YES

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


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

After renaming modulo { (0,0)->0, (0,1)->1, (0,2)->2, (1,0)->3, (1,1)->4, (1,2)->5, (2,0)->6, (2,1)->7, (2,2)->8, (3,0)->9, (3,1)->10, (3,2)->11, (2,4)->12 },
it remains to prove termination of the 52-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  3 0 -> 3 ,
  3 1 -> 4 ,
  3 2 -> 5 ,
  6 0 -> 6 ,
  6 1 -> 7 ,
  6 2 -> 8 ,
  9 0 -> 9 ,
  9 1 -> 10 ,
  9 2 -> 11 ,
  0 1 3 -> 2 6 ,
  0 1 4 -> 2 7 ,
  0 1 5 -> 2 8 ,
  3 1 3 -> 5 6 ,
  3 1 4 -> 5 7 ,
  3 1 5 -> 5 8 ,
  6 1 3 -> 8 6 ,
  6 1 4 -> 8 7 ,
  6 1 5 -> 8 8 ,
  9 1 3 -> 11 6 ,
  9 1 4 -> 11 7 ,
  9 1 5 -> 11 8 ,
  1 3 -> 0 ,
  1 4 -> 1 ,
  1 5 -> 2 ,
  4 3 -> 3 ,
  4 4 -> 4 ,
  4 5 -> 5 ,
  7 3 -> 6 ,
  7 4 -> 7 ,
  7 5 -> 8 ,
  10 3 -> 9 ,
  10 4 -> 10 ,
  10 5 -> 11 ,
  2 8 6 -> 1 4 3 0 2 6 ,
  2 8 7 -> 1 4 3 0 2 7 ,
  2 8 8 -> 1 4 3 0 2 8 ,
  2 8 12 -> 1 4 3 0 2 12 ,
  5 8 6 -> 4 4 3 0 2 6 ,
  5 8 7 -> 4 4 3 0 2 7 ,
  5 8 8 -> 4 4 3 0 2 8 ,
  5 8 12 -> 4 4 3 0 2 12 ,
  8 8 6 -> 7 4 3 0 2 6 ,
  8 8 7 -> 7 4 3 0 2 7 ,
  8 8 8 -> 7 4 3 0 2 8 ,
  8 8 12 -> 7 4 3 0 2 12 ,
  11 8 6 -> 10 4 3 0 2 6 ,
  11 8 7 -> 10 4 3 0 2 7 ,
  11 8 8 -> 10 4 3 0 2 8 ,
  11 8 12 -> 10 4 3 0 2 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 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


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

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

After renaming modulo { 0->0, 1->1, 2->2, 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 28-rule system
{ 0 1 -> 1 ,
  0 2 -> 2 ,
  3 0 -> 3 ,
  3 2 -> 4 ,
  5 0 -> 5 ,
  5 2 -> 6 ,
  7 0 -> 7 ,
  0 1 3 -> 2 5 ,
  0 1 8 -> 2 9 ,
  0 1 4 -> 2 6 ,
  3 1 3 -> 4 5 ,
  3 1 8 -> 4 9 ,
  3 1 4 -> 4 6 ,
  5 1 3 -> 6 5 ,
  5 1 8 -> 6 9 ,
  5 1 4 -> 6 6 ,
  1 8 -> 1 ,
  8 3 -> 3 ,
  8 8 -> 8 ,
  8 4 -> 4 ,
  9 3 -> 5 ,
  9 8 -> 9 ,
  9 4 -> 6 ,
  10 8 -> 10 ,
  2 6 5 -> 1 8 3 0 2 5 ,
  2 6 9 -> 1 8 3 0 2 9 ,
  2 6 6 -> 1 8 3 0 2 6 ,
  2 6 11 -> 1 8 3 0 2 11 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 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 27-rule system
{ 0 1 -> 1 ,
  0 2 -> 2 ,
  3 0 -> 3 ,
  3 2 -> 4 ,
  5 0 -> 5 ,
  5 2 -> 6 ,
  7 0 -> 7 ,
  0 1 3 -> 2 5 ,
  0 1 8 -> 2 9 ,
  0 1 4 -> 2 6 ,
  3 1 3 -> 4 5 ,
  3 1 8 -> 4 9 ,
  3 1 4 -> 4 6 ,
  5 1 3 -> 6 5 ,
  5 1 8 -> 6 9 ,
  5 1 4 -> 6 6 ,
  1 8 -> 1 ,
  8 3 -> 3 ,
  8 4 -> 4 ,
  9 3 -> 5 ,
  9 8 -> 9 ,
  9 4 -> 6 ,
  10 8 -> 10 ,
  2 6 5 -> 1 8 3 0 2 5 ,
  2 6 9 -> 1 8 3 0 2 9 ,
  2 6 6 -> 1 8 3 0 2 6 ,
  2 6 11 -> 1 8 3 0 2 11 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (2,false)->3, (2,true)->4, (3,true)->5, (0,false)->6, (5,true)->7, (7,true)->8, (3,false)->9, (5,false)->10, (8,false)->11, (9,false)->12, (9,true)->13, (4,false)->14, (6,false)->15, (8,true)->16, (10,true)->17, (11,false)->18, (7,false)->19, (10,false)->20 },
it remains to prove termination of the 68-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  5 6 -> 5 ,
  7 6 -> 7 ,
  8 6 -> 8 ,
  0 1 9 -> 4 10 ,
  0 1 9 -> 7 ,
  0 1 11 -> 4 12 ,
  0 1 11 -> 13 ,
  0 1 14 -> 4 15 ,
  5 1 9 -> 7 ,
  5 1 11 -> 13 ,
  7 1 9 -> 7 ,
  7 1 11 -> 13 ,
  2 11 -> 2 ,
  16 9 -> 5 ,
  13 9 -> 7 ,
  13 11 -> 13 ,
  17 11 -> 17 ,
  4 15 10 -> 2 11 9 6 3 10 ,
  4 15 10 -> 16 9 6 3 10 ,
  4 15 10 -> 5 6 3 10 ,
  4 15 10 -> 0 3 10 ,
  4 15 10 -> 4 10 ,
  4 15 10 -> 7 ,
  4 15 12 -> 2 11 9 6 3 12 ,
  4 15 12 -> 16 9 6 3 12 ,
  4 15 12 -> 5 6 3 12 ,
  4 15 12 -> 0 3 12 ,
  4 15 12 -> 4 12 ,
  4 15 12 -> 13 ,
  4 15 15 -> 2 11 9 6 3 15 ,
  4 15 15 -> 16 9 6 3 15 ,
  4 15 15 -> 5 6 3 15 ,
  4 15 15 -> 0 3 15 ,
  4 15 15 -> 4 15 ,
  4 15 18 -> 2 11 9 6 3 18 ,
  4 15 18 -> 16 9 6 3 18 ,
  4 15 18 -> 5 6 3 18 ,
  4 15 18 -> 0 3 18 ,
  4 15 18 -> 4 18 ,
  6 1 ->= 1 ,
  6 3 ->= 3 ,
  9 6 ->= 9 ,
  9 3 ->= 14 ,
  10 6 ->= 10 ,
  10 3 ->= 15 ,
  19 6 ->= 19 ,
  6 1 9 ->= 3 10 ,
  6 1 11 ->= 3 12 ,
  6 1 14 ->= 3 15 ,
  9 1 9 ->= 14 10 ,
  9 1 11 ->= 14 12 ,
  9 1 14 ->= 14 15 ,
  10 1 9 ->= 15 10 ,
  10 1 11 ->= 15 12 ,
  10 1 14 ->= 15 15 ,
  1 11 ->= 1 ,
  11 9 ->= 9 ,
  11 14 ->= 14 ,
  12 9 ->= 10 ,
  12 11 ->= 12 ,
  12 14 ->= 15 ,
  20 11 ->= 20 ,
  3 15 10 ->= 1 11 9 6 3 10 ,
  3 15 12 ->= 1 11 9 6 3 12 ,
  3 15 15 ->= 1 11 9 6 3 15 ,
  3 15 18 ->= 1 11 9 6 3 18 }


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 1 |
| 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 2 |
| 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 1 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
19 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
20 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 6->1, 7->2, 8->3, 2->4, 11->5, 13->6, 17->7, 1->8, 3->9, 9->10, 14->11, 10->12, 15->13, 19->14, 12->15, 20->16, 18->17 }, 
it remains to prove termination of the 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 -> 4 ,
  6 5 -> 6 ,
  7 5 -> 7 ,
  1 8 ->= 8 ,
  1 9 ->= 9 ,
  10 1 ->= 10 ,
  10 9 ->= 11 ,
  12 1 ->= 12 ,
  12 9 ->= 13 ,
  14 1 ->= 14 ,
  1 8 10 ->= 9 12 ,
  1 8 5 ->= 9 15 ,
  1 8 11 ->= 9 13 ,
  10 8 10 ->= 11 12 ,
  10 8 5 ->= 11 15 ,
  10 8 11 ->= 11 13 ,
  12 8 10 ->= 13 12 ,
  12 8 5 ->= 13 15 ,
  12 8 11 ->= 13 13 ,
  8 5 ->= 8 ,
  5 10 ->= 10 ,
  5 11 ->= 11 ,
  15 10 ->= 12 ,
  15 5 ->= 15 ,
  15 11 ->= 13 ,
  16 5 ->= 16 ,
  9 13 12 ->= 8 5 10 1 9 12 ,
  9 13 15 ->= 8 5 10 1 9 15 ,
  9 13 13 ->= 8 5 10 1 9 13 ,
  9 13 17 ->= 8 5 10 1 9 17 }


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
17 is interpreted by
 /     \
| 1 0 0 |
| 0 1 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, 16->15, 17->16 }, 
it remains to prove termination of the 32-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  9 1 ->= 9 ,
  9 8 ->= 10 ,
  11 1 ->= 11 ,
  11 8 ->= 12 ,
  13 1 ->= 13 ,
  1 7 9 ->= 8 11 ,
  1 7 4 ->= 8 14 ,
  1 7 10 ->= 8 12 ,
  9 7 9 ->= 10 11 ,
  9 7 4 ->= 10 14 ,
  9 7 10 ->= 10 12 ,
  11 7 9 ->= 12 11 ,
  11 7 4 ->= 12 14 ,
  11 7 10 ->= 12 12 ,
  7 4 ->= 7 ,
  4 9 ->= 9 ,
  4 10 ->= 10 ,
  14 9 ->= 11 ,
  14 4 ->= 14 ,
  14 10 ->= 12 ,
  15 4 ->= 15 ,
  8 12 11 ->= 7 4 9 1 8 11 ,
  8 12 14 ->= 7 4 9 1 8 14 ,
  8 12 12 ->= 7 4 9 1 8 12 ,
  8 12 16 ->= 7 4 9 1 8 16 }


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
14 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
15 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
16 is interpreted by
 /     \
| 1 0 0 |
| 0 1 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, 16->15 }, 
it remains to prove termination of the 31-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 ,
  4 3 -> 4 ,
  5 3 -> 5 ,
  1 6 ->= 6 ,
  1 7 ->= 7 ,
  8 1 ->= 8 ,
  8 7 ->= 9 ,
  10 1 ->= 10 ,
  10 7 ->= 11 ,
  12 1 ->= 12 ,
  1 6 8 ->= 7 10 ,
  1 6 3 ->= 7 13 ,
  1 6 9 ->= 7 11 ,
  8 6 8 ->= 9 10 ,
  8 6 3 ->= 9 13 ,
  8 6 9 ->= 9 11 ,
  10 6 8 ->= 11 10 ,
  10 6 3 ->= 11 13 ,
  10 6 9 ->= 11 11 ,
  6 3 ->= 6 ,
  3 8 ->= 8 ,
  3 9 ->= 9 ,
  13 8 ->= 10 ,
  13 3 ->= 13 ,
  13 9 ->= 11 ,
  14 3 ->= 14 ,
  7 11 10 ->= 6 3 8 1 7 10 ,
  7 11 13 ->= 6 3 8 1 7 13 ,
  7 11 11 ->= 6 3 8 1 7 11 ,
  7 11 15 ->= 6 3 8 1 7 15 }


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

After renaming modulo { 2->0, 3->1, 4->2, 5->3, 1->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 30-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 ->= 5 ,
  4 6 ->= 6 ,
  7 4 ->= 7 ,
  7 6 ->= 8 ,
  9 4 ->= 9 ,
  9 6 ->= 10 ,
  11 4 ->= 11 ,
  4 5 7 ->= 6 9 ,
  4 5 1 ->= 6 12 ,
  4 5 8 ->= 6 10 ,
  7 5 7 ->= 8 9 ,
  7 5 1 ->= 8 12 ,
  7 5 8 ->= 8 10 ,
  9 5 7 ->= 10 9 ,
  9 5 1 ->= 10 12 ,
  9 5 8 ->= 10 10 ,
  5 1 ->= 5 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  12 7 ->= 9 ,
  12 1 ->= 12 ,
  12 8 ->= 10 ,
  13 1 ->= 13 ,
  6 10 9 ->= 5 1 7 4 6 9 ,
  6 10 12 ->= 5 1 7 4 6 12 ,
  6 10 10 ->= 5 1 7 4 6 10 ,
  6 10 14 ->= 5 1 7 4 6 14 }


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


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 1 |
| 0 1 0 |
| 0 1 0 |
 \     /
2 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
6 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
7 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
8 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
9 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
10 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
11 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
12 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
13 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 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 }, 
it remains to prove termination of the 28-rule system
{ 0 1 -> 0 ,
  2 3 ->= 3 ,
  2 4 ->= 4 ,
  5 2 ->= 5 ,
  5 4 ->= 6 ,
  7 2 ->= 7 ,
  7 4 ->= 8 ,
  9 2 ->= 9 ,
  2 3 5 ->= 4 7 ,
  2 3 1 ->= 4 10 ,
  2 3 6 ->= 4 8 ,
  5 3 5 ->= 6 7 ,
  5 3 1 ->= 6 10 ,
  5 3 6 ->= 6 8 ,
  7 3 5 ->= 8 7 ,
  7 3 1 ->= 8 10 ,
  7 3 6 ->= 8 8 ,
  3 1 ->= 3 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  10 5 ->= 7 ,
  10 1 ->= 10 ,
  10 6 ->= 8 ,
  11 1 ->= 11 ,
  4 8 7 ->= 3 1 5 2 4 7 ,
  4 8 10 ->= 3 1 5 2 4 10 ,
  4 8 8 ->= 3 1 5 2 4 8 ,
  4 8 12 ->= 3 1 5 2 4 12 }


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

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

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

The system is trivially terminating.