YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 4-rule system
{ 0 -> ,
  0 0 -> 0 1 ,
  1 -> ,
  2 1 -> 0 1 2 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 64-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 ,
  0 0 1 -> 0 1 5 ,
  0 0 2 -> 0 1 6 ,
  0 0 3 -> 0 1 7 ,
  4 0 0 -> 4 1 4 ,
  4 0 1 -> 4 1 5 ,
  4 0 2 -> 4 1 6 ,
  4 0 3 -> 4 1 7 ,
  8 0 0 -> 8 1 4 ,
  8 0 1 -> 8 1 5 ,
  8 0 2 -> 8 1 6 ,
  8 0 3 -> 8 1 7 ,
  12 0 0 -> 12 1 4 ,
  12 0 1 -> 12 1 5 ,
  12 0 2 -> 12 1 6 ,
  12 0 3 -> 12 1 7 ,
  1 4 -> 0 ,
  1 5 -> 1 ,
  1 6 -> 2 ,
  1 7 -> 3 ,
  5 4 -> 4 ,
  5 5 -> 5 ,
  5 6 -> 6 ,
  5 7 -> 7 ,
  9 4 -> 8 ,
  9 5 -> 9 ,
  9 6 -> 10 ,
  9 7 -> 11 ,
  13 4 -> 12 ,
  13 5 -> 13 ,
  13 6 -> 14 ,
  13 7 -> 15 ,
  2 9 4 -> 0 1 6 10 8 ,
  2 9 5 -> 0 1 6 10 9 ,
  2 9 6 -> 0 1 6 10 10 ,
  2 9 7 -> 0 1 6 10 11 ,
  6 9 4 -> 4 1 6 10 8 ,
  6 9 5 -> 4 1 6 10 9 ,
  6 9 6 -> 4 1 6 10 10 ,
  6 9 7 -> 4 1 6 10 11 ,
  10 9 4 -> 8 1 6 10 8 ,
  10 9 5 -> 8 1 6 10 9 ,
  10 9 6 -> 8 1 6 10 10 ,
  10 9 7 -> 8 1 6 10 11 ,
  14 9 4 -> 12 1 6 10 8 ,
  14 9 5 -> 12 1 6 10 9 ,
  14 9 6 -> 12 1 6 10 10 ,
  14 9 7 -> 12 1 6 10 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 3 |
| 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 3 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 2 |
| 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 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (5,true)->0, (5,false)->1, (1,false)->2, (2,false)->3, (1,true)->4, (0,true)->5, (3,true)->6, (6,true)->7, (0,false)->8, (7,false)->9, (8,true)->10, (4,false)->11, (9,false)->12, (3,false)->13, (7,true)->14, (9,true)->15, (6,false)->16, (8,false)->17 },
it remains to prove termination of the 69-rule system
{ 0 1 2 -> 0 2 3 ,
  0 1 2 -> 4 3 ,
  5 1 2 -> 5 2 3 ,
  5 1 2 -> 4 3 ,
  6 1 2 -> 6 2 3 ,
  6 1 2 -> 4 3 ,
  7 1 2 -> 7 2 3 ,
  7 1 2 -> 4 3 ,
  4 8 -> 0 ,
  4 9 -> 10 ,
  10 11 8 -> 0 2 9 12 13 ,
  10 11 8 -> 4 9 12 13 ,
  10 11 8 -> 14 12 13 ,
  10 11 8 -> 15 13 ,
  10 11 8 -> 6 ,
  10 11 3 -> 0 2 9 12 11 ,
  10 11 3 -> 4 9 12 11 ,
  10 11 3 -> 14 12 11 ,
  10 11 3 -> 15 11 ,
  10 11 9 -> 0 2 9 12 12 ,
  10 11 9 -> 4 9 12 12 ,
  10 11 9 -> 14 12 12 ,
  10 11 9 -> 15 12 ,
  10 11 9 -> 15 ,
  14 11 8 -> 5 2 9 12 13 ,
  14 11 8 -> 4 9 12 13 ,
  14 11 8 -> 14 12 13 ,
  14 11 8 -> 15 13 ,
  14 11 8 -> 6 ,
  14 11 3 -> 5 2 9 12 11 ,
  14 11 3 -> 4 9 12 11 ,
  14 11 3 -> 14 12 11 ,
  14 11 3 -> 15 11 ,
  14 11 9 -> 5 2 9 12 12 ,
  14 11 9 -> 4 9 12 12 ,
  14 11 9 -> 14 12 12 ,
  14 11 9 -> 15 12 ,
  14 11 9 -> 15 ,
  15 11 8 -> 6 2 9 12 13 ,
  15 11 8 -> 4 9 12 13 ,
  15 11 8 -> 14 12 13 ,
  15 11 8 -> 15 13 ,
  15 11 8 -> 6 ,
  15 11 3 -> 6 2 9 12 11 ,
  15 11 3 -> 4 9 12 11 ,
  15 11 3 -> 14 12 11 ,
  15 11 3 -> 15 11 ,
  15 11 9 -> 6 2 9 12 12 ,
  15 11 9 -> 4 9 12 12 ,
  15 11 9 -> 14 12 12 ,
  15 11 9 -> 15 12 ,
  15 11 9 -> 15 ,
  8 2 ->= 3 ,
  13 2 ->= 11 ,
  1 1 2 ->= 1 2 3 ,
  8 1 2 ->= 8 2 3 ,
  13 1 2 ->= 13 2 3 ,
  16 1 2 ->= 16 2 3 ,
  2 8 ->= 1 ,
  2 9 ->= 17 ,
  17 11 8 ->= 1 2 9 12 13 ,
  17 11 3 ->= 1 2 9 12 11 ,
  17 11 9 ->= 1 2 9 12 12 ,
  9 11 8 ->= 8 2 9 12 13 ,
  9 11 3 ->= 8 2 9 12 11 ,
  9 11 9 ->= 8 2 9 12 12 ,
  12 11 8 ->= 13 2 9 12 13 ,
  12 11 3 ->= 13 2 9 12 11 ,
  12 11 9 ->= 13 2 9 12 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 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 0 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
17 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, 14->14, 15->15, 16->16, 17->17 }, 
it remains to prove termination of the 68-rule system
{ 0 1 2 -> 0 2 3 ,
  0 1 2 -> 4 3 ,
  5 1 2 -> 5 2 3 ,
  5 1 2 -> 4 3 ,
  6 1 2 -> 6 2 3 ,
  6 1 2 -> 4 3 ,
  7 1 2 -> 7 2 3 ,
  4 8 -> 0 ,
  4 9 -> 10 ,
  10 11 8 -> 0 2 9 12 13 ,
  10 11 8 -> 4 9 12 13 ,
  10 11 8 -> 14 12 13 ,
  10 11 8 -> 15 13 ,
  10 11 8 -> 6 ,
  10 11 3 -> 0 2 9 12 11 ,
  10 11 3 -> 4 9 12 11 ,
  10 11 3 -> 14 12 11 ,
  10 11 3 -> 15 11 ,
  10 11 9 -> 0 2 9 12 12 ,
  10 11 9 -> 4 9 12 12 ,
  10 11 9 -> 14 12 12 ,
  10 11 9 -> 15 12 ,
  10 11 9 -> 15 ,
  14 11 8 -> 5 2 9 12 13 ,
  14 11 8 -> 4 9 12 13 ,
  14 11 8 -> 14 12 13 ,
  14 11 8 -> 15 13 ,
  14 11 8 -> 6 ,
  14 11 3 -> 5 2 9 12 11 ,
  14 11 3 -> 4 9 12 11 ,
  14 11 3 -> 14 12 11 ,
  14 11 3 -> 15 11 ,
  14 11 9 -> 5 2 9 12 12 ,
  14 11 9 -> 4 9 12 12 ,
  14 11 9 -> 14 12 12 ,
  14 11 9 -> 15 12 ,
  14 11 9 -> 15 ,
  15 11 8 -> 6 2 9 12 13 ,
  15 11 8 -> 4 9 12 13 ,
  15 11 8 -> 14 12 13 ,
  15 11 8 -> 15 13 ,
  15 11 8 -> 6 ,
  15 11 3 -> 6 2 9 12 11 ,
  15 11 3 -> 4 9 12 11 ,
  15 11 3 -> 14 12 11 ,
  15 11 3 -> 15 11 ,
  15 11 9 -> 6 2 9 12 12 ,
  15 11 9 -> 4 9 12 12 ,
  15 11 9 -> 14 12 12 ,
  15 11 9 -> 15 12 ,
  15 11 9 -> 15 ,
  8 2 ->= 3 ,
  13 2 ->= 11 ,
  1 1 2 ->= 1 2 3 ,
  8 1 2 ->= 8 2 3 ,
  13 1 2 ->= 13 2 3 ,
  16 1 2 ->= 16 2 3 ,
  2 8 ->= 1 ,
  2 9 ->= 17 ,
  17 11 8 ->= 1 2 9 12 13 ,
  17 11 3 ->= 1 2 9 12 11 ,
  17 11 9 ->= 1 2 9 12 12 ,
  9 11 8 ->= 8 2 9 12 13 ,
  9 11 3 ->= 8 2 9 12 11 ,
  9 11 9 ->= 8 2 9 12 12 ,
  12 11 8 ->= 13 2 9 12 13 ,
  12 11 3 ->= 13 2 9 12 11 ,
  12 11 9 ->= 13 2 9 12 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 3 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 3 |
| 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 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 2 |
| 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 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 13->8, 11->9, 16->10, 9->11, 17->12, 12->13 }, 
it remains to prove termination of the 21-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 1 2 -> 5 2 3 ,
  6 1 2 -> 6 2 3 ,
  7 2 ->= 3 ,
  8 2 ->= 9 ,
  1 1 2 ->= 1 2 3 ,
  7 1 2 ->= 7 2 3 ,
  8 1 2 ->= 8 2 3 ,
  10 1 2 ->= 10 2 3 ,
  2 7 ->= 1 ,
  2 11 ->= 12 ,
  12 9 7 ->= 1 2 11 13 8 ,
  12 9 3 ->= 1 2 11 13 9 ,
  12 9 11 ->= 1 2 11 13 13 ,
  11 9 7 ->= 7 2 11 13 8 ,
  11 9 3 ->= 7 2 11 13 9 ,
  11 9 11 ->= 7 2 11 13 13 ,
  13 9 7 ->= 8 2 11 13 8 ,
  13 9 3 ->= 8 2 11 13 9 ,
  13 9 11 ->= 8 2 11 13 13 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->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 1 2 -> 4 2 3 ,
  5 1 2 -> 5 2 3 ,
  6 2 ->= 3 ,
  7 2 ->= 8 ,
  1 1 2 ->= 1 2 3 ,
  6 1 2 ->= 6 2 3 ,
  7 1 2 ->= 7 2 3 ,
  9 1 2 ->= 9 2 3 ,
  2 6 ->= 1 ,
  2 10 ->= 11 ,
  11 8 6 ->= 1 2 10 12 7 ,
  11 8 3 ->= 1 2 10 12 8 ,
  11 8 10 ->= 1 2 10 12 12 ,
  10 8 6 ->= 6 2 10 12 7 ,
  10 8 3 ->= 6 2 10 12 8 ,
  10 8 10 ->= 6 2 10 12 12 ,
  12 8 6 ->= 7 2 10 12 7 ,
  12 8 3 ->= 7 2 10 12 8 ,
  12 8 10 ->= 7 2 10 12 12 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 19-rule system
{ 0 1 2 -> 0 2 3 ,
  4 1 2 -> 4 2 3 ,
  5 2 ->= 3 ,
  6 2 ->= 7 ,
  1 1 2 ->= 1 2 3 ,
  5 1 2 ->= 5 2 3 ,
  6 1 2 ->= 6 2 3 ,
  8 1 2 ->= 8 2 3 ,
  2 5 ->= 1 ,
  2 9 ->= 10 ,
  10 7 5 ->= 1 2 9 11 6 ,
  10 7 3 ->= 1 2 9 11 7 ,
  10 7 9 ->= 1 2 9 11 11 ,
  9 7 5 ->= 5 2 9 11 6 ,
  9 7 3 ->= 5 2 9 11 7 ,
  9 7 9 ->= 5 2 9 11 11 ,
  11 7 5 ->= 6 2 9 11 6 ,
  11 7 3 ->= 6 2 9 11 7 ,
  11 7 9 ->= 6 2 9 11 11 }


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

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

After renaming modulo { 4->0, 1->1, 2->2, 3->3, 5->4, 6->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 2 ->= 3 ,
  5 2 ->= 6 ,
  1 1 2 ->= 1 2 3 ,
  4 1 2 ->= 4 2 3 ,
  5 1 2 ->= 5 2 3 ,
  7 1 2 ->= 7 2 3 ,
  2 4 ->= 1 ,
  2 8 ->= 9 ,
  9 6 4 ->= 1 2 8 10 5 ,
  9 6 3 ->= 1 2 8 10 6 ,
  9 6 8 ->= 1 2 8 10 10 ,
  8 6 4 ->= 4 2 8 10 5 ,
  8 6 3 ->= 4 2 8 10 6 ,
  8 6 8 ->= 4 2 8 10 10 ,
  10 6 4 ->= 5 2 8 10 5 ,
  10 6 3 ->= 5 2 8 10 6 ,
  10 6 8 ->= 5 2 8 10 10 }


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

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

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

The system is trivially terminating.