YES

After renaming modulo { p->0, 0->1, s->2, f->3, g->4, q->5, i->6 }, 
it remains to prove termination of the 8-rule system
{ 0 1 -> 2 2 1 2 2 0 ,
  0 2 1 -> 1 ,
  0 2 2 -> 2 0 2 ,
  3 2 -> 4 5 6 ,
  4 -> 3 0 0 ,
  5 6 -> 5 2 ,
  5 2 -> 2 2 ,
  6 -> 2 }


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

After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (0,2)->3, (2,2)->4, (2,1)->5, (2,0)->6, (1,8)->7, (0,8)->8, (3,0)->9, (3,2)->10, (6,0)->11, (6,2)->12, (3,1)->13, (6,1)->14, (2,8)->15, (7,3)->16, (7,4)->17, (4,5)->18, (5,6)->19, (6,8)->20, (4,2)->21, (0,5)->22, (5,2)->23, (7,5)->24, (7,2)->25 },
it remains to prove termination of the 66-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  0 1 7 -> 3 4 5 2 4 6 8 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  6 1 7 -> 4 4 5 2 4 6 8 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  9 1 7 -> 10 4 5 2 4 6 8 ,
  11 1 2 -> 12 4 5 2 4 6 3 ,
  11 1 7 -> 12 4 5 2 4 6 8 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 7 -> 1 7 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 7 -> 5 7 ,
  9 3 5 2 -> 13 2 ,
  9 3 5 7 -> 13 7 ,
  11 3 5 2 -> 14 2 ,
  11 3 5 7 -> 14 7 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 15 -> 3 6 3 15 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 15 -> 4 6 3 15 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 15 -> 10 6 3 15 ,
  11 3 4 6 -> 12 6 3 6 ,
  11 3 4 5 -> 12 6 3 5 ,
  11 3 4 4 -> 12 6 3 4 ,
  11 3 4 15 -> 12 6 3 15 ,
  16 10 6 -> 17 18 19 11 ,
  16 10 5 -> 17 18 19 14 ,
  16 10 4 -> 17 18 19 12 ,
  16 10 15 -> 17 18 19 20 ,
  17 21 -> 16 9 0 3 ,
  17 18 -> 16 9 0 22 ,
  22 19 11 -> 22 23 6 ,
  22 19 14 -> 22 23 5 ,
  22 19 12 -> 22 23 4 ,
  22 19 20 -> 22 23 15 ,
  18 19 11 -> 18 23 6 ,
  18 19 14 -> 18 23 5 ,
  18 19 12 -> 18 23 4 ,
  18 19 20 -> 18 23 15 ,
  24 19 11 -> 24 23 6 ,
  24 19 14 -> 24 23 5 ,
  24 19 12 -> 24 23 4 ,
  24 19 20 -> 24 23 15 ,
  22 23 6 -> 3 4 6 ,
  22 23 5 -> 3 4 5 ,
  22 23 4 -> 3 4 4 ,
  22 23 15 -> 3 4 15 ,
  18 23 6 -> 21 4 6 ,
  18 23 5 -> 21 4 5 ,
  18 23 4 -> 21 4 4 ,
  18 23 15 -> 21 4 15 ,
  24 23 6 -> 25 4 6 ,
  24 23 5 -> 25 4 5 ,
  24 23 4 -> 25 4 4 ,
  24 23 15 -> 25 4 15 ,
  19 11 -> 23 6 ,
  19 14 -> 23 5 ,
  19 12 -> 23 4 ,
  19 20 -> 23 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 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 |
 \   /
19 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
20 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
21 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
22 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
23 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
24 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
25 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 9->7, 10->8, 11->9, 12->10, 7->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23 }, 
it remains to prove termination of the 58-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  7 3 5 2 -> 12 2 ,
  7 3 5 11 -> 12 11 ,
  9 3 5 2 -> 13 2 ,
  9 3 5 11 -> 13 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 14 -> 3 6 3 14 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 14 -> 4 6 3 14 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 14 -> 8 6 3 14 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 14 -> 10 6 3 14 ,
  15 8 6 -> 16 17 18 9 ,
  15 8 5 -> 16 17 18 13 ,
  15 8 4 -> 16 17 18 10 ,
  15 8 14 -> 16 17 18 19 ,
  16 20 -> 15 7 0 3 ,
  16 17 -> 15 7 0 21 ,
  21 18 9 -> 21 22 6 ,
  21 18 13 -> 21 22 5 ,
  21 18 10 -> 21 22 4 ,
  21 18 19 -> 21 22 14 ,
  17 18 9 -> 17 22 6 ,
  17 18 13 -> 17 22 5 ,
  17 18 10 -> 17 22 4 ,
  17 18 19 -> 17 22 14 ,
  23 18 9 -> 23 22 6 ,
  23 18 13 -> 23 22 5 ,
  23 18 10 -> 23 22 4 ,
  23 18 19 -> 23 22 14 ,
  21 22 6 -> 3 4 6 ,
  21 22 5 -> 3 4 5 ,
  21 22 4 -> 3 4 4 ,
  21 22 14 -> 3 4 14 ,
  17 22 6 -> 20 4 6 ,
  17 22 5 -> 20 4 5 ,
  17 22 4 -> 20 4 4 ,
  17 22 14 -> 20 4 14 ,
  18 9 -> 22 6 ,
  18 13 -> 22 5 ,
  18 10 -> 22 4 ,
  18 19 -> 22 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 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 1 |
| 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 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 |
 \   /
21 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
22 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
23 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, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22 }, 
it remains to prove termination of the 56-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  9 3 5 2 -> 12 2 ,
  9 3 5 11 -> 12 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 13 -> 3 6 3 13 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 13 -> 4 6 3 13 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 13 -> 8 6 3 13 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 13 -> 10 6 3 13 ,
  14 8 6 -> 15 16 17 9 ,
  14 8 5 -> 15 16 17 12 ,
  14 8 4 -> 15 16 17 10 ,
  14 8 13 -> 15 16 17 18 ,
  15 19 -> 14 7 0 3 ,
  15 16 -> 14 7 0 20 ,
  20 17 9 -> 20 21 6 ,
  20 17 12 -> 20 21 5 ,
  20 17 10 -> 20 21 4 ,
  20 17 18 -> 20 21 13 ,
  16 17 9 -> 16 21 6 ,
  16 17 12 -> 16 21 5 ,
  16 17 10 -> 16 21 4 ,
  16 17 18 -> 16 21 13 ,
  22 17 9 -> 22 21 6 ,
  22 17 12 -> 22 21 5 ,
  22 17 10 -> 22 21 4 ,
  22 17 18 -> 22 21 13 ,
  20 21 6 -> 3 4 6 ,
  20 21 5 -> 3 4 5 ,
  20 21 4 -> 3 4 4 ,
  20 21 13 -> 3 4 13 ,
  16 21 6 -> 19 4 6 ,
  16 21 5 -> 19 4 5 ,
  16 21 4 -> 19 4 4 ,
  16 21 13 -> 19 4 13 ,
  17 9 -> 21 6 ,
  17 12 -> 21 5 ,
  17 10 -> 21 4 ,
  17 18 -> 21 13 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 19->18, 20->19, 21->20, 18->21, 22->22 }, 
it remains to prove termination of the 55-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  9 3 5 2 -> 12 2 ,
  9 3 5 11 -> 12 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 13 -> 3 6 3 13 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 13 -> 4 6 3 13 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 13 -> 8 6 3 13 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 13 -> 10 6 3 13 ,
  14 8 6 -> 15 16 17 9 ,
  14 8 5 -> 15 16 17 12 ,
  14 8 4 -> 15 16 17 10 ,
  15 18 -> 14 7 0 3 ,
  15 16 -> 14 7 0 19 ,
  19 17 9 -> 19 20 6 ,
  19 17 12 -> 19 20 5 ,
  19 17 10 -> 19 20 4 ,
  19 17 21 -> 19 20 13 ,
  16 17 9 -> 16 20 6 ,
  16 17 12 -> 16 20 5 ,
  16 17 10 -> 16 20 4 ,
  16 17 21 -> 16 20 13 ,
  22 17 9 -> 22 20 6 ,
  22 17 12 -> 22 20 5 ,
  22 17 10 -> 22 20 4 ,
  22 17 21 -> 22 20 13 ,
  19 20 6 -> 3 4 6 ,
  19 20 5 -> 3 4 5 ,
  19 20 4 -> 3 4 4 ,
  19 20 13 -> 3 4 13 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  16 20 13 -> 18 4 13 ,
  17 9 -> 20 6 ,
  17 12 -> 20 5 ,
  17 10 -> 20 4 ,
  17 21 -> 20 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 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 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 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 |
 \   /
21 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
22 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, 19->19, 20->20, 22->21 }, 
it remains to prove termination of the 51-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  9 3 5 2 -> 12 2 ,
  9 3 5 11 -> 12 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 13 -> 3 6 3 13 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 13 -> 4 6 3 13 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 13 -> 8 6 3 13 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 13 -> 10 6 3 13 ,
  14 8 6 -> 15 16 17 9 ,
  14 8 5 -> 15 16 17 12 ,
  14 8 4 -> 15 16 17 10 ,
  15 18 -> 14 7 0 3 ,
  15 16 -> 14 7 0 19 ,
  19 17 9 -> 19 20 6 ,
  19 17 12 -> 19 20 5 ,
  19 17 10 -> 19 20 4 ,
  16 17 9 -> 16 20 6 ,
  16 17 12 -> 16 20 5 ,
  16 17 10 -> 16 20 4 ,
  21 17 9 -> 21 20 6 ,
  21 17 12 -> 21 20 5 ,
  21 17 10 -> 21 20 4 ,
  19 20 6 -> 3 4 6 ,
  19 20 5 -> 3 4 5 ,
  19 20 4 -> 3 4 4 ,
  19 20 13 -> 3 4 13 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  16 20 13 -> 18 4 13 ,
  17 9 -> 20 6 ,
  17 12 -> 20 5 ,
  17 10 -> 20 4 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 50-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  9 3 5 2 -> 12 2 ,
  9 3 5 11 -> 12 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 13 -> 3 6 3 13 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 13 -> 4 6 3 13 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 13 -> 8 6 3 13 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 13 -> 10 6 3 13 ,
  14 8 6 -> 15 16 17 9 ,
  14 8 5 -> 15 16 17 12 ,
  14 8 4 -> 15 16 17 10 ,
  15 18 -> 14 7 0 3 ,
  15 16 -> 14 7 0 19 ,
  19 17 9 -> 19 20 6 ,
  19 17 12 -> 19 20 5 ,
  19 17 10 -> 19 20 4 ,
  16 17 9 -> 16 20 6 ,
  16 17 12 -> 16 20 5 ,
  16 17 10 -> 16 20 4 ,
  21 17 12 -> 21 20 5 ,
  21 17 10 -> 21 20 4 ,
  19 20 6 -> 3 4 6 ,
  19 20 5 -> 3 4 5 ,
  19 20 4 -> 3 4 4 ,
  19 20 13 -> 3 4 13 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  16 20 13 -> 18 4 13 ,
  17 9 -> 20 6 ,
  17 12 -> 20 5 ,
  17 10 -> 20 4 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 49-rule system
{ 0 1 2 -> 3 4 5 2 4 6 3 ,
  6 1 2 -> 4 4 5 2 4 6 3 ,
  7 1 2 -> 8 4 5 2 4 6 3 ,
  9 1 2 -> 10 4 5 2 4 6 3 ,
  0 3 5 2 -> 1 2 ,
  0 3 5 11 -> 1 11 ,
  6 3 5 2 -> 5 2 ,
  6 3 5 11 -> 5 11 ,
  9 3 5 2 -> 12 2 ,
  9 3 5 11 -> 12 11 ,
  0 3 4 6 -> 3 6 3 6 ,
  0 3 4 5 -> 3 6 3 5 ,
  0 3 4 4 -> 3 6 3 4 ,
  0 3 4 13 -> 3 6 3 13 ,
  6 3 4 6 -> 4 6 3 6 ,
  6 3 4 5 -> 4 6 3 5 ,
  6 3 4 4 -> 4 6 3 4 ,
  6 3 4 13 -> 4 6 3 13 ,
  7 3 4 6 -> 8 6 3 6 ,
  7 3 4 5 -> 8 6 3 5 ,
  7 3 4 4 -> 8 6 3 4 ,
  7 3 4 13 -> 8 6 3 13 ,
  9 3 4 6 -> 10 6 3 6 ,
  9 3 4 5 -> 10 6 3 5 ,
  9 3 4 4 -> 10 6 3 4 ,
  9 3 4 13 -> 10 6 3 13 ,
  14 8 6 -> 15 16 17 9 ,
  14 8 5 -> 15 16 17 12 ,
  14 8 4 -> 15 16 17 10 ,
  15 18 -> 14 7 0 3 ,
  15 16 -> 14 7 0 19 ,
  19 17 9 -> 19 20 6 ,
  19 17 12 -> 19 20 5 ,
  19 17 10 -> 19 20 4 ,
  16 17 9 -> 16 20 6 ,
  16 17 12 -> 16 20 5 ,
  16 17 10 -> 16 20 4 ,
  21 17 12 -> 21 20 5 ,
  21 17 10 -> 21 20 4 ,
  19 20 6 -> 3 4 6 ,
  19 20 5 -> 3 4 5 ,
  19 20 4 -> 3 4 4 ,
  19 20 13 -> 3 4 13 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  17 9 -> 20 6 ,
  17 12 -> 20 5 ,
  17 10 -> 20 4 }


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

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

After renaming modulo { 6->0, 1->1, 2->2, 4->3, 5->4, 3->5, 7->6, 8->7, 9->8, 10->9, 0->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 48-rule system
{ 0 1 2 -> 3 3 4 2 3 0 5 ,
  6 1 2 -> 7 3 4 2 3 0 5 ,
  8 1 2 -> 9 3 4 2 3 0 5 ,
  10 5 4 2 -> 1 2 ,
  10 5 4 11 -> 1 11 ,
  0 5 4 2 -> 4 2 ,
  0 5 4 11 -> 4 11 ,
  8 5 4 2 -> 12 2 ,
  8 5 4 11 -> 12 11 ,
  10 5 3 0 -> 5 0 5 0 ,
  10 5 3 4 -> 5 0 5 4 ,
  10 5 3 3 -> 5 0 5 3 ,
  10 5 3 13 -> 5 0 5 13 ,
  0 5 3 0 -> 3 0 5 0 ,
  0 5 3 4 -> 3 0 5 4 ,
  0 5 3 3 -> 3 0 5 3 ,
  0 5 3 13 -> 3 0 5 13 ,
  6 5 3 0 -> 7 0 5 0 ,
  6 5 3 4 -> 7 0 5 4 ,
  6 5 3 3 -> 7 0 5 3 ,
  6 5 3 13 -> 7 0 5 13 ,
  8 5 3 0 -> 9 0 5 0 ,
  8 5 3 4 -> 9 0 5 4 ,
  8 5 3 3 -> 9 0 5 3 ,
  8 5 3 13 -> 9 0 5 13 ,
  14 7 0 -> 15 16 17 8 ,
  14 7 4 -> 15 16 17 12 ,
  14 7 3 -> 15 16 17 9 ,
  15 18 -> 14 6 10 5 ,
  15 16 -> 14 6 10 19 ,
  19 17 8 -> 19 20 0 ,
  19 17 12 -> 19 20 4 ,
  19 17 9 -> 19 20 3 ,
  16 17 8 -> 16 20 0 ,
  16 17 12 -> 16 20 4 ,
  16 17 9 -> 16 20 3 ,
  21 17 12 -> 21 20 4 ,
  21 17 9 -> 21 20 3 ,
  19 20 0 -> 5 3 0 ,
  19 20 4 -> 5 3 4 ,
  19 20 3 -> 5 3 3 ,
  19 20 13 -> 5 3 13 ,
  16 20 0 -> 18 3 0 ,
  16 20 4 -> 18 3 4 ,
  16 20 3 -> 18 3 3 ,
  17 8 -> 20 0 ,
  17 12 -> 20 4 ,
  17 9 -> 20 3 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 47-rule system
{ 0 1 2 -> 3 3 4 2 3 0 5 ,
  6 1 2 -> 7 3 4 2 3 0 5 ,
  8 1 2 -> 9 3 4 2 3 0 5 ,
  10 5 4 2 -> 1 2 ,
  10 5 4 11 -> 1 11 ,
  0 5 4 2 -> 4 2 ,
  0 5 4 11 -> 4 11 ,
  8 5 4 2 -> 12 2 ,
  8 5 4 11 -> 12 11 ,
  10 5 3 0 -> 5 0 5 0 ,
  10 5 3 4 -> 5 0 5 4 ,
  10 5 3 3 -> 5 0 5 3 ,
  10 5 3 13 -> 5 0 5 13 ,
  0 5 3 0 -> 3 0 5 0 ,
  0 5 3 4 -> 3 0 5 4 ,
  0 5 3 3 -> 3 0 5 3 ,
  0 5 3 13 -> 3 0 5 13 ,
  6 5 3 0 -> 7 0 5 0 ,
  6 5 3 4 -> 7 0 5 4 ,
  6 5 3 3 -> 7 0 5 3 ,
  8 5 3 0 -> 9 0 5 0 ,
  8 5 3 4 -> 9 0 5 4 ,
  8 5 3 3 -> 9 0 5 3 ,
  8 5 3 13 -> 9 0 5 13 ,
  14 7 0 -> 15 16 17 8 ,
  14 7 4 -> 15 16 17 12 ,
  14 7 3 -> 15 16 17 9 ,
  15 18 -> 14 6 10 5 ,
  15 16 -> 14 6 10 19 ,
  19 17 8 -> 19 20 0 ,
  19 17 12 -> 19 20 4 ,
  19 17 9 -> 19 20 3 ,
  16 17 8 -> 16 20 0 ,
  16 17 12 -> 16 20 4 ,
  16 17 9 -> 16 20 3 ,
  21 17 12 -> 21 20 4 ,
  21 17 9 -> 21 20 3 ,
  19 20 0 -> 5 3 0 ,
  19 20 4 -> 5 3 4 ,
  19 20 3 -> 5 3 3 ,
  19 20 13 -> 5 3 13 ,
  16 20 0 -> 18 3 0 ,
  16 20 4 -> 18 3 4 ,
  16 20 3 -> 18 3 3 ,
  17 8 -> 20 0 ,
  17 12 -> 20 4 ,
  17 9 -> 20 3 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 46-rule system
{ 0 1 2 -> 3 3 4 2 3 0 5 ,
  6 1 2 -> 7 3 4 2 3 0 5 ,
  8 1 2 -> 9 3 4 2 3 0 5 ,
  10 5 4 2 -> 1 2 ,
  10 5 4 11 -> 1 11 ,
  0 5 4 2 -> 4 2 ,
  0 5 4 11 -> 4 11 ,
  8 5 4 2 -> 12 2 ,
  8 5 4 11 -> 12 11 ,
  10 5 3 0 -> 5 0 5 0 ,
  10 5 3 4 -> 5 0 5 4 ,
  10 5 3 3 -> 5 0 5 3 ,
  10 5 3 13 -> 5 0 5 13 ,
  0 5 3 0 -> 3 0 5 0 ,
  0 5 3 4 -> 3 0 5 4 ,
  0 5 3 3 -> 3 0 5 3 ,
  0 5 3 13 -> 3 0 5 13 ,
  6 5 3 0 -> 7 0 5 0 ,
  6 5 3 4 -> 7 0 5 4 ,
  6 5 3 3 -> 7 0 5 3 ,
  8 5 3 0 -> 9 0 5 0 ,
  8 5 3 4 -> 9 0 5 4 ,
  8 5 3 3 -> 9 0 5 3 ,
  8 5 3 13 -> 9 0 5 13 ,
  14 7 0 -> 15 16 17 8 ,
  14 7 4 -> 15 16 17 12 ,
  14 7 3 -> 15 16 17 9 ,
  15 18 -> 14 6 10 5 ,
  15 16 -> 14 6 10 19 ,
  19 17 8 -> 19 20 0 ,
  19 17 12 -> 19 20 4 ,
  19 17 9 -> 19 20 3 ,
  16 17 8 -> 16 20 0 ,
  16 17 12 -> 16 20 4 ,
  16 17 9 -> 16 20 3 ,
  21 17 12 -> 21 20 4 ,
  21 17 9 -> 21 20 3 ,
  19 20 0 -> 5 3 0 ,
  19 20 4 -> 5 3 4 ,
  19 20 3 -> 5 3 3 ,
  16 20 0 -> 18 3 0 ,
  16 20 4 -> 18 3 4 ,
  16 20 3 -> 18 3 3 ,
  17 8 -> 20 0 ,
  17 12 -> 20 4 ,
  17 9 -> 20 3 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 45-rule system
{ 0 1 2 -> 3 3 4 2 3 0 5 ,
  6 1 2 -> 7 3 4 2 3 0 5 ,
  8 1 2 -> 9 3 4 2 3 0 5 ,
  10 5 4 2 -> 1 2 ,
  10 5 4 11 -> 1 11 ,
  0 5 4 2 -> 4 2 ,
  0 5 4 11 -> 4 11 ,
  8 5 4 2 -> 12 2 ,
  8 5 4 11 -> 12 11 ,
  10 5 3 0 -> 5 0 5 0 ,
  10 5 3 4 -> 5 0 5 4 ,
  10 5 3 3 -> 5 0 5 3 ,
  0 5 3 0 -> 3 0 5 0 ,
  0 5 3 4 -> 3 0 5 4 ,
  0 5 3 3 -> 3 0 5 3 ,
  0 5 3 13 -> 3 0 5 13 ,
  6 5 3 0 -> 7 0 5 0 ,
  6 5 3 4 -> 7 0 5 4 ,
  6 5 3 3 -> 7 0 5 3 ,
  8 5 3 0 -> 9 0 5 0 ,
  8 5 3 4 -> 9 0 5 4 ,
  8 5 3 3 -> 9 0 5 3 ,
  8 5 3 13 -> 9 0 5 13 ,
  14 7 0 -> 15 16 17 8 ,
  14 7 4 -> 15 16 17 12 ,
  14 7 3 -> 15 16 17 9 ,
  15 18 -> 14 6 10 5 ,
  15 16 -> 14 6 10 19 ,
  19 17 8 -> 19 20 0 ,
  19 17 12 -> 19 20 4 ,
  19 17 9 -> 19 20 3 ,
  16 17 8 -> 16 20 0 ,
  16 17 12 -> 16 20 4 ,
  16 17 9 -> 16 20 3 ,
  21 17 12 -> 21 20 4 ,
  21 17 9 -> 21 20 3 ,
  19 20 0 -> 5 3 0 ,
  19 20 4 -> 5 3 4 ,
  19 20 3 -> 5 3 3 ,
  16 20 0 -> 18 3 0 ,
  16 20 4 -> 18 3 4 ,
  16 20 3 -> 18 3 3 ,
  17 8 -> 20 0 ,
  17 12 -> 20 4 ,
  17 9 -> 20 3 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 44-rule system
{ 0 1 2 -> 3 3 4 2 3 0 5 ,
  6 1 2 -> 7 3 4 2 3 0 5 ,
  8 1 2 -> 9 3 4 2 3 0 5 ,
  10 5 4 2 -> 1 2 ,
  10 5 4 11 -> 1 11 ,
  0 5 4 2 -> 4 2 ,
  0 5 4 11 -> 4 11 ,
  8 5 4 2 -> 12 2 ,
  8 5 4 11 -> 12 11 ,
  10 5 3 0 -> 5 0 5 0 ,
  10 5 3 4 -> 5 0 5 4 ,
  10 5 3 3 -> 5 0 5 3 ,
  0 5 3 0 -> 3 0 5 0 ,
  0 5 3 4 -> 3 0 5 4 ,
  0 5 3 3 -> 3 0 5 3 ,
  0 5 3 13 -> 3 0 5 13 ,
  6 5 3 0 -> 7 0 5 0 ,
  6 5 3 4 -> 7 0 5 4 ,
  6 5 3 3 -> 7 0 5 3 ,
  8 5 3 0 -> 9 0 5 0 ,
  8 5 3 4 -> 9 0 5 4 ,
  8 5 3 3 -> 9 0 5 3 ,
  8 5 3 13 -> 9 0 5 13 ,
  14 7 0 -> 15 16 17 8 ,
  14 7 4 -> 15 16 17 12 ,
  14 7 3 -> 15 16 17 9 ,
  15 18 -> 14 6 10 5 ,
  15 16 -> 14 6 10 19 ,
  19 17 8 -> 19 20 0 ,
  19 17 12 -> 19 20 4 ,
  19 17 9 -> 19 20 3 ,
  16 17 8 -> 16 20 0 ,
  16 17 12 -> 16 20 4 ,
  16 17 9 -> 16 20 3 ,
  21 17 9 -> 21 20 3 ,
  19 20 0 -> 5 3 0 ,
  19 20 4 -> 5 3 4 ,
  19 20 3 -> 5 3 3 ,
  16 20 0 -> 18 3 0 ,
  16 20 4 -> 18 3 4 ,
  16 20 3 -> 18 3 3 ,
  17 8 -> 20 0 ,
  17 12 -> 20 4 ,
  17 9 -> 20 3 }


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

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

After renaming modulo { 6->0, 1->1, 2->2, 7->3, 3->4, 4->5, 0->6, 5->7, 10->8, 11->9, 8->10, 12->11, 13->12, 9->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21 }, 
it remains to prove termination of the 42-rule system
{ 0 1 2 -> 3 4 5 2 4 6 7 ,
  8 7 5 2 -> 1 2 ,
  8 7 5 9 -> 1 9 ,
  6 7 5 2 -> 5 2 ,
  6 7 5 9 -> 5 9 ,
  10 7 5 2 -> 11 2 ,
  10 7 5 9 -> 11 9 ,
  8 7 4 6 -> 7 6 7 6 ,
  8 7 4 5 -> 7 6 7 5 ,
  8 7 4 4 -> 7 6 7 4 ,
  6 7 4 6 -> 4 6 7 6 ,
  6 7 4 5 -> 4 6 7 5 ,
  6 7 4 4 -> 4 6 7 4 ,
  6 7 4 12 -> 4 6 7 12 ,
  0 7 4 6 -> 3 6 7 6 ,
  0 7 4 5 -> 3 6 7 5 ,
  0 7 4 4 -> 3 6 7 4 ,
  10 7 4 6 -> 13 6 7 6 ,
  10 7 4 5 -> 13 6 7 5 ,
  10 7 4 4 -> 13 6 7 4 ,
  10 7 4 12 -> 13 6 7 12 ,
  14 3 6 -> 15 16 17 10 ,
  14 3 5 -> 15 16 17 11 ,
  14 3 4 -> 15 16 17 13 ,
  15 18 -> 14 0 8 7 ,
  15 16 -> 14 0 8 19 ,
  19 17 10 -> 19 20 6 ,
  19 17 11 -> 19 20 5 ,
  19 17 13 -> 19 20 4 ,
  16 17 10 -> 16 20 6 ,
  16 17 11 -> 16 20 5 ,
  16 17 13 -> 16 20 4 ,
  21 17 13 -> 21 20 4 ,
  19 20 6 -> 7 4 6 ,
  19 20 5 -> 7 4 5 ,
  19 20 4 -> 7 4 4 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  17 10 -> 20 6 ,
  17 11 -> 20 5 ,
  17 13 -> 20 4 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 41-rule system
{ 0 1 2 -> 3 4 5 2 4 6 7 ,
  8 7 5 2 -> 1 2 ,
  8 7 5 9 -> 1 9 ,
  6 7 5 2 -> 5 2 ,
  6 7 5 9 -> 5 9 ,
  10 7 5 2 -> 11 2 ,
  10 7 5 9 -> 11 9 ,
  8 7 4 6 -> 7 6 7 6 ,
  8 7 4 5 -> 7 6 7 5 ,
  8 7 4 4 -> 7 6 7 4 ,
  6 7 4 6 -> 4 6 7 6 ,
  6 7 4 5 -> 4 6 7 5 ,
  6 7 4 4 -> 4 6 7 4 ,
  6 7 4 12 -> 4 6 7 12 ,
  0 7 4 6 -> 3 6 7 6 ,
  0 7 4 5 -> 3 6 7 5 ,
  0 7 4 4 -> 3 6 7 4 ,
  10 7 4 6 -> 13 6 7 6 ,
  10 7 4 5 -> 13 6 7 5 ,
  10 7 4 4 -> 13 6 7 4 ,
  10 7 4 12 -> 13 6 7 12 ,
  14 3 6 -> 15 16 17 10 ,
  14 3 5 -> 15 16 17 11 ,
  14 3 4 -> 15 16 17 13 ,
  15 18 -> 14 0 8 7 ,
  15 16 -> 14 0 8 19 ,
  19 17 10 -> 19 20 6 ,
  19 17 11 -> 19 20 5 ,
  19 17 13 -> 19 20 4 ,
  16 17 10 -> 16 20 6 ,
  16 17 11 -> 16 20 5 ,
  16 17 13 -> 16 20 4 ,
  19 20 6 -> 7 4 6 ,
  19 20 5 -> 7 4 5 ,
  19 20 4 -> 7 4 4 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  17 10 -> 20 6 ,
  17 11 -> 20 5 ,
  17 13 -> 20 4 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 13:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 40-rule system
{ 0 1 2 -> 3 4 5 2 4 6 7 ,
  8 7 5 2 -> 1 2 ,
  8 7 5 9 -> 1 9 ,
  6 7 5 2 -> 5 2 ,
  6 7 5 9 -> 5 9 ,
  10 7 5 2 -> 11 2 ,
  10 7 5 9 -> 11 9 ,
  8 7 4 6 -> 7 6 7 6 ,
  8 7 4 5 -> 7 6 7 5 ,
  8 7 4 4 -> 7 6 7 4 ,
  6 7 4 6 -> 4 6 7 6 ,
  6 7 4 5 -> 4 6 7 5 ,
  6 7 4 4 -> 4 6 7 4 ,
  6 7 4 12 -> 4 6 7 12 ,
  0 7 4 6 -> 3 6 7 6 ,
  0 7 4 5 -> 3 6 7 5 ,
  0 7 4 4 -> 3 6 7 4 ,
  10 7 4 6 -> 13 6 7 6 ,
  10 7 4 5 -> 13 6 7 5 ,
  10 7 4 4 -> 13 6 7 4 ,
  14 3 6 -> 15 16 17 10 ,
  14 3 5 -> 15 16 17 11 ,
  14 3 4 -> 15 16 17 13 ,
  15 18 -> 14 0 8 7 ,
  15 16 -> 14 0 8 19 ,
  19 17 10 -> 19 20 6 ,
  19 17 11 -> 19 20 5 ,
  19 17 13 -> 19 20 4 ,
  16 17 10 -> 16 20 6 ,
  16 17 11 -> 16 20 5 ,
  16 17 13 -> 16 20 4 ,
  19 20 6 -> 7 4 6 ,
  19 20 5 -> 7 4 5 ,
  19 20 4 -> 7 4 4 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  17 10 -> 20 6 ,
  17 11 -> 20 5 ,
  17 13 -> 20 4 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 39-rule system
{ 0 1 2 -> 3 4 5 2 4 6 7 ,
  8 7 5 9 -> 1 9 ,
  6 7 5 2 -> 5 2 ,
  6 7 5 9 -> 5 9 ,
  10 7 5 2 -> 11 2 ,
  10 7 5 9 -> 11 9 ,
  8 7 4 6 -> 7 6 7 6 ,
  8 7 4 5 -> 7 6 7 5 ,
  8 7 4 4 -> 7 6 7 4 ,
  6 7 4 6 -> 4 6 7 6 ,
  6 7 4 5 -> 4 6 7 5 ,
  6 7 4 4 -> 4 6 7 4 ,
  6 7 4 12 -> 4 6 7 12 ,
  0 7 4 6 -> 3 6 7 6 ,
  0 7 4 5 -> 3 6 7 5 ,
  0 7 4 4 -> 3 6 7 4 ,
  10 7 4 6 -> 13 6 7 6 ,
  10 7 4 5 -> 13 6 7 5 ,
  10 7 4 4 -> 13 6 7 4 ,
  14 3 6 -> 15 16 17 10 ,
  14 3 5 -> 15 16 17 11 ,
  14 3 4 -> 15 16 17 13 ,
  15 18 -> 14 0 8 7 ,
  15 16 -> 14 0 8 19 ,
  19 17 10 -> 19 20 6 ,
  19 17 11 -> 19 20 5 ,
  19 17 13 -> 19 20 4 ,
  16 17 10 -> 16 20 6 ,
  16 17 11 -> 16 20 5 ,
  16 17 13 -> 16 20 4 ,
  19 20 6 -> 7 4 6 ,
  19 20 5 -> 7 4 5 ,
  19 20 4 -> 7 4 4 ,
  16 20 6 -> 18 4 6 ,
  16 20 5 -> 18 4 5 ,
  16 20 4 -> 18 4 4 ,
  17 10 -> 20 6 ,
  17 11 -> 20 5 ,
  17 13 -> 20 4 }


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

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

After renaming modulo { 8->0, 7->1, 5->2, 9->3, 1->4, 6->5, 2->6, 10->7, 11->8, 4->9, 12->10, 0->11, 3->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 38-rule system
{ 0 1 2 3 -> 4 3 ,
  5 1 2 6 -> 2 6 ,
  5 1 2 3 -> 2 3 ,
  7 1 2 6 -> 8 6 ,
  7 1 2 3 -> 8 3 ,
  0 1 9 5 -> 1 5 1 5 ,
  0 1 9 2 -> 1 5 1 2 ,
  0 1 9 9 -> 1 5 1 9 ,
  5 1 9 5 -> 9 5 1 5 ,
  5 1 9 2 -> 9 5 1 2 ,
  5 1 9 9 -> 9 5 1 9 ,
  5 1 9 10 -> 9 5 1 10 ,
  11 1 9 5 -> 12 5 1 5 ,
  11 1 9 2 -> 12 5 1 2 ,
  11 1 9 9 -> 12 5 1 9 ,
  7 1 9 5 -> 13 5 1 5 ,
  7 1 9 2 -> 13 5 1 2 ,
  7 1 9 9 -> 13 5 1 9 ,
  14 12 5 -> 15 16 17 7 ,
  14 12 2 -> 15 16 17 8 ,
  14 12 9 -> 15 16 17 13 ,
  15 18 -> 14 11 0 1 ,
  15 16 -> 14 11 0 19 ,
  19 17 7 -> 19 20 5 ,
  19 17 8 -> 19 20 2 ,
  19 17 13 -> 19 20 9 ,
  16 17 7 -> 16 20 5 ,
  16 17 8 -> 16 20 2 ,
  16 17 13 -> 16 20 9 ,
  19 20 5 -> 1 9 5 ,
  19 20 2 -> 1 9 2 ,
  19 20 9 -> 1 9 9 ,
  16 20 5 -> 18 9 5 ,
  16 20 2 -> 18 9 2 ,
  16 20 9 -> 18 9 9 ,
  17 7 -> 20 5 ,
  17 8 -> 20 2 ,
  17 13 -> 20 9 }


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

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

After renaming modulo { 5->0, 1->1, 2->2, 6->3, 3->4, 7->5, 8->6, 9->7, 10->8, 11->9, 12->10, 13->11, 14->12, 15->13, 16->14, 17->15, 18->16, 0->17, 19->18, 20->19 }, 
it remains to prove termination of the 34-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  0 1 7 8 -> 7 0 1 8 ,
  9 1 7 0 -> 10 0 1 0 ,
  9 1 7 2 -> 10 0 1 2 ,
  9 1 7 7 -> 10 0 1 7 ,
  5 1 7 0 -> 11 0 1 0 ,
  5 1 7 2 -> 11 0 1 2 ,
  5 1 7 7 -> 11 0 1 7 ,
  12 10 0 -> 13 14 15 5 ,
  12 10 2 -> 13 14 15 6 ,
  12 10 7 -> 13 14 15 11 ,
  13 16 -> 12 9 17 1 ,
  13 14 -> 12 9 17 18 ,
  18 15 5 -> 18 19 0 ,
  18 15 6 -> 18 19 2 ,
  18 15 11 -> 18 19 7 ,
  14 15 5 -> 14 19 0 ,
  14 15 6 -> 14 19 2 ,
  14 15 11 -> 14 19 7 ,
  18 19 0 -> 1 7 0 ,
  18 19 2 -> 1 7 2 ,
  18 19 7 -> 1 7 7 ,
  14 19 0 -> 16 7 0 ,
  14 19 2 -> 16 7 2 ,
  14 19 7 -> 16 7 7 ,
  15 5 -> 19 0 ,
  15 6 -> 19 2 ,
  15 11 -> 19 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19 }, 
it remains to prove termination of the 33-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  0 1 7 8 -> 7 0 1 8 ,
  9 1 7 2 -> 10 0 1 2 ,
  9 1 7 7 -> 10 0 1 7 ,
  5 1 7 0 -> 11 0 1 0 ,
  5 1 7 2 -> 11 0 1 2 ,
  5 1 7 7 -> 11 0 1 7 ,
  12 10 0 -> 13 14 15 5 ,
  12 10 2 -> 13 14 15 6 ,
  12 10 7 -> 13 14 15 11 ,
  13 16 -> 12 9 17 1 ,
  13 14 -> 12 9 17 18 ,
  18 15 5 -> 18 19 0 ,
  18 15 6 -> 18 19 2 ,
  18 15 11 -> 18 19 7 ,
  14 15 5 -> 14 19 0 ,
  14 15 6 -> 14 19 2 ,
  14 15 11 -> 14 19 7 ,
  18 19 0 -> 1 7 0 ,
  18 19 2 -> 1 7 2 ,
  18 19 7 -> 1 7 7 ,
  14 19 0 -> 16 7 0 ,
  14 19 2 -> 16 7 2 ,
  14 19 7 -> 16 7 7 ,
  15 5 -> 19 0 ,
  15 6 -> 19 2 ,
  15 11 -> 19 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 8:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18 }, 
it remains to prove termination of the 32-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  8 1 7 2 -> 9 0 1 2 ,
  8 1 7 7 -> 9 0 1 7 ,
  5 1 7 0 -> 10 0 1 0 ,
  5 1 7 2 -> 10 0 1 2 ,
  5 1 7 7 -> 10 0 1 7 ,
  11 9 0 -> 12 13 14 5 ,
  11 9 2 -> 12 13 14 6 ,
  11 9 7 -> 12 13 14 10 ,
  12 15 -> 11 8 16 1 ,
  12 13 -> 11 8 16 17 ,
  17 14 5 -> 17 18 0 ,
  17 14 6 -> 17 18 2 ,
  17 14 10 -> 17 18 7 ,
  13 14 5 -> 13 18 0 ,
  13 14 6 -> 13 18 2 ,
  13 14 10 -> 13 18 7 ,
  17 18 0 -> 1 7 0 ,
  17 18 2 -> 1 7 2 ,
  17 18 7 -> 1 7 7 ,
  13 18 0 -> 15 7 0 ,
  13 18 2 -> 15 7 2 ,
  13 18 7 -> 15 7 7 ,
  14 5 -> 18 0 ,
  14 6 -> 18 2 ,
  14 10 -> 18 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 31-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  8 1 7 2 -> 9 0 1 2 ,
  5 1 7 0 -> 10 0 1 0 ,
  5 1 7 2 -> 10 0 1 2 ,
  5 1 7 7 -> 10 0 1 7 ,
  11 9 0 -> 12 13 14 5 ,
  11 9 2 -> 12 13 14 6 ,
  11 9 7 -> 12 13 14 10 ,
  12 15 -> 11 8 16 1 ,
  12 13 -> 11 8 16 17 ,
  17 14 5 -> 17 18 0 ,
  17 14 6 -> 17 18 2 ,
  17 14 10 -> 17 18 7 ,
  13 14 5 -> 13 18 0 ,
  13 14 6 -> 13 18 2 ,
  13 14 10 -> 13 18 7 ,
  17 18 0 -> 1 7 0 ,
  17 18 2 -> 1 7 2 ,
  17 18 7 -> 1 7 7 ,
  13 18 0 -> 15 7 0 ,
  13 18 2 -> 15 7 2 ,
  13 18 7 -> 15 7 7 ,
  14 5 -> 18 0 ,
  14 6 -> 18 2 ,
  14 10 -> 18 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 30-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  8 1 7 2 -> 9 0 1 2 ,
  5 1 7 2 -> 10 0 1 2 ,
  5 1 7 7 -> 10 0 1 7 ,
  11 9 0 -> 12 13 14 5 ,
  11 9 2 -> 12 13 14 6 ,
  11 9 7 -> 12 13 14 10 ,
  12 15 -> 11 8 16 1 ,
  12 13 -> 11 8 16 17 ,
  17 14 5 -> 17 18 0 ,
  17 14 6 -> 17 18 2 ,
  17 14 10 -> 17 18 7 ,
  13 14 5 -> 13 18 0 ,
  13 14 6 -> 13 18 2 ,
  13 14 10 -> 13 18 7 ,
  17 18 0 -> 1 7 0 ,
  17 18 2 -> 1 7 2 ,
  17 18 7 -> 1 7 7 ,
  13 18 0 -> 15 7 0 ,
  13 18 2 -> 15 7 2 ,
  13 18 7 -> 15 7 7 ,
  14 5 -> 18 0 ,
  14 6 -> 18 2 ,
  14 10 -> 18 7 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 10->8, 11->9, 9->10, 12->11, 13->12, 14->13, 15->14, 8->15, 16->16, 17->17, 18->18 }, 
it remains to prove termination of the 29-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  5 1 7 2 -> 8 0 1 2 ,
  5 1 7 7 -> 8 0 1 7 ,
  9 10 0 -> 11 12 13 5 ,
  9 10 2 -> 11 12 13 6 ,
  9 10 7 -> 11 12 13 8 ,
  11 14 -> 9 15 16 1 ,
  11 12 -> 9 15 16 17 ,
  17 13 5 -> 17 18 0 ,
  17 13 6 -> 17 18 2 ,
  17 13 8 -> 17 18 7 ,
  12 13 5 -> 12 18 0 ,
  12 13 6 -> 12 18 2 ,
  12 13 8 -> 12 18 7 ,
  17 18 0 -> 1 7 0 ,
  17 18 2 -> 1 7 2 ,
  17 18 7 -> 1 7 7 ,
  12 18 0 -> 14 7 0 ,
  12 18 2 -> 14 7 2 ,
  12 18 7 -> 14 7 7 ,
  13 5 -> 18 0 ,
  13 6 -> 18 2 ,
  13 8 -> 18 7 }


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 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 1 |
| 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, 7->7, 8->8, 11->9, 14->10, 9->11, 15->12, 16->13, 12->14, 17->15, 13->16, 18->17 }, 
it remains to prove termination of the 26-rule system
{ 0 1 2 3 -> 2 3 ,
  0 1 2 4 -> 2 4 ,
  5 1 2 3 -> 6 3 ,
  5 1 2 4 -> 6 4 ,
  0 1 7 0 -> 7 0 1 0 ,
  0 1 7 2 -> 7 0 1 2 ,
  0 1 7 7 -> 7 0 1 7 ,
  5 1 7 2 -> 8 0 1 2 ,
  5 1 7 7 -> 8 0 1 7 ,
  9 10 -> 11 12 13 1 ,
  9 14 -> 11 12 13 15 ,
  15 16 5 -> 15 17 0 ,
  15 16 6 -> 15 17 2 ,
  15 16 8 -> 15 17 7 ,
  14 16 5 -> 14 17 0 ,
  14 16 6 -> 14 17 2 ,
  14 16 8 -> 14 17 7 ,
  15 17 0 -> 1 7 0 ,
  15 17 2 -> 1 7 2 ,
  15 17 7 -> 1 7 7 ,
  14 17 0 -> 10 7 0 ,
  14 17 2 -> 10 7 2 ,
  14 17 7 -> 10 7 7 ,
  16 5 -> 17 0 ,
  16 6 -> 17 2 ,
  16 8 -> 17 7 }


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

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


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

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


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 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

0 is interpreted by
 /         \
| 1 0 1 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 1 0 0 |
| 0 1 0 0 0 |
 \         /
1 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 1 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
 \         /
2 is interpreted by
 /         \
| 1 0 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 1 |
| 0 1 0 0 0 |
 \         /

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

The system is trivially terminating.