YES

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


The system was reversed.

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


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

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

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


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

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

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 2 3 -> 4 5 3 6 7 0 1 ,
  0 1 2 5 -> 4 5 3 6 7 0 4 ,
  7 1 2 3 -> 2 5 3 6 7 0 1 ,
  7 1 2 5 -> 2 5 3 6 7 0 4 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 9 -> 9 ,
  10 5 -> 10 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 6 -> 6 ,
  6 2 -> 2 ,
  6 11 -> 11 ,
  3 6 -> 3 ,
  12 6 -> 12 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 13 -> 13 ,
  7 0 -> 7 ,
  7 4 -> 2 ,
  8 0 -> 8 ,
  14 0 -> 14 }


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

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
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 25-rule system
{ 0 1 2 3 -> 4 5 3 6 7 0 1 ,
  0 1 2 5 -> 4 5 3 6 7 0 4 ,
  7 1 2 3 -> 2 5 3 6 7 0 1 ,
  7 1 2 5 -> 2 5 3 6 7 0 4 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 9 -> 9 ,
  10 5 -> 10 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 2 -> 2 ,
  6 11 -> 11 ,
  3 6 -> 3 ,
  12 6 -> 12 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 13 -> 13 ,
  7 0 -> 7 ,
  7 4 -> 2 ,
  8 0 -> 8 ,
  14 0 -> 14 }


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

0 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 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 24-rule system
{ 0 1 2 3 -> 4 5 3 6 7 0 1 ,
  0 1 2 5 -> 4 5 3 6 7 0 4 ,
  7 1 2 3 -> 2 5 3 6 7 0 1 ,
  7 1 2 5 -> 2 5 3 6 7 0 4 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 9 -> 9 ,
  10 5 -> 10 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 2 -> 2 ,
  6 11 -> 11 ,
  3 6 -> 3 ,
  12 6 -> 12 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 13 -> 13 ,
  7 0 -> 7 ,
  7 4 -> 2 ,
  8 0 -> 8 ,
  14 0 -> 14 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,false)->2, (3,false)->3, (4,true)->4, (5,false)->5, (6,false)->6, (7,false)->7, (0,false)->8, (5,true)->9, (3,true)->10, (6,true)->11, (7,true)->12, (1,true)->13, (4,false)->14, (2,true)->15, (8,false)->16, (8,true)->17, (10,true)->18, (12,true)->19, (14,true)->20, (9,false)->21, (10,false)->22, (11,false)->23, (12,false)->24, (13,false)->25, (14,false)->26 },
it remains to prove termination of the 69-rule system
{ 0 1 2 3 -> 4 5 3 6 7 8 1 ,
  0 1 2 3 -> 9 3 6 7 8 1 ,
  0 1 2 3 -> 10 6 7 8 1 ,
  0 1 2 3 -> 11 7 8 1 ,
  0 1 2 3 -> 12 8 1 ,
  0 1 2 3 -> 0 1 ,
  0 1 2 3 -> 13 ,
  0 1 2 5 -> 4 5 3 6 7 8 14 ,
  0 1 2 5 -> 9 3 6 7 8 14 ,
  0 1 2 5 -> 10 6 7 8 14 ,
  0 1 2 5 -> 11 7 8 14 ,
  0 1 2 5 -> 12 8 14 ,
  0 1 2 5 -> 0 14 ,
  0 1 2 5 -> 4 ,
  12 1 2 3 -> 15 5 3 6 7 8 1 ,
  12 1 2 3 -> 9 3 6 7 8 1 ,
  12 1 2 3 -> 10 6 7 8 1 ,
  12 1 2 3 -> 11 7 8 1 ,
  12 1 2 3 -> 12 8 1 ,
  12 1 2 3 -> 0 1 ,
  12 1 2 3 -> 13 ,
  12 1 2 5 -> 15 5 3 6 7 8 14 ,
  12 1 2 5 -> 9 3 6 7 8 14 ,
  12 1 2 5 -> 10 6 7 8 14 ,
  12 1 2 5 -> 11 7 8 14 ,
  12 1 2 5 -> 12 8 14 ,
  12 1 2 5 -> 0 14 ,
  12 1 2 5 -> 4 ,
  4 3 -> 13 ,
  4 5 -> 4 ,
  15 5 -> 15 ,
  9 16 -> 17 ,
  9 3 -> 10 ,
  18 5 -> 18 ,
  13 6 -> 13 ,
  11 7 -> 12 ,
  11 2 -> 15 ,
  10 6 -> 10 ,
  19 6 -> 19 ,
  0 1 -> 13 ,
  0 14 -> 4 ,
  12 8 -> 12 ,
  12 14 -> 15 ,
  17 8 -> 17 ,
  20 8 -> 20 ,
  8 1 2 3 ->= 14 5 3 6 7 8 1 ,
  8 1 2 5 ->= 14 5 3 6 7 8 14 ,
  7 1 2 3 ->= 2 5 3 6 7 8 1 ,
  7 1 2 5 ->= 2 5 3 6 7 8 14 ,
  14 3 ->= 1 ,
  14 5 ->= 14 ,
  2 5 ->= 2 ,
  5 16 ->= 16 ,
  5 3 ->= 3 ,
  5 21 ->= 21 ,
  22 5 ->= 22 ,
  1 6 ->= 1 ,
  6 7 ->= 7 ,
  6 2 ->= 2 ,
  6 23 ->= 23 ,
  3 6 ->= 3 ,
  24 6 ->= 24 ,
  8 1 ->= 1 ,
  8 14 ->= 14 ,
  8 25 ->= 25 ,
  7 8 ->= 7 ,
  7 14 ->= 2 ,
  16 8 ->= 16 ,
  26 8 ->= 26 }


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
19 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
20 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
21 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
22 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
23 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
24 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
25 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
26 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, 18->16, 19->17, 17->18, 20->19, 16->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26 }, 
it remains to prove termination of the 68-rule system
{ 0 1 2 3 -> 4 5 3 6 7 8 1 ,
  0 1 2 3 -> 9 3 6 7 8 1 ,
  0 1 2 3 -> 10 6 7 8 1 ,
  0 1 2 3 -> 11 7 8 1 ,
  0 1 2 3 -> 12 8 1 ,
  0 1 2 3 -> 0 1 ,
  0 1 2 3 -> 13 ,
  0 1 2 5 -> 4 5 3 6 7 8 14 ,
  0 1 2 5 -> 9 3 6 7 8 14 ,
  0 1 2 5 -> 10 6 7 8 14 ,
  0 1 2 5 -> 11 7 8 14 ,
  0 1 2 5 -> 12 8 14 ,
  0 1 2 5 -> 0 14 ,
  0 1 2 5 -> 4 ,
  12 1 2 3 -> 15 5 3 6 7 8 1 ,
  12 1 2 3 -> 9 3 6 7 8 1 ,
  12 1 2 3 -> 10 6 7 8 1 ,
  12 1 2 3 -> 11 7 8 1 ,
  12 1 2 3 -> 12 8 1 ,
  12 1 2 3 -> 0 1 ,
  12 1 2 3 -> 13 ,
  12 1 2 5 -> 15 5 3 6 7 8 14 ,
  12 1 2 5 -> 9 3 6 7 8 14 ,
  12 1 2 5 -> 10 6 7 8 14 ,
  12 1 2 5 -> 11 7 8 14 ,
  12 1 2 5 -> 12 8 14 ,
  12 1 2 5 -> 0 14 ,
  12 1 2 5 -> 4 ,
  4 3 -> 13 ,
  4 5 -> 4 ,
  15 5 -> 15 ,
  9 3 -> 10 ,
  16 5 -> 16 ,
  13 6 -> 13 ,
  11 7 -> 12 ,
  11 2 -> 15 ,
  10 6 -> 10 ,
  17 6 -> 17 ,
  0 1 -> 13 ,
  0 14 -> 4 ,
  12 8 -> 12 ,
  12 14 -> 15 ,
  18 8 -> 18 ,
  19 8 -> 19 ,
  8 1 2 3 ->= 14 5 3 6 7 8 1 ,
  8 1 2 5 ->= 14 5 3 6 7 8 14 ,
  7 1 2 3 ->= 2 5 3 6 7 8 1 ,
  7 1 2 5 ->= 2 5 3 6 7 8 14 ,
  14 3 ->= 1 ,
  14 5 ->= 14 ,
  2 5 ->= 2 ,
  5 20 ->= 20 ,
  5 3 ->= 3 ,
  5 21 ->= 21 ,
  22 5 ->= 22 ,
  1 6 ->= 1 ,
  6 7 ->= 7 ,
  6 2 ->= 2 ,
  6 23 ->= 23 ,
  3 6 ->= 3 ,
  24 6 ->= 24 ,
  8 1 ->= 1 ,
  8 14 ->= 14 ,
  8 25 ->= 25 ,
  7 8 ->= 7 ,
  7 14 ->= 2 ,
  20 8 ->= 20 ,
  26 8 ->= 26 }


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

After renaming modulo { 4->0, 5->1, 15->2, 16->3, 13->4, 6->5, 10->6, 17->7, 12->8, 8->9, 18->10, 19->11, 1->12, 2->13, 3->14, 14->15, 7->16, 20->17, 21->18, 22->19, 23->20, 24->21, 25->22, 26->23 }, 
it remains to prove termination of the 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 -> 4 ,
  6 5 -> 6 ,
  7 5 -> 7 ,
  8 9 -> 8 ,
  10 9 -> 10 ,
  11 9 -> 11 ,
  9 12 13 14 ->= 15 1 14 5 16 9 12 ,
  9 12 13 1 ->= 15 1 14 5 16 9 15 ,
  16 12 13 14 ->= 13 1 14 5 16 9 12 ,
  16 12 13 1 ->= 13 1 14 5 16 9 15 ,
  15 14 ->= 12 ,
  15 1 ->= 15 ,
  13 1 ->= 13 ,
  1 17 ->= 17 ,
  1 14 ->= 14 ,
  1 18 ->= 18 ,
  19 1 ->= 19 ,
  12 5 ->= 12 ,
  5 16 ->= 16 ,
  5 13 ->= 13 ,
  5 20 ->= 20 ,
  14 5 ->= 14 ,
  21 5 ->= 21 ,
  9 12 ->= 12 ,
  9 15 ->= 15 ,
  9 22 ->= 22 ,
  16 9 ->= 16 ,
  16 15 ->= 13 ,
  17 9 ->= 17 ,
  23 9 ->= 23 }


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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 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 32-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  7 8 -> 7 ,
  9 8 -> 9 ,
  10 8 -> 10 ,
  8 11 12 13 ->= 14 1 13 4 15 8 11 ,
  8 11 12 1 ->= 14 1 13 4 15 8 14 ,
  15 11 12 13 ->= 12 1 13 4 15 8 11 ,
  15 11 12 1 ->= 12 1 13 4 15 8 14 ,
  14 13 ->= 11 ,
  14 1 ->= 14 ,
  12 1 ->= 12 ,
  1 16 ->= 16 ,
  1 13 ->= 13 ,
  1 17 ->= 17 ,
  18 1 ->= 18 ,
  11 4 ->= 11 ,
  4 15 ->= 15 ,
  4 12 ->= 12 ,
  4 19 ->= 19 ,
  13 4 ->= 13 ,
  20 4 ->= 20 ,
  8 11 ->= 11 ,
  8 14 ->= 14 ,
  8 21 ->= 21 ,
  15 8 ->= 15 ,
  15 14 ->= 12 ,
  16 8 ->= 16 ,
  22 8 ->= 22 }


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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20, 22->21 }, 
it remains to prove termination of the 31-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 ,
  4 3 -> 4 ,
  5 3 -> 5 ,
  6 7 -> 6 ,
  8 7 -> 8 ,
  9 7 -> 9 ,
  7 10 11 12 ->= 13 1 12 3 14 7 10 ,
  7 10 11 1 ->= 13 1 12 3 14 7 13 ,
  14 10 11 12 ->= 11 1 12 3 14 7 10 ,
  14 10 11 1 ->= 11 1 12 3 14 7 13 ,
  13 12 ->= 10 ,
  13 1 ->= 13 ,
  11 1 ->= 11 ,
  1 15 ->= 15 ,
  1 12 ->= 12 ,
  1 16 ->= 16 ,
  17 1 ->= 17 ,
  10 3 ->= 10 ,
  3 14 ->= 14 ,
  3 11 ->= 11 ,
  3 18 ->= 18 ,
  12 3 ->= 12 ,
  19 3 ->= 19 ,
  7 10 ->= 10 ,
  7 13 ->= 13 ,
  7 20 ->= 20 ,
  14 7 ->= 14 ,
  14 13 ->= 11 ,
  15 7 ->= 15 ,
  21 7 ->= 21 }


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

After renaming modulo { 2->0, 3->1, 4->2, 5->3, 6->4, 7->5, 8->6, 9->7, 10->8, 11->9, 12->10, 13->11, 1->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20 }, 
it remains to prove termination of the 30-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 -> 4 ,
  6 5 -> 6 ,
  7 5 -> 7 ,
  5 8 9 10 ->= 11 12 10 1 13 5 8 ,
  5 8 9 12 ->= 11 12 10 1 13 5 11 ,
  13 8 9 10 ->= 9 12 10 1 13 5 8 ,
  13 8 9 12 ->= 9 12 10 1 13 5 11 ,
  11 10 ->= 8 ,
  11 12 ->= 11 ,
  9 12 ->= 9 ,
  12 14 ->= 14 ,
  12 10 ->= 10 ,
  12 15 ->= 15 ,
  16 12 ->= 16 ,
  8 1 ->= 8 ,
  1 13 ->= 13 ,
  1 9 ->= 9 ,
  1 17 ->= 17 ,
  10 1 ->= 10 ,
  18 1 ->= 18 ,
  5 8 ->= 8 ,
  5 11 ->= 11 ,
  5 19 ->= 19 ,
  13 5 ->= 13 ,
  13 11 ->= 9 ,
  14 5 ->= 14 ,
  20 5 ->= 20 }


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

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19 }, 
it remains to prove termination of the 29-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  4 7 8 9 ->= 10 11 9 1 12 4 7 ,
  4 7 8 11 ->= 10 11 9 1 12 4 10 ,
  12 7 8 9 ->= 8 11 9 1 12 4 7 ,
  12 7 8 11 ->= 8 11 9 1 12 4 10 ,
  10 9 ->= 7 ,
  10 11 ->= 10 ,
  8 11 ->= 8 ,
  11 13 ->= 13 ,
  11 9 ->= 9 ,
  11 14 ->= 14 ,
  15 11 ->= 15 ,
  7 1 ->= 7 ,
  1 12 ->= 12 ,
  1 8 ->= 8 ,
  1 16 ->= 16 ,
  9 1 ->= 9 ,
  17 1 ->= 17 ,
  4 7 ->= 7 ,
  4 10 ->= 10 ,
  4 18 ->= 18 ,
  12 4 ->= 12 ,
  12 10 ->= 8 ,
  13 4 ->= 13 ,
  19 4 ->= 19 }


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

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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18 }, 
it remains to prove termination of the 28-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 ,
  4 3 -> 4 ,
  5 3 -> 5 ,
  3 6 7 8 ->= 9 10 8 1 11 3 6 ,
  3 6 7 10 ->= 9 10 8 1 11 3 9 ,
  11 6 7 8 ->= 7 10 8 1 11 3 6 ,
  11 6 7 10 ->= 7 10 8 1 11 3 9 ,
  9 8 ->= 6 ,
  9 10 ->= 9 ,
  7 10 ->= 7 ,
  10 12 ->= 12 ,
  10 8 ->= 8 ,
  10 13 ->= 13 ,
  14 10 ->= 14 ,
  6 1 ->= 6 ,
  1 11 ->= 11 ,
  1 7 ->= 7 ,
  1 15 ->= 15 ,
  8 1 ->= 8 ,
  16 1 ->= 16 ,
  3 6 ->= 6 ,
  3 9 ->= 9 ,
  3 17 ->= 17 ,
  11 3 ->= 11 ,
  11 9 ->= 7 ,
  12 3 ->= 12 ,
  18 3 ->= 18 }


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

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

After renaming modulo { 2->0, 3->1, 4->2, 5->3, 6->4, 7->5, 8->6, 9->7, 10->8, 1->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17 }, 
it remains to prove termination of the 27-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 5 6 ->= 7 8 6 9 10 1 4 ,
  1 4 5 8 ->= 7 8 6 9 10 1 7 ,
  10 4 5 6 ->= 5 8 6 9 10 1 4 ,
  10 4 5 8 ->= 5 8 6 9 10 1 7 ,
  7 6 ->= 4 ,
  7 8 ->= 7 ,
  5 8 ->= 5 ,
  8 11 ->= 11 ,
  8 6 ->= 6 ,
  8 12 ->= 12 ,
  13 8 ->= 13 ,
  4 9 ->= 4 ,
  9 10 ->= 10 ,
  9 5 ->= 5 ,
  9 14 ->= 14 ,
  6 9 ->= 6 ,
  15 9 ->= 15 ,
  1 4 ->= 4 ,
  1 7 ->= 7 ,
  1 16 ->= 16 ,
  10 1 ->= 10 ,
  10 7 ->= 5 ,
  11 1 ->= 11 ,
  17 1 ->= 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 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 |
 \     /
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 { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16 }, 
it remains to prove termination of the 26-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 3 4 5 ->= 6 7 5 8 9 1 3 ,
  1 3 4 7 ->= 6 7 5 8 9 1 6 ,
  9 3 4 5 ->= 4 7 5 8 9 1 3 ,
  9 3 4 7 ->= 4 7 5 8 9 1 6 ,
  6 5 ->= 3 ,
  6 7 ->= 6 ,
  4 7 ->= 4 ,
  7 10 ->= 10 ,
  7 5 ->= 5 ,
  7 11 ->= 11 ,
  12 7 ->= 12 ,
  3 8 ->= 3 ,
  8 9 ->= 9 ,
  8 4 ->= 4 ,
  8 13 ->= 13 ,
  5 8 ->= 5 ,
  14 8 ->= 14 ,
  1 3 ->= 3 ,
  1 6 ->= 6 ,
  1 15 ->= 15 ,
  9 1 ->= 9 ,
  9 6 ->= 4 ,
  10 1 ->= 10 ,
  16 1 ->= 16 }


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

0 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 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 { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15 }, 
it remains to prove termination of the 25-rule system
{ 0 1 -> 0 ,
  1 2 3 4 ->= 5 6 4 7 8 1 2 ,
  1 2 3 6 ->= 5 6 4 7 8 1 5 ,
  8 2 3 4 ->= 3 6 4 7 8 1 2 ,
  8 2 3 6 ->= 3 6 4 7 8 1 5 ,
  5 4 ->= 2 ,
  5 6 ->= 5 ,
  3 6 ->= 3 ,
  6 9 ->= 9 ,
  6 4 ->= 4 ,
  6 10 ->= 10 ,
  11 6 ->= 11 ,
  2 7 ->= 2 ,
  7 8 ->= 8 ,
  7 3 ->= 3 ,
  7 12 ->= 12 ,
  4 7 ->= 4 ,
  13 7 ->= 13 ,
  1 2 ->= 2 ,
  1 5 ->= 5 ,
  1 14 ->= 14 ,
  8 1 ->= 8 ,
  8 5 ->= 3 ,
  9 1 ->= 9 ,
  15 1 ->= 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 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 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 { 1->0, 2->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 24-rule system
{ 0 1 2 3 ->= 4 5 3 6 7 0 1 ,
  0 1 2 5 ->= 4 5 3 6 7 0 4 ,
  7 1 2 3 ->= 2 5 3 6 7 0 1 ,
  7 1 2 5 ->= 2 5 3 6 7 0 4 ,
  4 3 ->= 1 ,
  4 5 ->= 4 ,
  2 5 ->= 2 ,
  5 8 ->= 8 ,
  5 3 ->= 3 ,
  5 9 ->= 9 ,
  10 5 ->= 10 ,
  1 6 ->= 1 ,
  6 7 ->= 7 ,
  6 2 ->= 2 ,
  6 11 ->= 11 ,
  3 6 ->= 3 ,
  12 6 ->= 12 ,
  0 1 ->= 1 ,
  0 4 ->= 4 ,
  0 13 ->= 13 ,
  7 0 ->= 7 ,
  7 4 ->= 2 ,
  8 0 ->= 8 ,
  14 0 ->= 14 }

The system is trivially terminating.