YES

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


The system was reversed.

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


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

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


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

0 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 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 1 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (3,false)->3, (4,false)->4, (5,false)->5, (5,true)->6, (6,false)->7, (7,false)->8, (7,true)->9, (8,false)->10, (9,false)->11, (4,true)->12, (6,true)->13, (0,false)->14, (11,true)->15, (2,false)->16, (10,false)->17, (11,false)->18 },
it remains to prove termination of the 79-rule system
{ 0 1 -> 2 3 ,
  0 4 -> 2 5 ,
  0 4 -> 6 ,
  0 7 -> 2 8 ,
  0 7 -> 9 ,
  0 10 -> 2 11 ,
  12 3 1 -> 13 14 4 3 ,
  12 3 1 -> 0 4 3 ,
  12 3 1 -> 12 3 ,
  12 3 4 -> 13 14 4 5 ,
  12 3 4 -> 0 4 5 ,
  12 3 4 -> 12 5 ,
  12 3 4 -> 6 ,
  12 3 7 -> 13 14 4 8 ,
  12 3 7 -> 0 4 8 ,
  12 3 7 -> 12 8 ,
  12 3 7 -> 9 ,
  12 3 10 -> 13 14 4 11 ,
  12 3 10 -> 0 4 11 ,
  12 3 10 -> 12 11 ,
  6 3 1 -> 9 14 4 3 ,
  6 3 1 -> 0 4 3 ,
  6 3 1 -> 12 3 ,
  6 3 4 -> 9 14 4 5 ,
  6 3 4 -> 0 4 5 ,
  6 3 4 -> 12 5 ,
  6 3 4 -> 6 ,
  6 3 7 -> 9 14 4 8 ,
  6 3 7 -> 0 4 8 ,
  6 3 7 -> 12 8 ,
  6 3 7 -> 9 ,
  6 3 10 -> 9 14 4 11 ,
  6 3 10 -> 0 4 11 ,
  6 3 10 -> 12 11 ,
  2 3 1 -> 0 4 3 ,
  2 3 1 -> 12 3 ,
  2 3 4 -> 0 4 5 ,
  2 3 4 -> 12 5 ,
  2 3 4 -> 6 ,
  2 3 7 -> 0 4 8 ,
  2 3 7 -> 12 8 ,
  2 3 7 -> 9 ,
  2 3 10 -> 0 4 11 ,
  2 3 10 -> 12 11 ,
  12 5 5 -> 12 ,
  12 5 8 -> 13 ,
  6 5 5 -> 6 ,
  6 5 8 -> 9 ,
  2 5 5 -> 2 ,
  15 5 5 -> 15 ,
  14 1 ->= 16 3 ,
  14 4 ->= 16 5 ,
  14 7 ->= 16 8 ,
  14 10 ->= 16 11 ,
  4 3 1 ->= 7 14 4 3 ,
  4 3 4 ->= 7 14 4 5 ,
  4 3 7 ->= 7 14 4 8 ,
  4 3 10 ->= 7 14 4 11 ,
  5 3 1 ->= 8 14 4 3 ,
  5 3 4 ->= 8 14 4 5 ,
  5 3 7 ->= 8 14 4 8 ,
  5 3 10 ->= 8 14 4 11 ,
  16 3 1 ->= 17 14 4 3 ,
  16 3 4 ->= 17 14 4 5 ,
  16 3 7 ->= 17 14 4 8 ,
  16 3 10 ->= 17 14 4 11 ,
  4 5 3 ->= 1 ,
  4 5 5 ->= 4 ,
  4 5 8 ->= 7 ,
  4 5 11 ->= 10 ,
  5 5 3 ->= 3 ,
  5 5 5 ->= 5 ,
  5 5 8 ->= 8 ,
  5 5 11 ->= 11 ,
  16 5 5 ->= 16 ,
  16 5 8 ->= 17 ,
  18 5 5 ->= 18 ,
  7 17 14 ->= 1 1 ,
  8 17 14 ->= 3 1 }


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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 2 |
| 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 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

After renaming modulo { 2->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14 }, 
it remains to prove termination of the 32-rule system
{ 0 1 1 -> 0 ,
  2 1 1 -> 2 ,
  3 1 1 -> 3 ,
  4 5 ->= 6 7 ,
  4 8 ->= 6 1 ,
  4 9 ->= 6 10 ,
  4 11 ->= 6 12 ,
  8 7 5 ->= 9 4 8 7 ,
  8 7 8 ->= 9 4 8 1 ,
  8 7 9 ->= 9 4 8 10 ,
  8 7 11 ->= 9 4 8 12 ,
  1 7 5 ->= 10 4 8 7 ,
  1 7 8 ->= 10 4 8 1 ,
  1 7 9 ->= 10 4 8 10 ,
  1 7 11 ->= 10 4 8 12 ,
  6 7 5 ->= 13 4 8 7 ,
  6 7 8 ->= 13 4 8 1 ,
  6 7 9 ->= 13 4 8 10 ,
  6 7 11 ->= 13 4 8 12 ,
  8 1 7 ->= 5 ,
  8 1 1 ->= 8 ,
  8 1 10 ->= 9 ,
  8 1 12 ->= 11 ,
  1 1 7 ->= 7 ,
  1 1 1 ->= 1 ,
  1 1 10 ->= 10 ,
  1 1 12 ->= 12 ,
  6 1 1 ->= 6 ,
  6 1 10 ->= 13 ,
  14 1 1 ->= 14 ,
  9 13 4 ->= 5 5 ,
  10 13 4 ->= 7 5 }


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 1 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 1 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 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, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13 }, 
it remains to prove termination of the 31-rule system
{ 0 1 1 -> 0 ,
  2 1 1 -> 2 ,
  3 4 ->= 5 6 ,
  3 7 ->= 5 1 ,
  3 8 ->= 5 9 ,
  3 10 ->= 5 11 ,
  7 6 4 ->= 8 3 7 6 ,
  7 6 7 ->= 8 3 7 1 ,
  7 6 8 ->= 8 3 7 9 ,
  7 6 10 ->= 8 3 7 11 ,
  1 6 4 ->= 9 3 7 6 ,
  1 6 7 ->= 9 3 7 1 ,
  1 6 8 ->= 9 3 7 9 ,
  1 6 10 ->= 9 3 7 11 ,
  5 6 4 ->= 12 3 7 6 ,
  5 6 7 ->= 12 3 7 1 ,
  5 6 8 ->= 12 3 7 9 ,
  5 6 10 ->= 12 3 7 11 ,
  7 1 6 ->= 4 ,
  7 1 1 ->= 7 ,
  7 1 9 ->= 8 ,
  7 1 11 ->= 10 ,
  1 1 6 ->= 6 ,
  1 1 1 ->= 1 ,
  1 1 9 ->= 9 ,
  1 1 11 ->= 11 ,
  5 1 1 ->= 5 ,
  5 1 9 ->= 12 ,
  13 1 1 ->= 13 ,
  8 12 3 ->= 4 4 ,
  9 12 3 ->= 6 4 }


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 1 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 1 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 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 { 0->0, 1->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12 }, 
it remains to prove termination of the 30-rule system
{ 0 1 1 -> 0 ,
  2 3 ->= 4 5 ,
  2 6 ->= 4 1 ,
  2 7 ->= 4 8 ,
  2 9 ->= 4 10 ,
  6 5 3 ->= 7 2 6 5 ,
  6 5 6 ->= 7 2 6 1 ,
  6 5 7 ->= 7 2 6 8 ,
  6 5 9 ->= 7 2 6 10 ,
  1 5 3 ->= 8 2 6 5 ,
  1 5 6 ->= 8 2 6 1 ,
  1 5 7 ->= 8 2 6 8 ,
  1 5 9 ->= 8 2 6 10 ,
  4 5 3 ->= 11 2 6 5 ,
  4 5 6 ->= 11 2 6 1 ,
  4 5 7 ->= 11 2 6 8 ,
  4 5 9 ->= 11 2 6 10 ,
  6 1 5 ->= 3 ,
  6 1 1 ->= 6 ,
  6 1 8 ->= 7 ,
  6 1 10 ->= 9 ,
  1 1 5 ->= 5 ,
  1 1 1 ->= 1 ,
  1 1 8 ->= 8 ,
  1 1 10 ->= 10 ,
  4 1 1 ->= 4 ,
  4 1 8 ->= 11 ,
  12 1 1 ->= 12 ,
  7 11 2 ->= 3 3 ,
  8 11 2 ->= 5 3 }


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 1 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 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 |
 \       /

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

The system is trivially terminating.