YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 0 -> 0 1 2 ,
  1 -> ,
  2 1 -> 1 0 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 },
it remains to prove termination of the 48-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 ,
  0 0 0 -> 0 1 5 6 ,
  0 0 1 -> 0 1 5 7 ,
  0 0 2 -> 0 1 5 8 ,
  3 0 0 -> 3 1 5 6 ,
  3 0 1 -> 3 1 5 7 ,
  3 0 2 -> 3 1 5 8 ,
  6 0 0 -> 6 1 5 6 ,
  6 0 1 -> 6 1 5 7 ,
  6 0 2 -> 6 1 5 8 ,
  9 0 0 -> 9 1 5 6 ,
  9 0 1 -> 9 1 5 7 ,
  9 0 2 -> 9 1 5 8 ,
  1 3 -> 0 ,
  1 4 -> 1 ,
  1 5 -> 2 ,
  4 3 -> 3 ,
  4 4 -> 4 ,
  4 5 -> 5 ,
  7 3 -> 6 ,
  7 4 -> 7 ,
  7 5 -> 8 ,
  10 3 -> 9 ,
  10 4 -> 10 ,
  10 5 -> 11 ,
  2 7 3 -> 1 3 2 6 ,
  2 7 4 -> 1 3 2 7 ,
  2 7 5 -> 1 3 2 8 ,
  5 7 3 -> 4 3 2 6 ,
  5 7 4 -> 4 3 2 7 ,
  5 7 5 -> 4 3 2 8 ,
  8 7 3 -> 7 3 2 6 ,
  8 7 4 -> 7 3 2 7 ,
  8 7 5 -> 7 3 2 8 ,
  11 7 3 -> 10 3 2 6 ,
  11 7 4 -> 10 3 2 7 ,
  11 7 5 -> 10 3 2 8 }


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 3 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 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 2 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (3,false)->1, (4,true)->2, (5,true)->3, (7,true)->4, (8,true)->5, (8,false)->6, (1,false)->7, (4,false)->8, (6,false)->9, (1,true)->10, (7,false)->11, (9,true)->12, (0,false)->13, (3,true)->14, (5,false)->15, (2,false)->16, (9,false)->17 },
it remains to prove termination of the 80-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  5 6 7 -> 5 7 8 9 ,
  5 6 7 -> 10 8 9 ,
  5 6 7 -> 2 9 ,
  5 6 1 -> 5 7 8 11 ,
  5 6 1 -> 10 8 11 ,
  5 6 1 -> 2 11 ,
  5 6 1 -> 4 ,
  0 6 7 -> 0 7 8 9 ,
  0 6 7 -> 10 8 9 ,
  0 6 7 -> 2 9 ,
  0 6 1 -> 0 7 8 11 ,
  0 6 1 -> 10 8 11 ,
  0 6 1 -> 2 11 ,
  0 6 1 -> 4 ,
  3 6 7 -> 3 7 8 9 ,
  3 6 7 -> 10 8 9 ,
  3 6 7 -> 2 9 ,
  3 6 1 -> 3 7 8 11 ,
  3 6 1 -> 10 8 11 ,
  3 6 1 -> 2 11 ,
  3 6 1 -> 4 ,
  12 6 7 -> 12 7 8 9 ,
  12 6 7 -> 10 8 9 ,
  12 6 7 -> 2 9 ,
  12 6 1 -> 12 7 8 11 ,
  12 6 1 -> 10 8 11 ,
  12 6 1 -> 2 11 ,
  12 6 1 -> 4 ,
  10 13 -> 5 ,
  14 9 13 -> 10 13 1 15 ,
  14 9 13 -> 0 1 15 ,
  14 9 13 -> 14 15 ,
  14 9 13 -> 3 ,
  14 9 16 -> 10 13 1 9 ,
  14 9 16 -> 0 1 9 ,
  14 9 16 -> 14 9 ,
  14 9 8 -> 10 13 1 11 ,
  14 9 8 -> 0 1 11 ,
  14 9 8 -> 14 11 ,
  14 9 8 -> 4 ,
  2 9 13 -> 0 1 15 ,
  2 9 13 -> 14 15 ,
  2 9 13 -> 3 ,
  2 9 16 -> 0 1 9 ,
  2 9 16 -> 14 9 ,
  2 9 8 -> 0 1 11 ,
  2 9 8 -> 14 11 ,
  2 9 8 -> 4 ,
  4 9 13 -> 0 1 15 ,
  4 9 13 -> 14 15 ,
  4 9 13 -> 3 ,
  4 9 16 -> 0 1 9 ,
  4 9 16 -> 14 9 ,
  4 9 8 -> 0 1 11 ,
  4 9 8 -> 14 11 ,
  4 9 8 -> 4 ,
  13 7 ->= 16 ,
  13 1 ->= 8 ,
  15 7 ->= 9 ,
  15 1 ->= 11 ,
  6 6 7 ->= 6 7 8 9 ,
  6 6 1 ->= 6 7 8 11 ,
  13 6 7 ->= 13 7 8 9 ,
  13 6 1 ->= 13 7 8 11 ,
  15 6 7 ->= 15 7 8 9 ,
  15 6 1 ->= 15 7 8 11 ,
  17 6 7 ->= 17 7 8 9 ,
  17 6 1 ->= 17 7 8 11 ,
  7 13 ->= 6 ,
  1 9 13 ->= 7 13 1 15 ,
  1 9 16 ->= 7 13 1 9 ,
  1 9 8 ->= 7 13 1 11 ,
  8 9 13 ->= 16 13 1 15 ,
  8 9 16 ->= 16 13 1 9 ,
  8 9 8 ->= 16 13 1 11 ,
  11 9 13 ->= 9 13 1 15 ,
  11 9 16 ->= 9 13 1 9 ,
  11 9 8 ->= 9 13 1 11 }


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 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 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, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 75-rule system
{ 0 1 -> 2 ,
  3 1 -> 4 ,
  5 6 7 -> 5 7 8 9 ,
  5 6 7 -> 10 8 9 ,
  5 6 7 -> 2 9 ,
  5 6 1 -> 5 7 8 11 ,
  5 6 1 -> 10 8 11 ,
  5 6 1 -> 2 11 ,
  5 6 1 -> 4 ,
  0 6 7 -> 0 7 8 9 ,
  0 6 7 -> 10 8 9 ,
  0 6 7 -> 2 9 ,
  0 6 1 -> 0 7 8 11 ,
  0 6 1 -> 10 8 11 ,
  0 6 1 -> 2 11 ,
  0 6 1 -> 4 ,
  3 6 7 -> 3 7 8 9 ,
  3 6 7 -> 10 8 9 ,
  3 6 7 -> 2 9 ,
  3 6 1 -> 3 7 8 11 ,
  3 6 1 -> 10 8 11 ,
  3 6 1 -> 2 11 ,
  3 6 1 -> 4 ,
  12 6 7 -> 12 7 8 9 ,
  12 6 1 -> 12 7 8 11 ,
  10 13 -> 5 ,
  14 9 13 -> 10 13 1 15 ,
  14 9 13 -> 0 1 15 ,
  14 9 13 -> 14 15 ,
  14 9 13 -> 3 ,
  14 9 16 -> 10 13 1 9 ,
  14 9 16 -> 0 1 9 ,
  14 9 16 -> 14 9 ,
  14 9 8 -> 10 13 1 11 ,
  14 9 8 -> 0 1 11 ,
  14 9 8 -> 14 11 ,
  14 9 8 -> 4 ,
  2 9 13 -> 0 1 15 ,
  2 9 13 -> 14 15 ,
  2 9 13 -> 3 ,
  2 9 16 -> 0 1 9 ,
  2 9 16 -> 14 9 ,
  2 9 8 -> 0 1 11 ,
  2 9 8 -> 14 11 ,
  2 9 8 -> 4 ,
  4 9 13 -> 0 1 15 ,
  4 9 13 -> 14 15 ,
  4 9 13 -> 3 ,
  4 9 16 -> 0 1 9 ,
  4 9 16 -> 14 9 ,
  4 9 8 -> 0 1 11 ,
  4 9 8 -> 14 11 ,
  4 9 8 -> 4 ,
  13 7 ->= 16 ,
  13 1 ->= 8 ,
  15 7 ->= 9 ,
  15 1 ->= 11 ,
  6 6 7 ->= 6 7 8 9 ,
  6 6 1 ->= 6 7 8 11 ,
  13 6 7 ->= 13 7 8 9 ,
  13 6 1 ->= 13 7 8 11 ,
  15 6 7 ->= 15 7 8 9 ,
  15 6 1 ->= 15 7 8 11 ,
  17 6 7 ->= 17 7 8 9 ,
  17 6 1 ->= 17 7 8 11 ,
  7 13 ->= 6 ,
  1 9 13 ->= 7 13 1 15 ,
  1 9 16 ->= 7 13 1 9 ,
  1 9 8 ->= 7 13 1 11 ,
  8 9 13 ->= 16 13 1 15 ,
  8 9 16 ->= 16 13 1 9 ,
  8 9 8 ->= 16 13 1 11 ,
  11 9 13 ->= 9 13 1 15 ,
  11 9 16 ->= 9 13 1 9 ,
  11 9 8 ->= 9 13 1 11 }


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

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

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


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 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 1 |
| 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 1 0 0 0 |
| 0 1 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 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 1 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 |
 \         /

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 }, 
it remains to prove termination of the 29-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 1 2 -> 7 2 3 4 ,
  7 1 5 -> 7 2 3 6 ,
  8 1 2 -> 8 2 3 4 ,
  9 1 2 -> 9 2 3 4 ,
  9 1 5 -> 9 2 3 6 ,
  10 2 ->= 11 ,
  10 5 ->= 3 ,
  12 2 ->= 4 ,
  12 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  10 1 2 ->= 10 2 3 4 ,
  10 1 5 ->= 10 2 3 6 ,
  12 1 2 ->= 12 2 3 4 ,
  12 1 5 ->= 12 2 3 6 ,
  13 1 2 ->= 13 2 3 4 ,
  13 1 5 ->= 13 2 3 6 ,
  2 10 ->= 1 ,
  5 4 10 ->= 2 10 5 12 ,
  5 4 11 ->= 2 10 5 4 ,
  5 4 3 ->= 2 10 5 6 ,
  3 4 10 ->= 11 10 5 12 ,
  3 4 11 ->= 11 10 5 4 ,
  3 4 3 ->= 11 10 5 6 ,
  6 4 10 ->= 4 10 5 12 ,
  6 4 11 ->= 4 10 5 4 ,
  6 4 3 ->= 4 10 5 6 }


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 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 1 |
| 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 1 0 0 0 |
| 0 1 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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 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 1 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 }, 
it remains to prove termination of the 28-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 1 2 -> 7 2 3 4 ,
  7 1 5 -> 7 2 3 6 ,
  8 1 2 -> 8 2 3 4 ,
  9 1 2 -> 9 2 3 4 ,
  9 1 5 -> 9 2 3 6 ,
  10 2 ->= 11 ,
  10 5 ->= 3 ,
  12 2 ->= 4 ,
  12 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  10 1 2 ->= 10 2 3 4 ,
  10 1 5 ->= 10 2 3 6 ,
  12 1 2 ->= 12 2 3 4 ,
  12 1 5 ->= 12 2 3 6 ,
  13 1 2 ->= 13 2 3 4 ,
  2 10 ->= 1 ,
  5 4 10 ->= 2 10 5 12 ,
  5 4 11 ->= 2 10 5 4 ,
  5 4 3 ->= 2 10 5 6 ,
  3 4 10 ->= 11 10 5 12 ,
  3 4 11 ->= 11 10 5 4 ,
  3 4 3 ->= 11 10 5 6 ,
  6 4 10 ->= 4 10 5 12 ,
  6 4 11 ->= 4 10 5 4 ,
  6 4 3 ->= 4 10 5 6 }


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 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 1 |
| 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 1 0 0 0 |
| 0 1 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 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 1 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 |
 \         /

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


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 0 0 |
| 0 1 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 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 1 0 0 0 |
| 0 1 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 0 0 0 |
| 0 1 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 0 0 |
| 0 0 0 1 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 |
 \         /

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

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


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 1 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 1 |
| 0 1 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 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 1 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 1 0 0 0 |
| 0 1 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 |
 \         /

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


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 1 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 1 |
| 0 1 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 0 |
| 0 0 0 1 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 1 0 0 0 |
| 0 1 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 |
 \         /

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


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 1 0 |
| 0 1 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 1 |
| 0 1 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 1 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 1 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 1 0 0 0 |
| 0 1 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 |
 \         /

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


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 1 0 |
| 0 1 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 1 |
| 0 1 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 1 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 1 0 0 0 |
| 0 1 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 |
 \         /

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


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 1 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 1 |
| 0 1 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 1 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 1 0 0 0 |
| 0 1 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 |
 \         /

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

The system is trivially terminating.