YES

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


The system was reversed.

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (1,0)->3, (1,1)->4, (1,2)->5, (2,0)->6, (2,1)->7, (2,2)->8, (3,0)->9, (3,1)->10, (3,2)->11, (2,4)->12 },
it remains to prove termination of the 40-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 4 ,
  3 2 -> 5 ,
  6 0 -> 6 ,
  6 1 -> 7 ,
  6 2 -> 8 ,
  9 0 -> 9 ,
  9 1 -> 10 ,
  9 2 -> 11 ,
  1 3 0 -> 0 2 6 ,
  1 3 1 -> 0 2 7 ,
  1 3 2 -> 0 2 8 ,
  4 3 0 -> 3 2 6 ,
  4 3 1 -> 3 2 7 ,
  4 3 2 -> 3 2 8 ,
  7 3 0 -> 6 2 6 ,
  7 3 1 -> 6 2 7 ,
  7 3 2 -> 6 2 8 ,
  10 3 0 -> 9 2 6 ,
  10 3 1 -> 9 2 7 ,
  10 3 2 -> 9 2 8 ,
  2 8 6 -> 0 1 5 7 5 6 ,
  2 8 7 -> 0 1 5 7 5 7 ,
  2 8 8 -> 0 1 5 7 5 8 ,
  2 8 12 -> 0 1 5 7 5 12 ,
  5 8 6 -> 3 1 5 7 5 6 ,
  5 8 7 -> 3 1 5 7 5 7 ,
  5 8 8 -> 3 1 5 7 5 8 ,
  5 8 12 -> 3 1 5 7 5 12 ,
  8 8 6 -> 6 1 5 7 5 6 ,
  8 8 7 -> 6 1 5 7 5 7 ,
  8 8 8 -> 6 1 5 7 5 8 ,
  8 8 12 -> 6 1 5 7 5 12 ,
  11 8 6 -> 9 1 5 7 5 6 ,
  11 8 7 -> 9 1 5 7 5 7 ,
  11 8 8 -> 9 1 5 7 5 8 ,
  11 8 12 -> 9 1 5 7 5 12 }


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

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

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


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

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

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


Applying the dependency pairs transformation.

After renaming modulo { (2,true)->0, (0,false)->1, (3,false)->2, (4,true)->3, (5,true)->4, (6,true)->5, (8,true)->6, (9,true)->7, (3,true)->8, (2,false)->9, (0,true)->10, (1,false)->11, (5,false)->12, (6,false)->13, (7,false)->14, (10,true)->15, (10,false)->16, (11,false)->17, (4,false)->18, (8,false)->19, (9,false)->20 },
it remains to prove termination of the 72-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  6 2 -> 7 ,
  8 9 1 -> 10 11 12 ,
  8 9 1 -> 4 ,
  8 9 2 -> 10 11 13 ,
  8 9 2 -> 5 ,
  8 9 11 -> 10 11 14 ,
  3 9 1 -> 0 11 12 ,
  3 9 1 -> 4 ,
  3 9 2 -> 0 11 13 ,
  3 9 2 -> 5 ,
  3 9 11 -> 0 11 14 ,
  5 9 1 -> 4 11 12 ,
  5 9 1 -> 4 ,
  5 9 2 -> 4 11 13 ,
  5 9 2 -> 5 ,
  5 9 11 -> 4 11 14 ,
  7 9 1 -> 6 11 12 ,
  7 9 1 -> 4 ,
  7 9 2 -> 6 11 13 ,
  7 9 2 -> 5 ,
  7 9 11 -> 6 11 14 ,
  15 14 12 -> 0 2 16 13 16 12 ,
  15 14 12 -> 8 16 13 16 12 ,
  15 14 12 -> 15 13 16 12 ,
  15 14 12 -> 5 16 12 ,
  15 14 12 -> 15 12 ,
  15 14 12 -> 4 ,
  15 14 13 -> 0 2 16 13 16 13 ,
  15 14 13 -> 8 16 13 16 13 ,
  15 14 13 -> 15 13 16 13 ,
  15 14 13 -> 5 16 13 ,
  15 14 13 -> 15 13 ,
  15 14 13 -> 5 ,
  15 14 14 -> 0 2 16 13 16 14 ,
  15 14 14 -> 8 16 13 16 14 ,
  15 14 14 -> 15 13 16 14 ,
  15 14 14 -> 5 16 14 ,
  15 14 14 -> 15 14 ,
  15 14 17 -> 0 2 16 13 16 17 ,
  15 14 17 -> 8 16 13 16 17 ,
  15 14 17 -> 15 13 16 17 ,
  15 14 17 -> 5 16 17 ,
  15 14 17 -> 15 17 ,
  1 11 ->= 11 ,
  9 1 ->= 9 ,
  9 2 ->= 18 ,
  12 1 ->= 12 ,
  12 2 ->= 13 ,
  12 11 ->= 14 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  2 9 1 ->= 1 11 12 ,
  2 9 2 ->= 1 11 13 ,
  2 9 11 ->= 1 11 14 ,
  18 9 1 ->= 9 11 12 ,
  18 9 2 ->= 9 11 13 ,
  18 9 11 ->= 9 11 14 ,
  13 9 1 ->= 12 11 12 ,
  13 9 2 ->= 12 11 13 ,
  13 9 11 ->= 12 11 14 ,
  20 9 1 ->= 19 11 12 ,
  20 9 2 ->= 19 11 13 ,
  20 9 11 ->= 19 11 14 ,
  16 14 12 ->= 9 2 16 13 16 12 ,
  16 14 13 ->= 9 2 16 13 16 13 ,
  16 14 14 ->= 9 2 16 13 16 14 ,
  16 14 17 ->= 9 2 16 13 16 17 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20 }, 
it remains to prove termination of the 58-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  6 2 -> 7 ,
  8 9 1 -> 10 11 12 ,
  8 9 1 -> 4 ,
  8 9 2 -> 10 11 13 ,
  8 9 2 -> 5 ,
  8 9 11 -> 10 11 14 ,
  3 9 1 -> 0 11 12 ,
  3 9 1 -> 4 ,
  3 9 2 -> 0 11 13 ,
  3 9 2 -> 5 ,
  3 9 11 -> 0 11 14 ,
  5 9 1 -> 4 11 12 ,
  5 9 1 -> 4 ,
  5 9 2 -> 4 11 13 ,
  5 9 2 -> 5 ,
  5 9 11 -> 4 11 14 ,
  7 9 1 -> 6 11 12 ,
  7 9 1 -> 4 ,
  7 9 2 -> 6 11 13 ,
  7 9 2 -> 5 ,
  7 9 11 -> 6 11 14 ,
  15 14 12 -> 15 13 16 12 ,
  15 14 12 -> 15 12 ,
  15 14 13 -> 15 13 16 13 ,
  15 14 13 -> 15 13 ,
  15 14 14 -> 15 13 16 14 ,
  15 14 14 -> 15 14 ,
  15 14 17 -> 15 13 16 17 ,
  15 14 17 -> 15 17 ,
  1 11 ->= 11 ,
  9 1 ->= 9 ,
  9 2 ->= 18 ,
  12 1 ->= 12 ,
  12 2 ->= 13 ,
  12 11 ->= 14 ,
  19 1 ->= 19 ,
  19 2 ->= 20 ,
  2 9 1 ->= 1 11 12 ,
  2 9 2 ->= 1 11 13 ,
  2 9 11 ->= 1 11 14 ,
  18 9 1 ->= 9 11 12 ,
  18 9 2 ->= 9 11 13 ,
  18 9 11 ->= 9 11 14 ,
  13 9 1 ->= 12 11 12 ,
  13 9 2 ->= 12 11 13 ,
  13 9 11 ->= 12 11 14 ,
  20 9 1 ->= 19 11 12 ,
  20 9 2 ->= 19 11 13 ,
  20 9 11 ->= 19 11 14 ,
  16 14 12 ->= 9 2 16 13 16 12 ,
  16 14 13 ->= 9 2 16 13 16 13 ,
  16 14 14 ->= 9 2 16 13 16 14 ,
  16 14 17 ->= 9 2 16 13 16 17 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8, 11->9, 12->10, 13->11, 14->12, 15->13, 16->14, 17->15, 18->16, 19->17, 20->18 }, 
it remains to prove termination of the 53-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  4 2 -> 5 ,
  6 1 -> 6 ,
  6 2 -> 7 ,
  3 8 1 -> 0 9 10 ,
  3 8 1 -> 4 ,
  3 8 2 -> 0 9 11 ,
  3 8 2 -> 5 ,
  3 8 9 -> 0 9 12 ,
  5 8 1 -> 4 9 10 ,
  5 8 1 -> 4 ,
  5 8 2 -> 4 9 11 ,
  5 8 2 -> 5 ,
  5 8 9 -> 4 9 12 ,
  7 8 1 -> 6 9 10 ,
  7 8 1 -> 4 ,
  7 8 2 -> 6 9 11 ,
  7 8 2 -> 5 ,
  7 8 9 -> 6 9 12 ,
  13 12 10 -> 13 11 14 10 ,
  13 12 10 -> 13 10 ,
  13 12 11 -> 13 11 14 11 ,
  13 12 11 -> 13 11 ,
  13 12 12 -> 13 11 14 12 ,
  13 12 12 -> 13 12 ,
  13 12 15 -> 13 11 14 15 ,
  13 12 15 -> 13 15 ,
  1 9 ->= 9 ,
  8 1 ->= 8 ,
  8 2 ->= 16 ,
  10 1 ->= 10 ,
  10 2 ->= 11 ,
  10 9 ->= 12 ,
  17 1 ->= 17 ,
  17 2 ->= 18 ,
  2 8 1 ->= 1 9 10 ,
  2 8 2 ->= 1 9 11 ,
  2 8 9 ->= 1 9 12 ,
  16 8 1 ->= 8 9 10 ,
  16 8 2 ->= 8 9 11 ,
  16 8 9 ->= 8 9 12 ,
  11 8 1 ->= 10 9 10 ,
  11 8 2 ->= 10 9 11 ,
  11 8 9 ->= 10 9 12 ,
  18 8 1 ->= 17 9 10 ,
  18 8 2 ->= 17 9 11 ,
  18 8 9 ->= 17 9 12 ,
  14 12 10 ->= 8 2 14 11 14 10 ,
  14 12 11 ->= 8 2 14 11 14 11 ,
  14 12 12 ->= 8 2 14 11 14 12 ,
  14 12 15 ->= 8 2 14 11 14 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 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 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 |
 \   /

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


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

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

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16 }, 
it remains to prove termination of the 35-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  2 3 -> 4 ,
  5 1 -> 5 ,
  5 3 -> 6 ,
  4 7 1 -> 2 8 9 ,
  4 7 3 -> 2 8 10 ,
  4 7 8 -> 2 8 11 ,
  6 7 1 -> 5 8 9 ,
  6 7 3 -> 5 8 10 ,
  6 7 8 -> 5 8 11 ,
  1 8 ->= 8 ,
  7 1 ->= 7 ,
  7 3 ->= 12 ,
  9 1 ->= 9 ,
  9 3 ->= 10 ,
  9 8 ->= 11 ,
  13 1 ->= 13 ,
  13 3 ->= 14 ,
  3 7 1 ->= 1 8 9 ,
  3 7 3 ->= 1 8 10 ,
  3 7 8 ->= 1 8 11 ,
  12 7 1 ->= 7 8 9 ,
  12 7 3 ->= 7 8 10 ,
  12 7 8 ->= 7 8 11 ,
  10 7 1 ->= 9 8 9 ,
  10 7 3 ->= 9 8 10 ,
  10 7 8 ->= 9 8 11 ,
  14 7 1 ->= 13 8 9 ,
  14 7 3 ->= 13 8 10 ,
  14 7 8 ->= 13 8 11 ,
  15 11 9 ->= 7 3 15 10 15 9 ,
  15 11 10 ->= 7 3 15 10 15 10 ,
  15 11 11 ->= 7 3 15 10 15 11 ,
  15 11 16 ->= 7 3 15 10 15 16 }


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

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

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


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

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

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


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

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

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 6->4, 5->5, 8->6, 11->7, 7->8, 9->9, 10->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 27-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 6 ->= 7 ,
  8 1 ->= 8 ,
  8 6 ->= 9 ,
  8 4 ->= 10 ,
  11 1 ->= 11 ,
  11 6 ->= 12 ,
  6 5 1 ->= 1 4 8 ,
  6 5 6 ->= 1 4 9 ,
  6 5 4 ->= 1 4 10 ,
  7 5 1 ->= 5 4 8 ,
  7 5 6 ->= 5 4 9 ,
  7 5 4 ->= 5 4 10 ,
  9 5 1 ->= 8 4 8 ,
  9 5 6 ->= 8 4 9 ,
  9 5 4 ->= 8 4 10 ,
  12 5 1 ->= 11 4 8 ,
  12 5 6 ->= 11 4 9 ,
  12 5 4 ->= 11 4 10 ,
  13 10 8 ->= 5 6 13 9 13 8 ,
  13 10 9 ->= 5 6 13 9 13 9 ,
  13 10 10 ->= 5 6 13 9 13 10 ,
  13 10 14 ->= 5 6 13 9 13 14 }


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

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

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


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

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

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


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

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

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 11->10, 12->11, 13->12 }, 
it remains to prove termination of the 21-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 6 ->= 7 ,
  8 1 ->= 8 ,
  8 4 ->= 9 ,
  6 5 1 ->= 1 4 8 ,
  6 5 6 ->= 1 4 10 ,
  6 5 4 ->= 1 4 9 ,
  7 5 1 ->= 5 4 8 ,
  7 5 6 ->= 5 4 10 ,
  7 5 4 ->= 5 4 9 ,
  10 5 1 ->= 8 4 8 ,
  10 5 6 ->= 8 4 10 ,
  10 5 4 ->= 8 4 9 ,
  11 9 8 ->= 5 6 11 10 11 8 ,
  11 9 10 ->= 5 6 11 10 11 10 ,
  11 9 9 ->= 5 6 11 10 11 9 ,
  11 9 12 ->= 5 6 11 10 11 12 }


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

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

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


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

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 19-rule system
{ 0 1 -> 0 ,
  1 2 ->= 2 ,
  3 1 ->= 3 ,
  3 4 ->= 5 ,
  6 1 ->= 6 ,
  6 2 ->= 7 ,
  4 3 1 ->= 1 2 6 ,
  4 3 4 ->= 1 2 8 ,
  4 3 2 ->= 1 2 7 ,
  5 3 1 ->= 3 2 6 ,
  5 3 4 ->= 3 2 8 ,
  5 3 2 ->= 3 2 7 ,
  8 3 1 ->= 6 2 6 ,
  8 3 4 ->= 6 2 8 ,
  8 3 2 ->= 6 2 7 ,
  9 7 6 ->= 3 4 9 8 9 6 ,
  9 7 8 ->= 3 4 9 8 9 8 ,
  9 7 7 ->= 3 4 9 8 9 7 ,
  9 7 10 ->= 3 4 9 8 9 10 }


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

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

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

The system is trivially terminating.