YES

After renaming modulo { r0->0, 0->1, 1->2, m->3, r1->4, b->5, qr->6, ql->7 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 1 0 ,
  0 2 -> 2 0 ,
  0 3 -> 3 0 ,
  4 1 -> 1 4 ,
  4 2 -> 2 4 ,
  4 3 -> 3 4 ,
  0 5 -> 6 1 5 ,
  4 5 -> 6 2 5 ,
  1 6 -> 6 1 ,
  2 6 -> 6 2 ,
  3 6 -> 7 3 ,
  1 7 -> 7 1 ,
  2 7 -> 7 2 ,
  5 7 1 -> 1 5 0 ,
  5 7 2 -> 2 5 4 }


The system was reversed.

After renaming modulo { 1->0, 0->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, 
it remains to prove termination of the 15-rule system
{ 0 1 -> 1 0 ,
  2 1 -> 1 2 ,
  3 1 -> 1 3 ,
  0 4 -> 4 0 ,
  2 4 -> 4 2 ,
  3 4 -> 4 3 ,
  5 1 -> 5 0 6 ,
  5 4 -> 5 2 6 ,
  6 0 -> 0 6 ,
  6 2 -> 2 6 ,
  6 3 -> 3 7 ,
  7 0 -> 0 7 ,
  7 2 -> 2 7 ,
  0 7 5 -> 1 5 0 ,
  2 7 5 -> 4 5 2 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (3,true)->3, (4,false)->4, (5,true)->5, (0,false)->6, (6,false)->7, (6,true)->8, (2,false)->9, (3,false)->10, (7,false)->11, (7,true)->12, (5,false)->13 },
it remains to prove termination of the 41-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  0 4 -> 0 ,
  2 4 -> 2 ,
  3 4 -> 3 ,
  5 1 -> 5 6 7 ,
  5 1 -> 0 7 ,
  5 1 -> 8 ,
  5 4 -> 5 9 7 ,
  5 4 -> 2 7 ,
  5 4 -> 8 ,
  8 6 -> 0 7 ,
  8 6 -> 8 ,
  8 9 -> 2 7 ,
  8 9 -> 8 ,
  8 10 -> 3 11 ,
  8 10 -> 12 ,
  12 6 -> 0 11 ,
  12 6 -> 12 ,
  12 9 -> 2 11 ,
  12 9 -> 12 ,
  0 11 13 -> 5 6 ,
  0 11 13 -> 0 ,
  2 11 13 -> 5 9 ,
  2 11 13 -> 2 ,
  6 1 ->= 1 6 ,
  9 1 ->= 1 9 ,
  10 1 ->= 1 10 ,
  6 4 ->= 4 6 ,
  9 4 ->= 4 9 ,
  10 4 ->= 4 10 ,
  13 1 ->= 13 6 7 ,
  13 4 ->= 13 9 7 ,
  7 6 ->= 6 7 ,
  7 9 ->= 9 7 ,
  7 10 ->= 10 11 ,
  11 6 ->= 6 11 ,
  11 9 ->= 9 11 ,
  6 11 13 ->= 1 13 6 ,
  9 11 13 ->= 4 13 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 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 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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 12->10, 11->11, 10->12, 13->13 }, 
it remains to prove termination of the 35-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  0 4 -> 0 ,
  2 4 -> 2 ,
  3 4 -> 3 ,
  5 1 -> 5 6 7 ,
  5 1 -> 0 7 ,
  5 1 -> 8 ,
  5 4 -> 5 9 7 ,
  5 4 -> 2 7 ,
  5 4 -> 8 ,
  8 6 -> 0 7 ,
  8 6 -> 8 ,
  8 9 -> 2 7 ,
  8 9 -> 8 ,
  10 6 -> 0 11 ,
  10 6 -> 10 ,
  10 9 -> 2 11 ,
  10 9 -> 10 ,
  6 1 ->= 1 6 ,
  9 1 ->= 1 9 ,
  12 1 ->= 1 12 ,
  6 4 ->= 4 6 ,
  9 4 ->= 4 9 ,
  12 4 ->= 4 12 ,
  13 1 ->= 13 6 7 ,
  13 4 ->= 13 9 7 ,
  7 6 ->= 6 7 ,
  7 9 ->= 9 7 ,
  7 12 ->= 12 11 ,
  11 6 ->= 6 11 ,
  11 9 ->= 9 11 ,
  6 11 13 ->= 1 13 6 ,
  9 11 13 ->= 4 13 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 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 1 |
| 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 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 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, 9->8, 8->9, 10->10, 12->11, 13->12, 11->13 }, 
it remains to prove termination of the 29-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  0 4 -> 0 ,
  2 4 -> 2 ,
  3 4 -> 3 ,
  5 1 -> 5 6 7 ,
  5 4 -> 5 8 7 ,
  9 6 -> 0 7 ,
  9 6 -> 9 ,
  9 8 -> 2 7 ,
  9 8 -> 9 ,
  10 6 -> 10 ,
  10 8 -> 10 ,
  6 1 ->= 1 6 ,
  8 1 ->= 1 8 ,
  11 1 ->= 1 11 ,
  6 4 ->= 4 6 ,
  8 4 ->= 4 8 ,
  11 4 ->= 4 11 ,
  12 1 ->= 12 6 7 ,
  12 4 ->= 12 8 7 ,
  7 6 ->= 6 7 ,
  7 8 ->= 8 7 ,
  7 11 ->= 11 13 ,
  13 6 ->= 6 13 ,
  13 8 ->= 8 13 ,
  6 13 12 ->= 1 12 6 ,
  8 13 12 ->= 4 12 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 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 1 |
| 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 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

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


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


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 1 |
 \     /
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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /

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


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

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 18-rule system
{ 0 1 -> 0 2 3 ,
  0 4 -> 0 5 3 ,
  6 5 -> 6 ,
  2 1 ->= 1 2 ,
  5 1 ->= 1 5 ,
  7 1 ->= 1 7 ,
  2 4 ->= 4 2 ,
  5 4 ->= 4 5 ,
  7 4 ->= 4 7 ,
  8 1 ->= 8 2 3 ,
  8 4 ->= 8 5 3 ,
  3 2 ->= 2 3 ,
  3 5 ->= 5 3 ,
  3 7 ->= 7 9 ,
  9 2 ->= 2 9 ,
  9 5 ->= 5 9 ,
  2 9 8 ->= 1 8 2 ,
  5 9 8 ->= 4 8 5 }


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 1 |
 \     /
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 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /

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


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

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 -> 0 2 3 ,
  0 4 -> 0 5 3 ,
  2 1 ->= 1 2 ,
  5 1 ->= 1 5 ,
  6 1 ->= 1 6 ,
  2 4 ->= 4 2 ,
  5 4 ->= 4 5 ,
  7 1 ->= 7 2 3 ,
  7 4 ->= 7 5 3 ,
  3 2 ->= 2 3 ,
  3 5 ->= 5 3 ,
  3 6 ->= 6 8 ,
  8 2 ->= 2 8 ,
  8 5 ->= 5 8 ,
  2 8 7 ->= 1 7 2 ,
  5 8 7 ->= 4 7 5 }


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

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

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


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


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 |
 \   /
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 1 |
| 0 1 |
 \   /

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

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

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

The system is trivially terminating.