 ->= 2 ,
  2 15 ->= 14 ,
  17 13 ->= 10 ,
  17 12 ->= 17 ,
  12 13 ->= 13 ,
  12 9 ->= 9 ,
  12 12 ->= 12 ,
  12 15 ->= 15 ,
  19 13 ->= 18 ,
  19 12 ->= 19 }


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 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, 9->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 66-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  7 2 -> 8 ,
  3 9 10 1 -> 0 11 10 2 12 13 ,
  3 9 10 11 -> 0 11 10 2 12 9 ,
  3 9 10 2 -> 0 11 10 2 12 12 ,
  3 9 10 14 -> 0 11 10 2 12 15 ,
  6 9 10 1 -> 5 11 10 2 12 13 ,
  6 9 10 11 -> 5 11 10 2 12 9 ,
  6 9 10 2 -> 5 11 10 2 12 12 ,
  6 9 10 14 -> 5 11 10 2 12 15 ,
  8 9 10 1 -> 7 11 10 2 12 13 ,
  8 9 10 11 -> 7 11 10 2 12 9 ,
  8 9 10 2 -> 7 11 10 2 12 12 ,
  8 9 10 14 -> 7 11 10 2 12 15 ,
  3 13 -> 0 ,
  3 12 -> 3 ,
  16 12 -> 16 ,
  6 13 -> 5 ,
  6 12 -> 6 ,
  8 13 -> 7 ,
  8 12 -> 8 ,
  1 11 ->= 11 ,
  1 14 ->= 14 ,
  10 1 ->= 10 ,
  10 2 ->= 17 ,
  13 11 ->= 9 ,
  13 14 ->= 15 ,
  18 1 ->= 18 ,
  18 2 ->= 19 ,
  1 11 ->= 11 20 ,
  10 1 ->= 20 10 ,
  10 2 ->= 20 17 ,
  13 11 ->= 9 20 ,
  2 9 10 1 ->= 1 11 10 2 12 13 ,
  2 9 10 11 ->= 1 11 10 2 12 9 ,
  2 9 10 2 ->= 1 11 10 2 12 12 ,
  2 9 10 14 ->= 1 11 10 2 12 15 ,
  17 9 10 1 ->= 10 11 10 2 12 13 ,
  17 9 10 11 ->= 10 11 10 2 12 9 ,
  17 9 10 2 ->= 10 11 10 2 12 12 ,
  17 9 10 14 ->= 10 11 10 2 12 15 ,
  12 9 10 1 ->= 13 11 10 2 12 13 ,
  12 9 10 11 ->= 13 11 10 2 12 9 ,
  12 9 10 2 ->= 13 11 10 2 12 12 ,
  12 9 10 14 ->= 13 11 10 2 12 15 ,
  19 9 10 1 ->= 18 11 10 2 12 13 ,
  19 9 10 11 ->= 18 11 10 2 12 9 ,
  19 9 10 2 ->= 18 11 10 2 12 12 ,
  19 9 10 14 ->= 18 11 10 2 12 15 ,
  2 13 ->= 1 ,
  2 9 ->= 11 ,
  2 12 ->= 2 ,
  2 15 ->= 14 ,
  17 13 ->= 10 ,
  17 12 ->= 17 ,
  12 13 ->= 13 ,
  12 9 ->= 9 ,
  12 12 ->= 12 ,
  12 15 ->= 15 ,
  19 13 ->= 18 ,
  19 12 ->= 19 }


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 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 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 1 1 |
 \     /
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 1 |
| 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, 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, 17->16, 18->17, 19->18, 20->19 }, 
it remains to prove termination of the 65-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  7 2 -> 8 ,
  3 9 10 1 -> 0 11 10 2 12 13 ,
  3 9 10 11 -> 0 11 10 2 12 9 ,
  3 9 10 2 -> 0 11 10 2 12 12 ,
  3 9 10 14 -> 0 11 10 2 12 15 ,
  6 9 10 1 -> 5 11 10 2 12 13 ,
  6 9 10 11 -> 5 11 10 2 12 9 ,
  6 9 10 2 -> 5 11 10 2 12 12 ,
  6 9 10 14 -> 5 11 10 2 12 15 ,
  8 9 10 1 -> 7 11 10 2 12 13 ,
  8 9 10 11 -> 7 11 10 2 12 9 ,
  8 9 10 2 -> 7 11 10 2 12 12 ,
  8 9 10 14 -> 7 11 10 2 12 15 ,
  3 13 -> 0 ,
  3 12 -> 3 ,
  6 13 -> 5 ,
  6 12 -> 6 ,
  8 13 -> 7 ,
  8 12 -> 8 ,
  1 11 ->= 11 ,
  1 14 ->= 14 ,
  10 1 ->= 10 ,
  10 2 ->= 16 ,
  13 11 ->= 9 ,
  13 14 ->= 15 ,
  17 1 ->= 17 ,
  17 2 ->= 18 ,
  1 11 ->= 11 19 ,
  10 1 ->= 19 10 ,
  10 2 ->= 19 16 ,
  13 11 ->= 9 19 ,
  2 9 10 1 ->= 1 11 10 2 12 13 ,
  2 9 10 11 ->= 1 11 10 2 12 9 ,
  2 9 10 2 ->= 1 11 10 2 12 12 ,
  2 9 10 14 ->= 1 11 10 2 12 15 ,
  16 9 10 1 ->= 10 11 10 2 12 13 ,
  16 9 10 11 ->= 10 11 10 2 12 9 ,
  16 9 10 2 ->= 10 11 10 2 12 12 ,
  16 9 10 14 ->= 10 11 10 2 12 15 ,
  12 9 10 1 ->= 13 11 10 2 12 13 ,
  12 9 10 11 ->= 13 11 10 2 12 9 ,
  12 9 10 2 ->= 13 11 10 2 12 12 ,
  12 9 10 14 ->= 13 11 10 2 12 15 ,
  18 9 10 1 ->= 17 11 10 2 12 13 ,
  18 9 10 11 ->= 17 11 10 2 12 9 ,
  18 9 10 2 ->= 17 11 10 2 12 12 ,
  18 9 10 14 ->= 17 11 10 2 12 15 ,
  2 13 ->= 1 ,
  2 9 ->= 11 ,
  2 12 ->= 2 ,
  2 15 ->= 14 ,
  16 13 ->= 10 ,
  16 12 ->= 16 ,
  12 13 ->= 13 ,
  12 9 ->= 9 ,
  12 12 ->= 12 ,
  12 15 ->= 15 ,
  18 13 ->= 17 ,
  18 12 ->= 18 }


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 0 |
 \     /
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 1 |
| 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 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 |
 \     /
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, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 8->15, 16->16, 17->17, 18->18, 19->19 }, 
it remains to prove termination of the 64-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  15 8 9 1 -> 7 10 9 2 11 12 ,
  15 8 9 10 -> 7 10 9 2 11 8 ,
  15 8 9 2 -> 7 10 9 2 11 11 ,
  15 8 9 13 -> 7 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  15 12 -> 7 ,
  15 11 -> 15 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 16 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  17 1 ->= 17 ,
  17 2 ->= 18 ,
  1 10 ->= 10 19 ,
  9 1 ->= 19 9 ,
  9 2 ->= 19 16 ,
  12 10 ->= 8 19 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  16 8 9 1 ->= 9 10 9 2 11 12 ,
  16 8 9 10 ->= 9 10 9 2 11 8 ,
  16 8 9 2 ->= 9 10 9 2 11 11 ,
  16 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  18 8 9 1 ->= 17 10 9 2 11 12 ,
  18 8 9 10 ->= 17 10 9 2 11 8 ,
  18 8 9 2 ->= 17 10 9 2 11 11 ,
  18 8 9 13 ->= 17 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  16 12 ->= 9 ,
  16 11 ->= 16 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  18 12 ->= 17 ,
  18 11 ->= 18 }


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 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 1 |
| 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, 8->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 59-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  15 11 -> 15 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 16 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  17 1 ->= 17 ,
  17 2 ->= 18 ,
  1 10 ->= 10 19 ,
  9 1 ->= 19 9 ,
  9 2 ->= 19 16 ,
  12 10 ->= 8 19 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  16 8 9 1 ->= 9 10 9 2 11 12 ,
  16 8 9 10 ->= 9 10 9 2 11 8 ,
  16 8 9 2 ->= 9 10 9 2 11 11 ,
  16 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  18 8 9 1 ->= 17 10 9 2 11 12 ,
  18 8 9 10 ->= 17 10 9 2 11 8 ,
  18 8 9 2 ->= 17 10 9 2 11 11 ,
  18 8 9 13 ->= 17 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  16 12 ->= 9 ,
  16 11 ->= 16 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  18 12 ->= 17 ,
  18 11 ->= 18 }


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 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 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 1 1 |
 \     /
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 1 |
| 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, 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 }, 
it remains to prove termination of the 58-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 15 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  16 1 ->= 16 ,
  16 2 ->= 17 ,
  1 10 ->= 10 18 ,
  9 1 ->= 18 9 ,
  9 2 ->= 18 15 ,
  12 10 ->= 8 18 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  15 8 9 1 ->= 9 10 9 2 11 12 ,
  15 8 9 10 ->= 9 10 9 2 11 8 ,
  15 8 9 2 ->= 9 10 9 2 11 11 ,
  15 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  17 8 9 1 ->= 16 10 9 2 11 12 ,
  17 8 9 10 ->= 16 10 9 2 11 8 ,
  17 8 9 2 ->= 16 10 9 2 11 11 ,
  17 8 9 13 ->= 16 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  15 12 ->= 9 ,
  15 11 ->= 15 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  17 12 ->= 16 ,
  17 11 ->= 17 }


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 0 |
 \     /
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 1 |
| 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 1 |
| 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, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 18->17, 17->18 }, 
it remains to prove termination of the 57-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 15 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  16 1 ->= 16 ,
  1 10 ->= 10 17 ,
  9 1 ->= 17 9 ,
  9 2 ->= 17 15 ,
  12 10 ->= 8 17 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  15 8 9 1 ->= 9 10 9 2 11 12 ,
  15 8 9 10 ->= 9 10 9 2 11 8 ,
  15 8 9 2 ->= 9 10 9 2 11 11 ,
  15 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  18 8 9 1 ->= 16 10 9 2 11 12 ,
  18 8 9 10 ->= 16 10 9 2 11 8 ,
  18 8 9 2 ->= 16 10 9 2 11 11 ,
  18 8 9 13 ->= 16 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  15 12 ->= 9 ,
  15 11 ->= 15 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  18 12 ->= 16 ,
  18 11 ->= 18 }


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 1 |
| 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 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 52-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 15 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  16 1 ->= 16 ,
  1 10 ->= 10 17 ,
  9 1 ->= 17 9 ,
  9 2 ->= 17 15 ,
  12 10 ->= 8 17 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  15 8 9 1 ->= 9 10 9 2 11 12 ,
  15 8 9 10 ->= 9 10 9 2 11 8 ,
  15 8 9 2 ->= 9 10 9 2 11 11 ,
  15 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  15 12 ->= 9 ,
  15 11 ->= 15 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  18 11 ->= 18 }


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 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 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 1 1 |
 \     /
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 1 |
| 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, 14->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 51-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 9 1 -> 0 10 9 2 11 12 ,
  3 8 9 10 -> 0 10 9 2 11 8 ,
  3 8 9 2 -> 0 10 9 2 11 11 ,
  3 8 9 13 -> 0 10 9 2 11 14 ,
  6 8 9 1 -> 5 10 9 2 11 12 ,
  6 8 9 10 -> 5 10 9 2 11 8 ,
  6 8 9 2 -> 5 10 9 2 11 11 ,
  6 8 9 13 -> 5 10 9 2 11 14 ,
  3 12 -> 0 ,
  3 11 -> 3 ,
  6 12 -> 5 ,
  6 11 -> 6 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 2 ->= 15 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  16 1 ->= 16 ,
  1 10 ->= 10 17 ,
  9 1 ->= 17 9 ,
  9 2 ->= 17 15 ,
  12 10 ->= 8 17 ,
  2 8 9 1 ->= 1 10 9 2 11 12 ,
  2 8 9 10 ->= 1 10 9 2 11 8 ,
  2 8 9 2 ->= 1 10 9 2 11 11 ,
  2 8 9 13 ->= 1 10 9 2 11 14 ,
  15 8 9 1 ->= 9 10 9 2 11 12 ,
  15 8 9 10 ->= 9 10 9 2 11 8 ,
  15 8 9 2 ->= 9 10 9 2 11 11 ,
  15 8 9 13 ->= 9 10 9 2 11 14 ,
  11 8 9 1 ->= 12 10 9 2 11 12 ,
  11 8 9 10 ->= 12 10 9 2 11 8 ,
  11 8 9 2 ->= 12 10 9 2 11 11 ,
  11 8 9 13 ->= 12 10 9 2 11 14 ,
  2 12 ->= 1 ,
  2 8 ->= 10 ,
  2 11 ->= 2 ,
  2 14 ->= 13 ,
  15 12 ->= 9 ,
  15 11 ->= 15 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
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 1 |
| 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, 4->2, 5->3, 2->4, 6->5, 7->6, 3->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 50-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  3 4 -> 5 ,
  6 1 -> 6 ,
  7 8 9 1 -> 0 10 9 4 11 12 ,
  7 8 9 10 -> 0 10 9 4 11 8 ,
  7 8 9 4 -> 0 10 9 4 11 11 ,
  7 8 9 13 -> 0 10 9 4 11 14 ,
  5 8 9 1 -> 3 10 9 4 11 12 ,
  5 8 9 10 -> 3 10 9 4 11 8 ,
  5 8 9 4 -> 3 10 9 4 11 11 ,
  5 8 9 13 -> 3 10 9 4 11 14 ,
  7 12 -> 0 ,
  7 11 -> 7 ,
  5 12 -> 3 ,
  5 11 -> 5 ,
  1 10 ->= 10 ,
  1 13 ->= 13 ,
  9 1 ->= 9 ,
  9 4 ->= 15 ,
  12 10 ->= 8 ,
  12 13 ->= 14 ,
  16 1 ->= 16 ,
  1 10 ->= 10 17 ,
  9 1 ->= 17 9 ,
  9 4 ->= 17 15 ,
  12 10 ->= 8 17 ,
  4 8 9 1 ->= 1 10 9 4 11 12 ,
  4 8 9 10 ->= 1 10 9 4 11 8 ,
  4 8 9 4 ->= 1 10 9 4 11 11 ,
  4 8 9 13 ->= 1 10 9 4 11 14 ,
  15 8 9 1 ->= 9 10 9 4 11 12 ,
  15 8 9 10 ->= 9 10 9 4 11 8 ,
  15 8 9 4 ->= 9 10 9 4 11 11 ,
  15 8 9 13 ->= 9 10 9 4 11 14 ,
  11 8 9 1 ->= 12 10 9 4 11 12 ,
  11 8 9 10 ->= 12 10 9 4 11 8 ,
  11 8 9 4 ->= 12 10 9 4 11 11 ,
  11 8 9 13 ->= 12 10 9 4 11 14 ,
  4 12 ->= 1 ,
  4 8 ->= 10 ,
  4 11 ->= 4 ,
  4 14 ->= 13 ,
  15 12 ->= 9 ,
  15 11 ->= 15 ,
  11 12 ->= 12 ,
  11 8 ->= 8 ,
  11 11 ->= 11 ,
  11 14 ->= 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 0 |
| 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 1 |
| 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 1 |
| 0 1 |
 \   /
17 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, 7->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 45-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  3 4 -> 5 ,
  6 1 -> 6 ,
  5 7 8 1 -> 3 9 8 4 10 11 ,
  5 7 8 9 -> 3 9 8 4 10 7 ,
  5 7 8 4 -> 3 9 8 4 10 10 ,
  5 7 8 12 -> 3 9 8 4 10 13 ,
  14 10 -> 14 ,
  5 11 -> 3 ,
  5 10 -> 5 ,
  1 9 ->= 9 ,
  1 12 ->= 12 ,
  8 1 ->= 8 ,
  8 4 ->= 15 ,
  11 9 ->= 7 ,
  11 12 ->= 13 ,
  16 1 ->= 16 ,
  1 9 ->= 9 17 ,
  8 1 ->= 17 8 ,
  8 4 ->= 17 15 ,
  11 9 ->= 7 17 ,
  4 7 8 1 ->= 1 9 8 4 10 11 ,
  4 7 8 9 ->= 1 9 8 4 10 7 ,
  4 7 8 4 ->= 1 9 8 4 10 10 ,
  4 7 8 12 ->= 1 9 8 4 10 13 ,
  15 7 8 1 ->= 8 9 8 4 10 11 ,
  15 7 8 9 ->= 8 9 8 4 10 7 ,
  15 7 8 4 ->= 8 9 8 4 10 10 ,
  15 7 8 12 ->= 8 9 8 4 10 13 ,
  10 7 8 1 ->= 11 9 8 4 10 11 ,
  10 7 8 9 ->= 11 9 8 4 10 7 ,
  10 7 8 4 ->= 11 9 8 4 10 10 ,
  10 7 8 12 ->= 11 9 8 4 10 13 ,
  4 11 ->= 1 ,
  4 7 ->= 9 ,
  4 10 ->= 4 ,
  4 13 ->= 12 ,
  15 11 ->= 8 ,
  15 10 ->= 15 ,
  10 11 ->= 11 ,
  10 7 ->= 7 ,
  10 10 ->= 10 ,
  10 13 ->= 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 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 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 1 1 |
 \     /
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 1 |
| 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, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 15->14, 16->15, 17->16 }, 
it remains to prove termination of the 44-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  3 4 -> 5 ,
  6 1 -> 6 ,
  5 7 8 1 -> 3 9 8 4 10 11 ,
  5 7 8 9 -> 3 9 8 4 10 7 ,
  5 7 8 4 -> 3 9 8 4 10 10 ,
  5 7 8 12 -> 3 9 8 4 10 13 ,
  5 11 -> 3 ,
  5 10 -> 5 ,
  1 9 ->= 9 ,
  1 12 ->= 12 ,
  8 1 ->= 8 ,
  8 4 ->= 14 ,
  11 9 ->= 7 ,
  11 12 ->= 13 ,
  15 1 ->= 15 ,
  1 9 ->= 9 16 ,
  8 1 ->= 16 8 ,
  8 4 ->= 16 14 ,
  11 9 ->= 7 16 ,
  4 7 8 1 ->= 1 9 8 4 10 11 ,
  4 7 8 9 ->= 1 9 8 4 10 7 ,
  4 7 8 4 ->= 1 9 8 4 10 10 ,
  4 7 8 12 ->= 1 9 8 4 10 13 ,
  14 7 8 1 ->= 8 9 8 4 10 11 ,
  14 7 8 9 ->= 8 9 8 4 10 7 ,
  14 7 8 4 ->= 8 9 8 4 10 10 ,
  14 7 8 12 ->= 8 9 8 4 10 13 ,
  10 7 8 1 ->= 11 9 8 4 10 11 ,
  10 7 8 9 ->= 11 9 8 4 10 7 ,
  10 7 8 4 ->= 11 9 8 4 10 10 ,
  10 7 8 12 ->= 11 9 8 4 10 13 ,
  4 11 ->= 1 ,
  4 7 ->= 9 ,
  4 10 ->= 4 ,
  4 13 ->= 12 ,
  14 11 ->= 8 ,
  14 10 ->= 14 ,
  10 11 ->= 11 ,
  10 7 ->= 7 ,
  10 10 ->= 10 ,
  10 13 ->= 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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
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 1 |
| 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, 6->4, 5->5, 7->6, 8->7, 9->8, 4->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16 }, 
it remains to prove termination of the 43-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 7 1 -> 3 8 7 9 10 11 ,
  5 6 7 8 -> 3 8 7 9 10 6 ,
  5 6 7 9 -> 3 8 7 9 10 10 ,
  5 6 7 12 -> 3 8 7 9 10 13 ,
  5 11 -> 3 ,
  5 10 -> 5 ,
  1 8 ->= 8 ,
  1 12 ->= 12 ,
  7 1 ->= 7 ,
  7 9 ->= 14 ,
  11 8 ->= 6 ,
  11 12 ->= 13 ,
  15 1 ->= 15 ,
  1 8 ->= 8 16 ,
  7 1 ->= 16 7 ,
  7 9 ->= 16 14 ,
  11 8 ->= 6 16 ,
  9 6 7 1 ->= 1 8 7 9 10 11 ,
  9 6 7 8 ->= 1 8 7 9 10 6 ,
  9 6 7 9 ->= 1 8 7 9 10 10 ,
  9 6 7 12 ->= 1 8 7 9 10 13 ,
  14 6 7 1 ->= 7 8 7 9 10 11 ,
  14 6 7 8 ->= 7 8 7 9 10 6 ,
  14 6 7 9 ->= 7 8 7 9 10 10 ,
  14 6 7 12 ->= 7 8 7 9 10 13 ,
  10 6 7 1 ->= 11 8 7 9 10 11 ,
  10 6 7 8 ->= 11 8 7 9 10 6 ,
  10 6 7 9 ->= 11 8 7 9 10 10 ,
  10 6 7 12 ->= 11 8 7 9 10 13 ,
  9 11 ->= 1 ,
  9 6 ->= 8 ,
  9 10 ->= 9 ,
  9 13 ->= 12 ,
  14 11 ->= 7 ,
  14 10 ->= 14 ,
  10 11 ->= 11 ,
  10 6 ->= 6 ,
  10 10 ->= 10 ,
  10 13 ->= 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 0 |
| 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 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 10->6, 8->7, 12->8, 7->9, 9->10, 14->11, 11->12, 6->13, 13->14, 15->15, 16->16 }, 
it remains to prove termination of the 38-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 -> 5 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  9 1 ->= 9 ,
  9 10 ->= 11 ,
  12 7 ->= 13 ,
  12 8 ->= 14 ,
  15 1 ->= 15 ,
  1 7 ->= 7 16 ,
  9 1 ->= 16 9 ,
  9 10 ->= 16 11 ,
  12 7 ->= 13 16 ,
  10 13 9 1 ->= 1 7 9 10 6 12 ,
  10 13 9 7 ->= 1 7 9 10 6 13 ,
  10 13 9 10 ->= 1 7 9 10 6 6 ,
  10 13 9 8 ->= 1 7 9 10 6 14 ,
  11 13 9 1 ->= 9 7 9 10 6 12 ,
  11 13 9 7 ->= 9 7 9 10 6 13 ,
  11 13 9 10 ->= 9 7 9 10 6 6 ,
  11 13 9 8 ->= 9 7 9 10 6 14 ,
  6 13 9 1 ->= 12 7 9 10 6 12 ,
  6 13 9 7 ->= 12 7 9 10 6 13 ,
  6 13 9 10 ->= 12 7 9 10 6 6 ,
  6 13 9 8 ->= 12 7 9 10 6 14 ,
  10 12 ->= 1 ,
  10 13 ->= 7 ,
  10 6 ->= 10 ,
  10 14 ->= 8 ,
  11 12 ->= 9 ,
  11 6 ->= 11 ,
  6 12 ->= 12 ,
  6 13 ->= 13 ,
  6 6 ->= 6 ,
  6 14 ->= 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 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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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 |
 \     /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 7->5, 8->6, 9->7, 10->8, 11->9, 12->10, 13->11, 14->12, 15->13, 16->14, 6->15 }, 
it remains to prove termination of the 37-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 ,
  1 5 ->= 5 14 ,
  7 1 ->= 14 7 ,
  7 8 ->= 14 9 ,
  10 5 ->= 11 14 ,
  8 11 7 1 ->= 1 5 7 8 15 10 ,
  8 11 7 5 ->= 1 5 7 8 15 11 ,
  8 11 7 8 ->= 1 5 7 8 15 15 ,
  8 11 7 6 ->= 1 5 7 8 15 12 ,
  9 11 7 1 ->= 7 5 7 8 15 10 ,
  9 11 7 5 ->= 7 5 7 8 15 11 ,
  9 11 7 8 ->= 7 5 7 8 15 15 ,
  9 11 7 6 ->= 7 5 7 8 15 12 ,
  15 11 7 1 ->= 10 5 7 8 15 10 ,
  15 11 7 5 ->= 10 5 7 8 15 11 ,
  15 11 7 8 ->= 10 5 7 8 15 15 ,
  15 11 7 6 ->= 10 5 7 8 15 12 ,
  8 10 ->= 1 ,
  8 11 ->= 5 ,
  8 15 ->= 8 ,
  8 12 ->= 6 ,
  9 10 ->= 7 ,
  9 15 ->= 9 ,
  15 10 ->= 10 ,
  15 11 ->= 11 ,
  15 15 ->= 15 ,
  15 12 ->= 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 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 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 1 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 35-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 ,
  1 5 ->= 5 12 ,
  6 1 ->= 12 6 ,
  6 7 ->= 12 8 ,
  9 5 ->= 10 12 ,
  7 10 6 1 ->= 1 5 6 7 13 9 ,
  7 10 6 5 ->= 1 5 6 7 13 10 ,
  7 10 6 7 ->= 1 5 6 7 13 13 ,
  7 10 6 14 ->= 1 5 6 7 13 15 ,
  8 10 6 1 ->= 6 5 6 7 13 9 ,
  8 10 6 5 ->= 6 5 6 7 13 10 ,
  8 10 6 7 ->= 6 5 6 7 13 13 ,
  8 10 6 14 ->= 6 5 6 7 13 15 ,
  13 10 6 1 ->= 9 5 6 7 13 9 ,
  13 10 6 5 ->= 9 5 6 7 13 10 ,
  13 10 6 7 ->= 9 5 6 7 13 13 ,
  13 10 6 14 ->= 9 5 6 7 13 15 ,
  7 9 ->= 1 ,
  7 10 ->= 5 ,
  7 13 ->= 7 ,
  7 15 ->= 14 ,
  8 9 ->= 6 ,
  8 13 ->= 8 ,
  13 9 ->= 9 ,
  13 10 ->= 10 ,
  13 13 ->= 13 ,
  13 15 ->= 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 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 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 1 |
| 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 1 |
| 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, 6->6, 7->7, 8->8, 9->9, 10->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 34-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 ,
  1 5 ->= 5 11 ,
  6 1 ->= 11 6 ,
  6 7 ->= 11 8 ,
  9 5 ->= 10 11 ,
  7 10 6 1 ->= 1 5 6 7 12 9 ,
  7 10 6 5 ->= 1 5 6 7 12 10 ,
  7 10 6 7 ->= 1 5 6 7 12 12 ,
  7 10 6 13 ->= 1 5 6 7 12 14 ,
  8 10 6 1 ->= 6 5 6 7 12 9 ,
  8 10 6 5 ->= 6 5 6 7 12 10 ,
  8 10 6 7 ->= 6 5 6 7 12 12 ,
  8 10 6 13 ->= 6 5 6 7 12 14 ,
  12 10 6 1 ->= 9 5 6 7 12 9 ,
  12 10 6 5 ->= 9 5 6 7 12 10 ,
  12 10 6 7 ->= 9 5 6 7 12 12 ,
  12 10 6 13 ->= 9 5 6 7 12 14 ,
  7 9 ->= 1 ,
  7 10 ->= 5 ,
  7 12 ->= 7 ,
  7 14 ->= 13 ,
  8 9 ->= 6 ,
  8 12 ->= 8 ,
  12 9 ->= 9 ,
  12 10 ->= 10 ,
  12 12 ->= 12 ,
  12 14 ->= 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 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 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 1 |
| 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 |
 \     /

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 }, 
it remains to prove termination of the 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 6 ->= 7 ,
  8 4 ->= 9 ,
  1 4 ->= 4 10 ,
  5 1 ->= 10 5 ,
  5 6 ->= 10 7 ,
  8 4 ->= 9 10 ,
  6 9 5 1 ->= 1 4 5 6 11 8 ,
  6 9 5 4 ->= 1 4 5 6 11 9 ,
  6 9 5 6 ->= 1 4 5 6 11 11 ,
  6 9 5 12 ->= 1 4 5 6 11 13 ,
  7 9 5 1 ->= 5 4 5 6 11 8 ,
  7 9 5 4 ->= 5 4 5 6 11 9 ,
  7 9 5 6 ->= 5 4 5 6 11 11 ,
  7 9 5 12 ->= 5 4 5 6 11 13 ,
  11 9 5 1 ->= 8 4 5 6 11 8 ,
  11 9 5 4 ->= 8 4 5 6 11 9 ,
  11 9 5 6 ->= 8 4 5 6 11 11 ,
  11 9 5 12 ->= 8 4 5 6 11 13 ,
  6 8 ->= 1 ,
  6 9 ->= 4 ,
  6 11 ->= 6 ,
  6 13 ->= 12 ,
  7 8 ->= 5 ,
  7 11 ->= 7 ,
  11 8 ->= 8 ,
  11 9 ->= 9 ,
  11 11 ->= 11 ,
  11 13 ->= 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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 1 |
| 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 32-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 3 ->= 3 ,
  4 1 ->= 4 ,
  4 5 ->= 6 ,
  7 3 ->= 8 ,
  1 3 ->= 3 9 ,
  4 1 ->= 9 4 ,
  4 5 ->= 9 6 ,
  7 3 ->= 8 9 ,
  5 8 4 1 ->= 1 3 4 5 10 7 ,
  5 8 4 3 ->= 1 3 4 5 10 8 ,
  5 8 4 5 ->= 1 3 4 5 10 10 ,
  5 8 4 11 ->= 1 3 4 5 10 12 ,
  6 8 4 1 ->= 4 3 4 5 10 7 ,
  6 8 4 3 ->= 4 3 4 5 10 8 ,
  6 8 4 5 ->= 4 3 4 5 10 10 ,
  6 8 4 11 ->= 4 3 4 5 10 12 ,
  10 8 4 1 ->= 7 3 4 5 10 7 ,
  10 8 4 3 ->= 7 3 4 5 10 8 ,
  10 8 4 5 ->= 7 3 4 5 10 10 ,
  10 8 4 11 ->= 7 3 4 5 10 12 ,
  5 7 ->= 1 ,
  5 8 ->= 3 ,
  5 10 ->= 5 ,
  5 12 ->= 11 ,
  6 7 ->= 4 ,
  6 10 ->= 6 ,
  10 7 ->= 7 ,
  10 8 ->= 8 ,
  10 10 ->= 10 ,
  10 12 ->= 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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
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 1 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 1 |
| 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 { 0->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 31-rule system
{ 0 1 -> 0 ,
  1 2 ->= 2 ,
  3 1 ->= 3 ,
  3 4 ->= 5 ,
  6 2 ->= 7 ,
  1 2 ->= 2 8 ,
  3 1 ->= 8 3 ,
  3 4 ->= 8 5 ,
  6 2 ->= 7 8 ,
  4 7 3 1 ->= 1 2 3 4 9 6 ,
  4 7 3 2 ->= 1 2 3 4 9 7 ,
  4 7 3 4 ->= 1 2 3 4 9 9 ,
  4 7 3 10 ->= 1 2 3 4 9 11 ,
  5 7 3 1 ->= 3 2 3 4 9 6 ,
  5 7 3 2 ->= 3 2 3 4 9 7 ,
  5 7 3 4 ->= 3 2 3 4 9 9 ,
  5 7 3 10 ->= 3 2 3 4 9 11 ,
  9 7 3 1 ->= 6 2 3 4 9 6 ,
  9 7 3 2 ->= 6 2 3 4 9 7 ,
  9 7 3 4 ->= 6 2 3 4 9 9 ,
  9 7 3 10 ->= 6 2 3 4 9 11 ,
  4 6 ->= 1 ,
  4 7 ->= 2 ,
  4 9 ->= 4 ,
  4 11 ->= 10 ,
  5 6 ->= 3 ,
  5 9 ->= 5 ,
  9 6 ->= 6 ,
  9 7 ->= 7 ,
  9 9 ->= 9 ,
  9 11 ->= 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 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 1 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 1 |
| 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 30-rule system
{ 0 1 ->= 1 ,
  2 0 ->= 2 ,
  2 3 ->= 4 ,
  5 1 ->= 6 ,
  0 1 ->= 1 7 ,
  2 0 ->= 7 2 ,
  2 3 ->= 7 4 ,
  5 1 ->= 6 7 ,
  3 6 2 0 ->= 0 1 2 3 8 5 ,
  3 6 2 1 ->= 0 1 2 3 8 6 ,
  3 6 2 3 ->= 0 1 2 3 8 8 ,
  3 6 2 9 ->= 0 1 2 3 8 10 ,
  4 6 2 0 ->= 2 1 2 3 8 5 ,
  4 6 2 1 ->= 2 1 2 3 8 6 ,
  4 6 2 3 ->= 2 1 2 3 8 8 ,
  4 6 2 9 ->= 2 1 2 3 8 10 ,
  8 6 2 0 ->= 5 1 2 3 8 5 ,
  8 6 2 1 ->= 5 1 2 3 8 6 ,
  8 6 2 3 ->= 5 1 2 3 8 8 ,
  8 6 2 9 ->= 5 1 2 3 8 10 ,
  3 5 ->= 0 ,
  3 6 ->= 1 ,
  3 8 ->= 3 ,
  3 10 ->= 9 ,
  4 5 ->= 2 ,
  4 8 ->= 4 ,
  8 5 ->= 5 ,
  8 6 ->= 6 ,
  8 8 ->= 8 ,
  8 10 ->= 10 }

The system is trivially terminating.