YES

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (0,4)->3, (1,0)->4, (1,1)->5, (1,2)->6, (1,4)->7, (2,0)->8, (2,1)->9, (2,2)->10, (2,4)->11, (3,0)->12, (3,1)->13, (3,2)->14, (3,4)->15 },
it remains to prove termination of the 48-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  4 2 -> 6 ,
  4 3 -> 7 ,
  8 0 -> 8 ,
  8 1 -> 9 ,
  8 2 -> 10 ,
  8 3 -> 11 ,
  12 0 -> 12 ,
  12 1 -> 13 ,
  12 2 -> 14 ,
  12 3 -> 15 ,
  0 0 0 -> 0 1 4 2 8 0 ,
  0 0 1 -> 0 1 4 2 8 1 ,
  0 0 2 -> 0 1 4 2 8 2 ,
  0 0 3 -> 0 1 4 2 8 3 ,
  4 0 0 -> 4 1 4 2 8 0 ,
  4 0 1 -> 4 1 4 2 8 1 ,
  4 0 2 -> 4 1 4 2 8 2 ,
  4 0 3 -> 4 1 4 2 8 3 ,
  8 0 0 -> 8 1 4 2 8 0 ,
  8 0 1 -> 8 1 4 2 8 1 ,
  8 0 2 -> 8 1 4 2 8 2 ,
  8 0 3 -> 8 1 4 2 8 3 ,
  12 0 0 -> 12 1 4 2 8 0 ,
  12 0 1 -> 12 1 4 2 8 1 ,
  12 0 2 -> 12 1 4 2 8 2 ,
  12 0 3 -> 12 1 4 2 8 3 ,
  2 9 4 -> 0 2 8 ,
  2 9 5 -> 0 2 9 ,
  2 9 6 -> 0 2 10 ,
  2 9 7 -> 0 2 11 ,
  6 9 4 -> 4 2 8 ,
  6 9 5 -> 4 2 9 ,
  6 9 6 -> 4 2 10 ,
  6 9 7 -> 4 2 11 ,
  10 9 4 -> 8 2 8 ,
  10 9 5 -> 8 2 9 ,
  10 9 6 -> 8 2 10 ,
  10 9 7 -> 8 2 11 ,
  14 9 4 -> 12 2 8 ,
  14 9 5 -> 12 2 9 ,
  14 9 6 -> 12 2 10 ,
  14 9 7 -> 12 2 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 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 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 |
 \   /

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


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

0 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
14 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 }, 
it remains to prove termination of the 41-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  4 2 -> 6 ,
  7 0 -> 7 ,
  7 1 -> 8 ,
  7 2 -> 9 ,
  10 0 -> 10 ,
  10 1 -> 11 ,
  10 2 -> 12 ,
  0 0 0 -> 0 1 4 2 7 0 ,
  0 0 1 -> 0 1 4 2 7 1 ,
  0 0 2 -> 0 1 4 2 7 2 ,
  0 0 3 -> 0 1 4 2 7 3 ,
  4 0 0 -> 4 1 4 2 7 0 ,
  4 0 1 -> 4 1 4 2 7 1 ,
  4 0 2 -> 4 1 4 2 7 2 ,
  4 0 3 -> 4 1 4 2 7 3 ,
  7 0 0 -> 7 1 4 2 7 0 ,
  7 0 1 -> 7 1 4 2 7 1 ,
  7 0 2 -> 7 1 4 2 7 2 ,
  7 0 3 -> 7 1 4 2 7 3 ,
  10 0 0 -> 10 1 4 2 7 0 ,
  10 0 1 -> 10 1 4 2 7 1 ,
  10 0 2 -> 10 1 4 2 7 2 ,
  10 0 3 -> 10 1 4 2 7 3 ,
  2 8 4 -> 0 2 7 ,
  2 8 5 -> 0 2 8 ,
  2 8 6 -> 0 2 9 ,
  6 8 4 -> 4 2 7 ,
  6 8 5 -> 4 2 8 ,
  6 8 6 -> 4 2 9 ,
  9 8 4 -> 7 2 7 ,
  9 8 5 -> 7 2 8 ,
  9 8 6 -> 7 2 9 ,
  12 8 4 -> 10 2 7 ,
  12 8 5 -> 10 2 8 ,
  12 8 6 -> 10 2 9 }


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

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

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


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

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

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


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

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

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


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

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


Applying the dependency pairs transformation.

After renaming modulo { (8,true)->0, (8,false)->1, (1,false)->2, (0,false)->3, (3,false)->4, (5,false)->5, (0,true)->6, (3,true)->7, (5,true)->8, (9,false)->9, (10,true)->10, (6,false)->11, (2,false)->12, (4,false)->13, (7,false)->14, (10,false)->15 },
it remains to prove termination of the 87-rule system
{ 0 1 1 -> 0 2 3 4 5 1 ,
  0 1 1 -> 6 4 5 1 ,
  0 1 1 -> 7 5 1 ,
  0 1 1 -> 8 1 ,
  0 1 1 -> 0 ,
  0 1 2 -> 0 2 3 4 5 2 ,
  0 1 2 -> 6 4 5 2 ,
  0 1 2 -> 7 5 2 ,
  0 1 2 -> 8 2 ,
  0 1 4 -> 0 2 3 4 5 4 ,
  0 1 4 -> 6 4 5 4 ,
  0 1 4 -> 7 5 4 ,
  0 1 4 -> 8 4 ,
  0 1 4 -> 7 ,
  6 1 1 -> 6 2 3 4 5 1 ,
  6 1 1 -> 6 4 5 1 ,
  6 1 1 -> 7 5 1 ,
  6 1 1 -> 8 1 ,
  6 1 1 -> 0 ,
  6 1 2 -> 6 2 3 4 5 2 ,
  6 1 2 -> 6 4 5 2 ,
  6 1 2 -> 7 5 2 ,
  6 1 2 -> 8 2 ,
  6 1 4 -> 6 2 3 4 5 4 ,
  6 1 4 -> 6 4 5 4 ,
  6 1 4 -> 7 5 4 ,
  6 1 4 -> 8 4 ,
  6 1 4 -> 7 ,
  8 1 1 -> 8 2 3 4 5 1 ,
  8 1 1 -> 6 4 5 1 ,
  8 1 1 -> 7 5 1 ,
  8 1 1 -> 8 1 ,
  8 1 1 -> 0 ,
  8 1 2 -> 8 2 3 4 5 2 ,
  8 1 2 -> 6 4 5 2 ,
  8 1 2 -> 7 5 2 ,
  8 1 2 -> 8 2 ,
  8 1 4 -> 8 2 3 4 5 4 ,
  8 1 4 -> 6 4 5 4 ,
  8 1 4 -> 7 5 4 ,
  8 1 4 -> 8 4 ,
  8 1 4 -> 7 ,
  8 1 9 -> 8 2 3 4 5 9 ,
  8 1 9 -> 6 4 5 9 ,
  8 1 9 -> 7 5 9 ,
  8 1 9 -> 8 9 ,
  10 1 1 -> 10 2 3 4 5 1 ,
  10 1 1 -> 6 4 5 1 ,
  10 1 1 -> 7 5 1 ,
  10 1 1 -> 8 1 ,
  10 1 1 -> 0 ,
  10 1 2 -> 10 2 3 4 5 2 ,
  10 1 2 -> 6 4 5 2 ,
  10 1 2 -> 7 5 2 ,
  10 1 2 -> 8 2 ,
  10 1 4 -> 10 2 3 4 5 4 ,
  10 1 4 -> 6 4 5 4 ,
  10 1 4 -> 7 5 4 ,
  10 1 4 -> 8 4 ,
  10 1 4 -> 7 ,
  7 11 3 -> 0 4 5 ,
  7 11 3 -> 7 5 ,
  7 11 3 -> 8 ,
  7 11 12 -> 0 4 11 ,
  7 11 12 -> 7 11 ,
  7 11 13 -> 0 4 14 ,
  7 11 13 -> 7 14 ,
  3 2 ->= 12 ,
  3 4 ->= 13 ,
  5 2 ->= 11 ,
  5 4 ->= 14 ,
  1 1 1 ->= 1 2 3 4 5 1 ,
  1 1 2 ->= 1 2 3 4 5 2 ,
  1 1 4 ->= 1 2 3 4 5 4 ,
  3 1 1 ->= 3 2 3 4 5 1 ,
  3 1 2 ->= 3 2 3 4 5 2 ,
  3 1 4 ->= 3 2 3 4 5 4 ,
  5 1 1 ->= 5 2 3 4 5 1 ,
  5 1 2 ->= 5 2 3 4 5 2 ,
  5 1 4 ->= 5 2 3 4 5 4 ,
  5 1 9 ->= 5 2 3 4 5 9 ,
  15 1 1 ->= 15 2 3 4 5 1 ,
  15 1 2 ->= 15 2 3 4 5 2 ,
  15 1 4 ->= 15 2 3 4 5 4 ,
  4 11 3 ->= 1 4 5 ,
  4 11 12 ->= 1 4 11 ,
  4 11 13 ->= 1 4 14 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15 }, 
it remains to prove termination of the 76-rule system
{ 0 1 1 -> 0 2 3 4 5 1 ,
  0 1 1 -> 6 4 5 1 ,
  0 1 1 -> 7 5 1 ,
  0 1 1 -> 8 1 ,
  0 1 1 -> 0 ,
  0 1 2 -> 0 2 3 4 5 2 ,
  0 1 2 -> 6 4 5 2 ,
  0 1 2 -> 7 5 2 ,
  0 1 2 -> 8 2 ,
  0 1 4 -> 0 2 3 4 5 4 ,
  0 1 4 -> 6 4 5 4 ,
  0 1 4 -> 7 5 4 ,
  0 1 4 -> 8 4 ,
  0 1 4 -> 7 ,
  6 1 1 -> 6 2 3 4 5 1 ,
  6 1 1 -> 6 4 5 1 ,
  6 1 1 -> 7 5 1 ,
  6 1 1 -> 8 1 ,
  6 1 1 -> 0 ,
  6 1 2 -> 6 2 3 4 5 2 ,
  6 1 2 -> 6 4 5 2 ,
  6 1 2 -> 7 5 2 ,
  6 1 2 -> 8 2 ,
  6 1 4 -> 6 2 3 4 5 4 ,
  6 1 4 -> 6 4 5 4 ,
  6 1 4 -> 7 5 4 ,
  6 1 4 -> 8 4 ,
  6 1 4 -> 7 ,
  8 1 1 -> 8 2 3 4 5 1 ,
  8 1 1 -> 6 4 5 1 ,
  8 1 1 -> 7 5 1 ,
  8 1 1 -> 8 1 ,
  8 1 1 -> 0 ,
  8 1 2 -> 8 2 3 4 5 2 ,
  8 1 2 -> 6 4 5 2 ,
  8 1 2 -> 7 5 2 ,
  8 1 2 -> 8 2 ,
  8 1 4 -> 8 2 3 4 5 4 ,
  8 1 4 -> 6 4 5 4 ,
  8 1 4 -> 7 5 4 ,
  8 1 4 -> 8 4 ,
  8 1 4 -> 7 ,
  8 1 9 -> 8 2 3 4 5 9 ,
  8 1 9 -> 6 4 5 9 ,
  8 1 9 -> 7 5 9 ,
  8 1 9 -> 8 9 ,
  10 1 1 -> 10 2 3 4 5 1 ,
  10 1 2 -> 10 2 3 4 5 2 ,
  10 1 4 -> 10 2 3 4 5 4 ,
  7 11 3 -> 0 4 5 ,
  7 11 3 -> 7 5 ,
  7 11 3 -> 8 ,
  7 11 12 -> 0 4 11 ,
  7 11 12 -> 7 11 ,
  7 11 13 -> 0 4 14 ,
  7 11 13 -> 7 14 ,
  3 2 ->= 12 ,
  3 4 ->= 13 ,
  5 2 ->= 11 ,
  5 4 ->= 14 ,
  1 1 1 ->= 1 2 3 4 5 1 ,
  1 1 2 ->= 1 2 3 4 5 2 ,
  1 1 4 ->= 1 2 3 4 5 4 ,
  3 1 1 ->= 3 2 3 4 5 1 ,
  3 1 2 ->= 3 2 3 4 5 2 ,
  3 1 4 ->= 3 2 3 4 5 4 ,
  5 1 1 ->= 5 2 3 4 5 1 ,
  5 1 2 ->= 5 2 3 4 5 2 ,
  5 1 4 ->= 5 2 3 4 5 4 ,
  5 1 9 ->= 5 2 3 4 5 9 ,
  15 1 1 ->= 15 2 3 4 5 1 ,
  15 1 2 ->= 15 2 3 4 5 2 ,
  15 1 4 ->= 15 2 3 4 5 4 ,
  4 11 3 ->= 1 4 5 ,
  4 11 12 ->= 1 4 11 ,
  4 11 13 ->= 1 4 14 }


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

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

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8, 10->9, 11->10, 12->11, 13->12, 8->13, 14->14 }, 
it remains to prove termination of the 32-rule system
{ 0 1 1 -> 0 2 3 4 5 1 ,
  0 1 2 -> 0 2 3 4 5 2 ,
  0 1 4 -> 0 2 3 4 5 4 ,
  6 1 1 -> 6 2 3 4 5 1 ,
  6 1 2 -> 6 2 3 4 5 2 ,
  6 1 4 -> 6 2 3 4 5 4 ,
  7 1 1 -> 7 2 3 4 5 1 ,
  7 1 2 -> 7 2 3 4 5 2 ,
  7 1 4 -> 7 2 3 4 5 4 ,
  8 1 1 -> 8 2 3 4 5 1 ,
  8 1 2 -> 8 2 3 4 5 2 ,
  8 1 4 -> 8 2 3 4 5 4 ,
  3 2 ->= 9 ,
  3 4 ->= 10 ,
  5 2 ->= 11 ,
  5 4 ->= 12 ,
  1 1 1 ->= 1 2 3 4 5 1 ,
  1 1 2 ->= 1 2 3 4 5 2 ,
  1 1 4 ->= 1 2 3 4 5 4 ,
  3 1 1 ->= 3 2 3 4 5 1 ,
  3 1 2 ->= 3 2 3 4 5 2 ,
  3 1 4 ->= 3 2 3 4 5 4 ,
  5 1 1 ->= 5 2 3 4 5 1 ,
  5 1 2 ->= 5 2 3 4 5 2 ,
  5 1 4 ->= 5 2 3 4 5 4 ,
  5 1 13 ->= 5 2 3 4 5 13 ,
  14 1 1 ->= 14 2 3 4 5 1 ,
  14 1 2 ->= 14 2 3 4 5 2 ,
  14 1 4 ->= 14 2 3 4 5 4 ,
  4 11 3 ->= 1 4 5 ,
  4 11 9 ->= 1 4 11 ,
  4 11 10 ->= 1 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 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
13 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
14 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

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

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

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

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

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

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

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

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

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

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

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

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


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

0 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 1 |
| 0 1 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 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 19-rule system
{ 0 1 2 -> 0 2 3 4 5 2 ,
  6 1 2 -> 6 2 3 4 5 2 ,
  7 1 2 -> 7 2 3 4 5 2 ,
  3 2 ->= 8 ,
  3 4 ->= 9 ,
  5 2 ->= 10 ,
  5 4 ->= 11 ,
  1 1 1 ->= 1 2 3 4 5 1 ,
  1 1 2 ->= 1 2 3 4 5 2 ,
  1 1 4 ->= 1 2 3 4 5 4 ,
  3 1 1 ->= 3 2 3 4 5 1 ,
  3 1 2 ->= 3 2 3 4 5 2 ,
  3 1 4 ->= 3 2 3 4 5 4 ,
  5 1 1 ->= 5 2 3 4 5 1 ,
  5 1 2 ->= 5 2 3 4 5 2 ,
  5 1 4 ->= 5 2 3 4 5 4 ,
  4 10 3 ->= 1 4 5 ,
  4 10 8 ->= 1 4 10 ,
  4 10 9 ->= 1 4 11 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 18-rule system
{ 0 1 2 -> 0 2 3 4 5 2 ,
  6 1 2 -> 6 2 3 4 5 2 ,
  3 2 ->= 7 ,
  3 4 ->= 8 ,
  5 2 ->= 9 ,
  5 4 ->= 10 ,
  1 1 1 ->= 1 2 3 4 5 1 ,
  1 1 2 ->= 1 2 3 4 5 2 ,
  1 1 4 ->= 1 2 3 4 5 4 ,
  3 1 1 ->= 3 2 3 4 5 1 ,
  3 1 2 ->= 3 2 3 4 5 2 ,
  3 1 4 ->= 3 2 3 4 5 4 ,
  5 1 1 ->= 5 2 3 4 5 1 ,
  5 1 2 ->= 5 2 3 4 5 2 ,
  5 1 4 ->= 5 2 3 4 5 4 ,
  4 9 3 ->= 1 4 5 ,
  4 9 7 ->= 1 4 9 ,
  4 9 8 ->= 1 4 10 }


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

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

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


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

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

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

The system is trivially terminating.