YES

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


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 1 4 -> 2 8 0 2 8 ,
  0 1 5 -> 2 8 0 2 9 ,
  0 1 6 -> 2 8 0 2 10 ,
  0 1 7 -> 2 8 0 2 11 ,
  4 1 4 -> 6 8 0 2 8 ,
  4 1 5 -> 6 8 0 2 9 ,
  4 1 6 -> 6 8 0 2 10 ,
  4 1 7 -> 6 8 0 2 11 ,
  8 1 4 -> 10 8 0 2 8 ,
  8 1 5 -> 10 8 0 2 9 ,
  8 1 6 -> 10 8 0 2 10 ,
  8 1 7 -> 10 8 0 2 11 ,
  12 1 4 -> 14 8 0 2 8 ,
  12 1 5 -> 14 8 0 2 9 ,
  12 1 6 -> 14 8 0 2 10 ,
  12 1 7 -> 14 8 0 2 11 ,
  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 10 8 -> 1 5 4 ,
  2 10 9 -> 1 5 5 ,
  2 10 10 -> 1 5 6 ,
  2 10 11 -> 1 5 7 ,
  6 10 8 -> 5 5 4 ,
  6 10 9 -> 5 5 5 ,
  6 10 10 -> 5 5 6 ,
  6 10 11 -> 5 5 7 ,
  10 10 8 -> 9 5 4 ,
  10 10 9 -> 9 5 5 ,
  10 10 10 -> 9 5 6 ,
  10 10 11 -> 9 5 7 ,
  14 10 8 -> 13 5 4 ,
  14 10 9 -> 13 5 5 ,
  14 10 10 -> 13 5 6 ,
  14 10 11 -> 13 5 7 }


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

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (2,false)->3, (2,true)->4, (4,true)->5, (0,false)->6, (6,true)->7, (8,true)->8, (4,false)->9, (6,false)->10, (9,false)->11, (10,false)->12, (10,true)->13, (5,false)->14, (7,false)->15, (11,false)->16, (12,false)->17, (9,true)->18, (13,true)->19, (3,false)->20, (8,false)->21, (13,false)->22 },
it remains to prove termination of the 101-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  5 6 -> 5 ,
  7 6 -> 7 ,
  8 6 -> 8 ,
  0 1 9 -> 4 10 6 3 10 ,
  0 1 9 -> 7 6 3 10 ,
  0 1 9 -> 0 3 10 ,
  0 1 9 -> 4 10 ,
  0 1 9 -> 7 ,
  0 1 11 -> 4 10 6 3 12 ,
  0 1 11 -> 7 6 3 12 ,
  0 1 11 -> 0 3 12 ,
  0 1 11 -> 4 12 ,
  0 1 11 -> 13 ,
  0 1 14 -> 4 10 6 3 15 ,
  0 1 14 -> 7 6 3 15 ,
  0 1 14 -> 0 3 15 ,
  0 1 14 -> 4 15 ,
  0 1 16 -> 4 10 6 3 17 ,
  0 1 16 -> 7 6 3 17 ,
  0 1 16 -> 0 3 17 ,
  0 1 16 -> 4 17 ,
  5 1 9 -> 7 6 3 10 ,
  5 1 9 -> 0 3 10 ,
  5 1 9 -> 4 10 ,
  5 1 9 -> 7 ,
  5 1 11 -> 7 6 3 12 ,
  5 1 11 -> 0 3 12 ,
  5 1 11 -> 4 12 ,
  5 1 11 -> 13 ,
  5 1 14 -> 7 6 3 15 ,
  5 1 14 -> 0 3 15 ,
  5 1 14 -> 4 15 ,
  5 1 16 -> 7 6 3 17 ,
  5 1 16 -> 0 3 17 ,
  5 1 16 -> 4 17 ,
  7 1 9 -> 7 6 3 10 ,
  7 1 9 -> 0 3 10 ,
  7 1 9 -> 4 10 ,
  7 1 9 -> 7 ,
  7 1 11 -> 7 6 3 12 ,
  7 1 11 -> 0 3 12 ,
  7 1 11 -> 4 12 ,
  7 1 11 -> 13 ,
  7 1 14 -> 7 6 3 15 ,
  7 1 14 -> 0 3 15 ,
  7 1 14 -> 4 15 ,
  7 1 16 -> 7 6 3 17 ,
  7 1 16 -> 0 3 17 ,
  7 1 16 -> 4 17 ,
  2 11 -> 2 ,
  18 9 -> 5 ,
  18 11 -> 18 ,
  13 9 -> 7 ,
  13 11 -> 13 ,
  19 11 -> 19 ,
  4 15 10 -> 2 11 9 ,
  4 15 10 -> 18 9 ,
  4 15 10 -> 5 ,
  4 15 12 -> 2 11 11 ,
  4 15 12 -> 18 11 ,
  4 15 12 -> 18 ,
  4 15 15 -> 2 11 14 ,
  4 15 15 -> 18 14 ,
  4 15 17 -> 2 11 16 ,
  4 15 17 -> 18 16 ,
  6 1 ->= 1 ,
  6 3 ->= 3 ,
  6 20 ->= 20 ,
  9 6 ->= 9 ,
  9 3 ->= 14 ,
  10 6 ->= 10 ,
  10 3 ->= 15 ,
  21 6 ->= 21 ,
  6 1 9 ->= 3 10 6 3 10 ,
  6 1 11 ->= 3 10 6 3 12 ,
  6 1 14 ->= 3 10 6 3 15 ,
  6 1 16 ->= 3 10 6 3 17 ,
  9 1 9 ->= 14 10 6 3 10 ,
  9 1 11 ->= 14 10 6 3 12 ,
  9 1 14 ->= 14 10 6 3 15 ,
  9 1 16 ->= 14 10 6 3 17 ,
  10 1 9 ->= 15 10 6 3 10 ,
  10 1 11 ->= 15 10 6 3 12 ,
  10 1 14 ->= 15 10 6 3 15 ,
  10 1 16 ->= 15 10 6 3 17 ,
  1 11 ->= 1 ,
  11 9 ->= 9 ,
  11 11 ->= 11 ,
  11 14 ->= 14 ,
  11 16 ->= 16 ,
  12 9 ->= 10 ,
  12 11 ->= 12 ,
  12 14 ->= 15 ,
  12 16 ->= 17 ,
  22 11 ->= 22 ,
  3 15 10 ->= 1 11 9 ,
  3 15 12 ->= 1 11 11 ,
  3 15 15 ->= 1 11 14 ,
  3 15 17 ->= 1 11 16 }


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 3 |
| 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 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 2 |
| 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 |
 \   /
21 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
22 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 5->0, 6->1, 7->2, 8->3, 2->4, 11->5, 18->6, 13->7, 19->8, 1->9, 3->10, 20->11, 9->12, 14->13, 10->14, 15->15, 21->16, 12->17, 16->18, 17->19, 22->20 }, 
it remains to prove termination of the 41-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 -> 4 ,
  6 5 -> 6 ,
  7 5 -> 7 ,
  8 5 -> 8 ,
  1 9 ->= 9 ,
  1 10 ->= 10 ,
  1 11 ->= 11 ,
  12 1 ->= 12 ,
  12 10 ->= 13 ,
  14 1 ->= 14 ,
  14 10 ->= 15 ,
  16 1 ->= 16 ,
  1 9 12 ->= 10 14 1 10 14 ,
  1 9 5 ->= 10 14 1 10 17 ,
  1 9 13 ->= 10 14 1 10 15 ,
  1 9 18 ->= 10 14 1 10 19 ,
  12 9 12 ->= 13 14 1 10 14 ,
  12 9 5 ->= 13 14 1 10 17 ,
  12 9 13 ->= 13 14 1 10 15 ,
  12 9 18 ->= 13 14 1 10 19 ,
  14 9 12 ->= 15 14 1 10 14 ,
  14 9 5 ->= 15 14 1 10 17 ,
  14 9 13 ->= 15 14 1 10 15 ,
  14 9 18 ->= 15 14 1 10 19 ,
  9 5 ->= 9 ,
  5 12 ->= 12 ,
  5 5 ->= 5 ,
  5 13 ->= 13 ,
  5 18 ->= 18 ,
  17 12 ->= 14 ,
  17 5 ->= 17 ,
  17 13 ->= 15 ,
  17 18 ->= 19 ,
  20 5 ->= 20 ,
  10 15 14 ->= 9 5 12 ,
  10 15 17 ->= 9 5 5 ,
  10 15 15 ->= 9 5 13 ,
  10 15 19 ->= 9 5 18 }


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 |
 \     /
18 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
19 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
20 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, 18->17, 19->18, 20->19 }, 
it remains to prove termination of the 40-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  7 4 -> 7 ,
  1 8 ->= 8 ,
  1 9 ->= 9 ,
  1 10 ->= 10 ,
  11 1 ->= 11 ,
  11 9 ->= 12 ,
  13 1 ->= 13 ,
  13 9 ->= 14 ,
  15 1 ->= 15 ,
  1 8 11 ->= 9 13 1 9 13 ,
  1 8 4 ->= 9 13 1 9 16 ,
  1 8 12 ->= 9 13 1 9 14 ,
  1 8 17 ->= 9 13 1 9 18 ,
  11 8 11 ->= 12 13 1 9 13 ,
  11 8 4 ->= 12 13 1 9 16 ,
  11 8 12 ->= 12 13 1 9 14 ,
  11 8 17 ->= 12 13 1 9 18 ,
  13 8 11 ->= 14 13 1 9 13 ,
  13 8 4 ->= 14 13 1 9 16 ,
  13 8 12 ->= 14 13 1 9 14 ,
  13 8 17 ->= 14 13 1 9 18 ,
  8 4 ->= 8 ,
  4 11 ->= 11 ,
  4 4 ->= 4 ,
  4 12 ->= 12 ,
  4 17 ->= 17 ,
  16 11 ->= 13 ,
  16 4 ->= 16 ,
  16 12 ->= 14 ,
  16 17 ->= 18 ,
  19 4 ->= 19 ,
  9 14 13 ->= 8 4 11 ,
  9 14 16 ->= 8 4 4 ,
  9 14 14 ->= 8 4 12 ,
  9 14 18 ->= 8 4 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 |
 \     /
18 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
19 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, 18->17, 19->18 }, 
it remains to prove termination of the 39-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 ,
  4 3 -> 4 ,
  5 3 -> 5 ,
  6 3 -> 6 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  1 9 ->= 9 ,
  10 1 ->= 10 ,
  10 8 ->= 11 ,
  12 1 ->= 12 ,
  12 8 ->= 13 ,
  14 1 ->= 14 ,
  1 7 10 ->= 8 12 1 8 12 ,
  1 7 3 ->= 8 12 1 8 15 ,
  1 7 11 ->= 8 12 1 8 13 ,
  1 7 16 ->= 8 12 1 8 17 ,
  10 7 10 ->= 11 12 1 8 12 ,
  10 7 3 ->= 11 12 1 8 15 ,
  10 7 11 ->= 11 12 1 8 13 ,
  10 7 16 ->= 11 12 1 8 17 ,
  12 7 10 ->= 13 12 1 8 12 ,
  12 7 3 ->= 13 12 1 8 15 ,
  12 7 11 ->= 13 12 1 8 13 ,
  12 7 16 ->= 13 12 1 8 17 ,
  7 3 ->= 7 ,
  3 10 ->= 10 ,
  3 3 ->= 3 ,
  3 11 ->= 11 ,
  3 16 ->= 16 ,
  15 10 ->= 12 ,
  15 3 ->= 15 ,
  15 11 ->= 13 ,
  15 16 ->= 17 ,
  18 3 ->= 18 ,
  8 13 12 ->= 7 3 10 ,
  8 13 15 ->= 7 3 3 ,
  8 13 13 ->= 7 3 11 ,
  8 13 17 ->= 7 3 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 |
 \     /
17 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
18 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, 1->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17 }, 
it remains to prove termination of the 38-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 ->= 6 ,
  5 7 ->= 7 ,
  5 8 ->= 8 ,
  9 5 ->= 9 ,
  9 7 ->= 10 ,
  11 5 ->= 11 ,
  11 7 ->= 12 ,
  13 5 ->= 13 ,
  5 6 9 ->= 7 11 5 7 11 ,
  5 6 1 ->= 7 11 5 7 14 ,
  5 6 10 ->= 7 11 5 7 12 ,
  5 6 15 ->= 7 11 5 7 16 ,
  9 6 9 ->= 10 11 5 7 11 ,
  9 6 1 ->= 10 11 5 7 14 ,
  9 6 10 ->= 10 11 5 7 12 ,
  9 6 15 ->= 10 11 5 7 16 ,
  11 6 9 ->= 12 11 5 7 11 ,
  11 6 1 ->= 12 11 5 7 14 ,
  11 6 10 ->= 12 11 5 7 12 ,
  11 6 15 ->= 12 11 5 7 16 ,
  6 1 ->= 6 ,
  1 9 ->= 9 ,
  1 1 ->= 1 ,
  1 10 ->= 10 ,
  1 15 ->= 15 ,
  14 9 ->= 11 ,
  14 1 ->= 14 ,
  14 10 ->= 12 ,
  14 15 ->= 16 ,
  17 1 ->= 17 ,
  7 12 11 ->= 6 1 9 ,
  7 12 14 ->= 6 1 1 ,
  7 12 12 ->= 6 1 10 ,
  7 12 16 ->= 6 1 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 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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 37-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 ->= 5 ,
  4 6 ->= 6 ,
  4 7 ->= 7 ,
  8 4 ->= 8 ,
  8 6 ->= 9 ,
  10 4 ->= 10 ,
  10 6 ->= 11 ,
  12 4 ->= 12 ,
  4 5 8 ->= 6 10 4 6 10 ,
  4 5 1 ->= 6 10 4 6 13 ,
  4 5 9 ->= 6 10 4 6 11 ,
  4 5 14 ->= 6 10 4 6 15 ,
  8 5 8 ->= 9 10 4 6 10 ,
  8 5 1 ->= 9 10 4 6 13 ,
  8 5 9 ->= 9 10 4 6 11 ,
  8 5 14 ->= 9 10 4 6 15 ,
  10 5 8 ->= 11 10 4 6 10 ,
  10 5 1 ->= 11 10 4 6 13 ,
  10 5 9 ->= 11 10 4 6 11 ,
  10 5 14 ->= 11 10 4 6 15 ,
  5 1 ->= 5 ,
  1 8 ->= 8 ,
  1 1 ->= 1 ,
  1 9 ->= 9 ,
  1 14 ->= 14 ,
  13 8 ->= 10 ,
  13 1 ->= 13 ,
  13 9 ->= 11 ,
  13 14 ->= 15 ,
  16 1 ->= 16 ,
  6 11 10 ->= 5 1 8 ,
  6 11 13 ->= 5 1 1 ,
  6 11 11 ->= 5 1 9 ,
  6 11 15 ->= 5 1 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 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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 36-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 4 ->= 4 ,
  3 5 ->= 5 ,
  3 6 ->= 6 ,
  7 3 ->= 7 ,
  7 5 ->= 8 ,
  9 3 ->= 9 ,
  9 5 ->= 10 ,
  11 3 ->= 11 ,
  3 4 7 ->= 5 9 3 5 9 ,
  3 4 1 ->= 5 9 3 5 12 ,
  3 4 8 ->= 5 9 3 5 10 ,
  3 4 13 ->= 5 9 3 5 14 ,
  7 4 7 ->= 8 9 3 5 9 ,
  7 4 1 ->= 8 9 3 5 12 ,
  7 4 8 ->= 8 9 3 5 10 ,
  7 4 13 ->= 8 9 3 5 14 ,
  9 4 7 ->= 10 9 3 5 9 ,
  9 4 1 ->= 10 9 3 5 12 ,
  9 4 8 ->= 10 9 3 5 10 ,
  9 4 13 ->= 10 9 3 5 14 ,
  4 1 ->= 4 ,
  1 7 ->= 7 ,
  1 1 ->= 1 ,
  1 8 ->= 8 ,
  1 13 ->= 13 ,
  12 7 ->= 9 ,
  12 1 ->= 12 ,
  12 8 ->= 10 ,
  12 13 ->= 14 ,
  15 1 ->= 15 ,
  5 10 9 ->= 4 1 7 ,
  5 10 12 ->= 4 1 1 ,
  5 10 10 ->= 4 1 8 ,
  5 10 14 ->= 4 1 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 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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, 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 35-rule system
{ 0 1 -> 0 ,
  2 3 ->= 3 ,
  2 4 ->= 4 ,
  2 5 ->= 5 ,
  6 2 ->= 6 ,
  6 4 ->= 7 ,
  8 2 ->= 8 ,
  8 4 ->= 9 ,
  10 2 ->= 10 ,
  2 3 6 ->= 4 8 2 4 8 ,
  2 3 1 ->= 4 8 2 4 11 ,
  2 3 7 ->= 4 8 2 4 9 ,
  2 3 12 ->= 4 8 2 4 13 ,
  6 3 6 ->= 7 8 2 4 8 ,
  6 3 1 ->= 7 8 2 4 11 ,
  6 3 7 ->= 7 8 2 4 9 ,
  6 3 12 ->= 7 8 2 4 13 ,
  8 3 6 ->= 9 8 2 4 8 ,
  8 3 1 ->= 9 8 2 4 11 ,
  8 3 7 ->= 9 8 2 4 9 ,
  8 3 12 ->= 9 8 2 4 13 ,
  3 1 ->= 3 ,
  1 6 ->= 6 ,
  1 1 ->= 1 ,
  1 7 ->= 7 ,
  1 12 ->= 12 ,
  11 6 ->= 8 ,
  11 1 ->= 11 ,
  11 7 ->= 9 ,
  11 12 ->= 13 ,
  14 1 ->= 14 ,
  4 9 8 ->= 3 1 6 ,
  4 9 11 ->= 3 1 1 ,
  4 9 9 ->= 3 1 7 ,
  4 9 13 ->= 3 1 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 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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, 3->1, 4->2, 5->3, 6->4, 7->5, 8->6, 9->7, 10->8, 1->9, 11->10, 12->11, 13->12, 14->13 }, 
it remains to prove termination of the 34-rule system
{ 0 1 ->= 1 ,
  0 2 ->= 2 ,
  0 3 ->= 3 ,
  4 0 ->= 4 ,
  4 2 ->= 5 ,
  6 0 ->= 6 ,
  6 2 ->= 7 ,
  8 0 ->= 8 ,
  0 1 4 ->= 2 6 0 2 6 ,
  0 1 9 ->= 2 6 0 2 10 ,
  0 1 5 ->= 2 6 0 2 7 ,
  0 1 11 ->= 2 6 0 2 12 ,
  4 1 4 ->= 5 6 0 2 6 ,
  4 1 9 ->= 5 6 0 2 10 ,
  4 1 5 ->= 5 6 0 2 7 ,
  4 1 11 ->= 5 6 0 2 12 ,
  6 1 4 ->= 7 6 0 2 6 ,
  6 1 9 ->= 7 6 0 2 10 ,
  6 1 5 ->= 7 6 0 2 7 ,
  6 1 11 ->= 7 6 0 2 12 ,
  1 9 ->= 1 ,
  9 4 ->= 4 ,
  9 9 ->= 9 ,
  9 5 ->= 5 ,
  9 11 ->= 11 ,
  10 4 ->= 6 ,
  10 9 ->= 10 ,
  10 5 ->= 7 ,
  10 11 ->= 12 ,
  13 9 ->= 13 ,
  2 7 6 ->= 1 9 4 ,
  2 7 10 ->= 1 9 9 ,
  2 7 7 ->= 1 9 5 ,
  2 7 12 ->= 1 9 11 }

The system is trivially terminating.