YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 5-rule system
{ 0 1 2 -> 2 2 2 1 1 1 0 0 0 ,
  2 1 -> 0 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 5-rule system
{ 0 1 2 -> 2 2 2 1 1 1 0 0 0 ,
  1 0 -> 2 2 2 ,
  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, (3,1)->13, (1,4)->14, (3,4)->15 },
it remains to prove termination of the 80-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  11 1 2 3 -> 12 5 5 6 7 7 8 0 0 0 ,
  11 1 2 6 -> 12 5 5 6 7 7 8 0 0 1 ,
  11 1 2 5 -> 12 5 5 6 7 7 8 0 0 4 ,
  11 1 2 9 -> 12 5 5 6 7 7 8 0 0 10 ,
  1 8 0 -> 4 5 5 3 ,
  1 8 1 -> 4 5 5 6 ,
  1 8 4 -> 4 5 5 5 ,
  1 8 10 -> 4 5 5 9 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  6 8 0 -> 5 5 5 3 ,
  6 8 1 -> 5 5 5 6 ,
  6 8 4 -> 5 5 5 5 ,
  6 8 10 -> 5 5 5 9 ,
  13 8 0 -> 12 5 5 3 ,
  13 8 1 -> 12 5 5 6 ,
  13 8 4 -> 12 5 5 5 ,
  13 8 10 -> 12 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 6 -> 7 ,
  2 5 -> 2 ,
  2 9 -> 14 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  12 3 -> 11 ,
  12 6 -> 13 ,
  12 5 -> 12 ,
  12 9 -> 15 ,
  1 8 -> 0 ,
  1 7 -> 1 ,
  1 2 -> 4 ,
  1 14 -> 10 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  7 14 -> 14 ,
  6 8 -> 3 ,
  6 7 -> 6 ,
  6 2 -> 5 ,
  6 14 -> 9 ,
  13 8 -> 11 ,
  13 7 -> 13 ,
  13 2 -> 12 ,
  13 14 -> 15 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 1 -> 7 ,
  8 4 -> 2 ,
  8 10 -> 14 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  11 0 -> 11 ,
  11 1 -> 13 ,
  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 2 |
| 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 2 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 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, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 14->13, 13->14 }, 
it remains to prove termination of the 51-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  11 1 2 3 -> 12 5 5 6 7 7 8 0 0 0 ,
  11 1 2 6 -> 12 5 5 6 7 7 8 0 0 1 ,
  11 1 2 5 -> 12 5 5 6 7 7 8 0 0 4 ,
  11 1 2 9 -> 12 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  12 3 -> 11 ,
  12 5 -> 12 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  7 13 -> 13 ,
  6 7 -> 6 ,
  14 7 -> 14 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  11 0 -> 11 ,
  11 4 -> 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 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 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
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 1 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, 14->13 }, 
it remains to prove termination of the 50-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  11 1 2 3 -> 12 5 5 6 7 7 8 0 0 0 ,
  11 1 2 6 -> 12 5 5 6 7 7 8 0 0 1 ,
  11 1 2 5 -> 12 5 5 6 7 7 8 0 0 4 ,
  11 1 2 9 -> 12 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  12 3 -> 11 ,
  12 5 -> 12 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  6 7 -> 6 ,
  13 7 -> 13 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  11 0 -> 11 ,
  11 4 -> 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 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 1 1 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /

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 }, 
it remains to prove termination of the 49-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  11 1 2 3 -> 12 5 5 6 7 7 8 0 0 0 ,
  11 1 2 6 -> 12 5 5 6 7 7 8 0 0 1 ,
  11 1 2 5 -> 12 5 5 6 7 7 8 0 0 4 ,
  11 1 2 9 -> 12 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  12 3 -> 11 ,
  12 5 -> 12 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  6 7 -> 6 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  11 0 -> 11 ,
  11 4 -> 12 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12 }, 
it remains to prove termination of the 48-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  11 1 2 3 -> 12 5 5 6 7 7 8 0 0 0 ,
  11 1 2 6 -> 12 5 5 6 7 7 8 0 0 1 ,
  11 1 2 5 -> 12 5 5 6 7 7 8 0 0 4 ,
  11 1 2 9 -> 12 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  12 5 -> 12 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  6 7 -> 6 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  11 0 -> 11 ,
  11 4 -> 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 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 1 |
| 0 1 |
 \   /
12 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, 12->11, 11->12 }, 
it remains to prove termination of the 43-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  11 5 -> 11 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  6 7 -> 6 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 ,
  12 0 -> 12 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 42-rule system
{ 0 1 2 3 -> 4 5 5 6 7 7 8 0 0 0 ,
  0 1 2 6 -> 4 5 5 6 7 7 8 0 0 1 ,
  0 1 2 5 -> 4 5 5 6 7 7 8 0 0 4 ,
  0 1 2 9 -> 4 5 5 6 7 7 8 0 0 10 ,
  8 1 2 3 -> 2 5 5 6 7 7 8 0 0 0 ,
  8 1 2 6 -> 2 5 5 6 7 7 8 0 0 1 ,
  8 1 2 5 -> 2 5 5 6 7 7 8 0 0 4 ,
  8 1 2 9 -> 2 5 5 6 7 7 8 0 0 10 ,
  3 1 2 3 -> 5 5 5 6 7 7 8 0 0 0 ,
  3 1 2 6 -> 5 5 5 6 7 7 8 0 0 1 ,
  3 1 2 5 -> 5 5 5 6 7 7 8 0 0 4 ,
  3 1 2 9 -> 5 5 5 6 7 7 8 0 0 10 ,
  7 8 0 -> 2 5 5 3 ,
  7 8 1 -> 2 5 5 6 ,
  7 8 4 -> 2 5 5 5 ,
  7 8 10 -> 2 5 5 9 ,
  4 3 -> 0 ,
  4 6 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 3 -> 8 ,
  2 5 -> 2 ,
  5 3 -> 3 ,
  5 6 -> 6 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  11 5 -> 11 ,
  1 7 -> 1 ,
  7 8 -> 8 ,
  7 7 -> 7 ,
  7 2 -> 2 ,
  6 7 -> 6 ,
  0 0 -> 0 ,
  0 1 -> 1 ,
  0 4 -> 4 ,
  0 10 -> 10 ,
  8 0 -> 8 ,
  8 4 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 6 ,
  3 4 -> 5 ,
  3 10 -> 9 }


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 3 0 |
| 0 3 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 1 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 3 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 1 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, 1->1, 2->2, 6->3, 4->4, 5->5, 7->6, 8->7, 3->8, 9->9, 10->10, 11->11 }, 
it remains to prove termination of the 22-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  6 7 0 -> 2 5 5 8 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  4 9 -> 10 ,
  2 8 -> 7 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 5 -> 5 ,
  5 9 -> 9 ,
  11 5 -> 11 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 6 -> 6 ,
  6 2 -> 2 ,
  3 6 -> 3 ,
  0 10 -> 10 ,
  7 0 -> 7 }


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 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 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 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, 11->10, 10->11 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  6 7 0 -> 2 5 5 8 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 8 -> 7 ,
  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 ,
  3 6 -> 3 ,
  0 11 -> 11 ,
  7 0 -> 7 }


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

0 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 1 |
 \     /
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 1 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, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 10->9, 11->10 }, 
it remains to prove termination of the 20-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  6 7 0 -> 2 5 5 8 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 8 -> 7 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 5 -> 5 ,
  9 5 -> 9 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 6 -> 6 ,
  6 2 -> 2 ,
  3 6 -> 3 ,
  0 10 -> 10 ,
  7 0 -> 7 }


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 1 1 |
 \     /
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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 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 }, 
it remains to prove termination of the 19-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  6 7 0 -> 2 5 5 8 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 8 -> 7 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 5 -> 5 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 6 -> 6 ,
  6 2 -> 2 ,
  3 6 -> 3 ,
  0 9 -> 9 ,
  7 0 -> 7 }


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 1 |
 \     /
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 1 0 |
 \     /

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


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, 
it remains to prove termination of the 16-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  6 7 0 -> 2 5 5 8 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 5 -> 5 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 6 -> 6 ,
  6 2 -> 2 ,
  3 6 -> 3 }


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 1 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 2 0 |
| 0 2 0 |
| 0 0 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 3 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 2 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 1 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 3 0 |
| 0 0 0 |
 \     /
8 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 }, 
it remains to prove termination of the 14-rule system
{ 0 1 2 3 -> 4 5 5 3 6 6 7 0 0 1 ,
  0 1 2 5 -> 4 5 5 3 6 6 7 0 0 4 ,
  7 1 2 3 -> 2 5 5 3 6 6 7 0 0 1 ,
  7 1 2 5 -> 2 5 5 3 6 6 7 0 0 4 ,
  4 3 -> 1 ,
  4 5 -> 4 ,
  2 5 -> 2 ,
  5 8 -> 8 ,
  5 3 -> 3 ,
  5 5 -> 5 ,
  1 6 -> 1 ,
  6 7 -> 7 ,
  6 2 -> 2 ,
  3 6 -> 3 }


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

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

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


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

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


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

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


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 1 |
| 0 1 |
 \   /

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


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

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


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

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

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


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

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

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


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

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

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


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

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

After renaming modulo { 1->0, 5->1, 2->2 }, 
it remains to prove termination of the 2-rule system
{ 0 1 -> 0 ,
  1 2 -> 2 }


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

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

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

The system is trivially terminating.