YES

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


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 ,
  1 4 0 -> 2 9 5 6 8 0 ,
  1 4 1 -> 2 9 5 6 8 1 ,
  1 4 2 -> 2 9 5 6 8 2 ,
  1 4 3 -> 2 9 5 6 8 3 ,
  5 4 0 -> 6 9 5 6 8 0 ,
  5 4 1 -> 6 9 5 6 8 1 ,
  5 4 2 -> 6 9 5 6 8 2 ,
  5 4 3 -> 6 9 5 6 8 3 ,
  9 4 0 -> 10 9 5 6 8 0 ,
  9 4 1 -> 10 9 5 6 8 1 ,
  9 4 2 -> 10 9 5 6 8 2 ,
  9 4 3 -> 10 9 5 6 8 3 ,
  13 4 0 -> 14 9 5 6 8 0 ,
  13 4 1 -> 14 9 5 6 8 1 ,
  13 4 2 -> 14 9 5 6 8 2 ,
  13 4 3 -> 14 9 5 6 8 3 ,
  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 -> 0 0 ,
  2 10 9 -> 0 1 ,
  2 10 10 -> 0 2 ,
  2 10 11 -> 0 3 ,
  6 10 8 -> 4 0 ,
  6 10 9 -> 4 1 ,
  6 10 10 -> 4 2 ,
  6 10 11 -> 4 3 ,
  10 10 8 -> 8 0 ,
  10 10 9 -> 8 1 ,
  10 10 10 -> 8 2 ,
  10 10 11 -> 8 3 ,
  14 10 8 -> 12 0 ,
  14 10 9 -> 12 1 ,
  14 10 10 -> 12 2 ,
  14 10 11 -> 12 3 }


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 2 |
| 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 2 |
| 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, 8->5, 9->6, 10->7, 11->8, 12->9, 5->10, 6->11, 7->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 ,
  5 0 -> 5 ,
  5 1 -> 6 ,
  5 2 -> 7 ,
  5 3 -> 8 ,
  9 0 -> 9 ,
  1 4 0 -> 2 6 10 11 5 0 ,
  1 4 1 -> 2 6 10 11 5 1 ,
  1 4 2 -> 2 6 10 11 5 2 ,
  1 4 3 -> 2 6 10 11 5 3 ,
  10 4 0 -> 11 6 10 11 5 0 ,
  10 4 1 -> 11 6 10 11 5 1 ,
  10 4 2 -> 11 6 10 11 5 2 ,
  10 4 3 -> 11 6 10 11 5 3 ,
  6 4 0 -> 7 6 10 11 5 0 ,
  6 4 1 -> 7 6 10 11 5 1 ,
  6 4 2 -> 7 6 10 11 5 2 ,
  6 4 3 -> 7 6 10 11 5 3 ,
  1 10 -> 1 ,
  1 11 -> 2 ,
  10 4 -> 4 ,
  10 10 -> 10 ,
  10 11 -> 11 ,
  10 12 -> 12 ,
  6 10 -> 6 ,
  6 11 -> 7 ,
  13 10 -> 13 ,
  11 7 5 -> 4 0 ,
  11 7 6 -> 4 1 ,
  11 7 7 -> 4 2 ,
  11 7 8 -> 4 3 }


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 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 1 |
| 0 1 0 |
| 0 1 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 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  5 0 -> 5 ,
  5 1 -> 6 ,
  5 2 -> 7 ,
  5 3 -> 8 ,
  9 0 -> 9 ,
  1 4 0 -> 2 6 10 11 5 0 ,
  1 4 1 -> 2 6 10 11 5 1 ,
  1 4 2 -> 2 6 10 11 5 2 ,
  1 4 3 -> 2 6 10 11 5 3 ,
  10 4 0 -> 11 6 10 11 5 0 ,
  10 4 1 -> 11 6 10 11 5 1 ,
  10 4 2 -> 11 6 10 11 5 2 ,
  10 4 3 -> 11 6 10 11 5 3 ,
  6 4 0 -> 7 6 10 11 5 0 ,
  6 4 1 -> 7 6 10 11 5 1 ,
  6 4 2 -> 7 6 10 11 5 2 ,
  6 4 3 -> 7 6 10 11 5 3 ,
  1 10 -> 1 ,
  1 11 -> 2 ,
  10 4 -> 4 ,
  10 11 -> 11 ,
  10 12 -> 12 ,
  6 10 -> 6 ,
  6 11 -> 7 ,
  13 10 -> 13 ,
  11 7 5 -> 4 0 ,
  11 7 6 -> 4 1 ,
  11 7 7 -> 4 2 ,
  11 7 8 -> 4 3 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (1,true)->3, (4,true)->4, (5,true)->5, (6,true)->6, (9,true)->7, (4,false)->8, (10,false)->9, (11,false)->10, (5,false)->11, (10,true)->12, (11,true)->13, (2,false)->14, (3,false)->15, (6,false)->16, (13,true)->17, (7,false)->18, (8,false)->19, (9,false)->20, (12,false)->21, (13,false)->22 },
it remains to prove termination of the 109-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  3 8 1 -> 6 9 10 11 1 ,
  3 8 1 -> 12 10 11 1 ,
  3 8 1 -> 13 11 1 ,
  3 8 1 -> 5 1 ,
  3 8 1 -> 0 ,
  3 8 2 -> 6 9 10 11 2 ,
  3 8 2 -> 12 10 11 2 ,
  3 8 2 -> 13 11 2 ,
  3 8 2 -> 5 2 ,
  3 8 2 -> 3 ,
  3 8 14 -> 6 9 10 11 14 ,
  3 8 14 -> 12 10 11 14 ,
  3 8 14 -> 13 11 14 ,
  3 8 14 -> 5 14 ,
  3 8 15 -> 6 9 10 11 15 ,
  3 8 15 -> 12 10 11 15 ,
  3 8 15 -> 13 11 15 ,
  3 8 15 -> 5 15 ,
  12 8 1 -> 13 16 9 10 11 1 ,
  12 8 1 -> 6 9 10 11 1 ,
  12 8 1 -> 12 10 11 1 ,
  12 8 1 -> 13 11 1 ,
  12 8 1 -> 5 1 ,
  12 8 1 -> 0 ,
  12 8 2 -> 13 16 9 10 11 2 ,
  12 8 2 -> 6 9 10 11 2 ,
  12 8 2 -> 12 10 11 2 ,
  12 8 2 -> 13 11 2 ,
  12 8 2 -> 5 2 ,
  12 8 2 -> 3 ,
  12 8 14 -> 13 16 9 10 11 14 ,
  12 8 14 -> 6 9 10 11 14 ,
  12 8 14 -> 12 10 11 14 ,
  12 8 14 -> 13 11 14 ,
  12 8 14 -> 5 14 ,
  12 8 15 -> 13 16 9 10 11 15 ,
  12 8 15 -> 6 9 10 11 15 ,
  12 8 15 -> 12 10 11 15 ,
  12 8 15 -> 13 11 15 ,
  12 8 15 -> 5 15 ,
  6 8 1 -> 6 9 10 11 1 ,
  6 8 1 -> 12 10 11 1 ,
  6 8 1 -> 13 11 1 ,
  6 8 1 -> 5 1 ,
  6 8 1 -> 0 ,
  6 8 2 -> 6 9 10 11 2 ,
  6 8 2 -> 12 10 11 2 ,
  6 8 2 -> 13 11 2 ,
  6 8 2 -> 5 2 ,
  6 8 2 -> 3 ,
  6 8 14 -> 6 9 10 11 14 ,
  6 8 14 -> 12 10 11 14 ,
  6 8 14 -> 13 11 14 ,
  6 8 14 -> 5 14 ,
  6 8 15 -> 6 9 10 11 15 ,
  6 8 15 -> 12 10 11 15 ,
  6 8 15 -> 13 11 15 ,
  6 8 15 -> 5 15 ,
  3 9 -> 3 ,
  12 8 -> 4 ,
  12 10 -> 13 ,
  6 9 -> 6 ,
  17 9 -> 17 ,
  13 18 11 -> 4 1 ,
  13 18 11 -> 0 ,
  13 18 16 -> 4 2 ,
  13 18 16 -> 3 ,
  13 18 18 -> 4 14 ,
  13 18 19 -> 4 15 ,
  1 1 ->= 1 ,
  1 2 ->= 2 ,
  1 14 ->= 14 ,
  1 15 ->= 15 ,
  8 1 ->= 8 ,
  11 1 ->= 11 ,
  11 2 ->= 16 ,
  11 14 ->= 18 ,
  11 15 ->= 19 ,
  20 1 ->= 20 ,
  2 8 1 ->= 14 16 9 10 11 1 ,
  2 8 2 ->= 14 16 9 10 11 2 ,
  2 8 14 ->= 14 16 9 10 11 14 ,
  2 8 15 ->= 14 16 9 10 11 15 ,
  9 8 1 ->= 10 16 9 10 11 1 ,
  9 8 2 ->= 10 16 9 10 11 2 ,
  9 8 14 ->= 10 16 9 10 11 14 ,
  9 8 15 ->= 10 16 9 10 11 15 ,
  16 8 1 ->= 18 16 9 10 11 1 ,
  16 8 2 ->= 18 16 9 10 11 2 ,
  16 8 14 ->= 18 16 9 10 11 14 ,
  16 8 15 ->= 18 16 9 10 11 15 ,
  2 9 ->= 2 ,
  2 10 ->= 14 ,
  9 8 ->= 8 ,
  9 10 ->= 10 ,
  9 21 ->= 21 ,
  16 9 ->= 16 ,
  16 10 ->= 18 ,
  22 9 ->= 22 ,
  10 18 11 ->= 8 1 ,
  10 18 16 ->= 8 2 ,
  10 18 18 ->= 8 14 ,
  10 18 19 ->= 8 15 }


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


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 |
 \     /
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 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  1 1 ->= 1 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  1 9 ->= 9 ,
  10 1 ->= 10 ,
  11 1 ->= 11 ,
  11 7 ->= 12 ,
  11 8 ->= 13 ,
  11 9 ->= 14 ,
  15 1 ->= 15 ,
  7 10 1 ->= 8 12 4 16 11 1 ,
  7 10 7 ->= 8 12 4 16 11 7 ,
  7 10 8 ->= 8 12 4 16 11 8 ,
  7 10 9 ->= 8 12 4 16 11 9 ,
  4 10 1 ->= 16 12 4 16 11 1 ,
  4 10 7 ->= 16 12 4 16 11 7 ,
  4 10 8 ->= 16 12 4 16 11 8 ,
  4 10 9 ->= 16 12 4 16 11 9 ,
  12 10 1 ->= 13 12 4 16 11 1 ,
  12 10 7 ->= 13 12 4 16 11 7 ,
  12 10 8 ->= 13 12 4 16 11 8 ,
  12 10 9 ->= 13 12 4 16 11 9 ,
  7 4 ->= 7 ,
  7 16 ->= 8 ,
  4 10 ->= 10 ,
  4 16 ->= 16 ,
  4 17 ->= 17 ,
  12 4 ->= 12 ,
  12 16 ->= 13 ,
  18 4 ->= 18 ,
  16 13 11 ->= 10 1 ,
  16 13 12 ->= 10 7 ,
  16 13 13 ->= 10 8 ,
  16 13 14 ->= 10 9 }


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 |
 \     /
18 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 }, 
it remains to prove termination of the 38-rule system
{ 0 1 -> 0 ,
  2 3 -> 2 ,
  4 3 -> 4 ,
  5 3 -> 5 ,
  1 1 ->= 1 ,
  1 6 ->= 6 ,
  1 7 ->= 7 ,
  1 8 ->= 8 ,
  9 1 ->= 9 ,
  10 1 ->= 10 ,
  10 6 ->= 11 ,
  10 7 ->= 12 ,
  10 8 ->= 13 ,
  14 1 ->= 14 ,
  6 9 1 ->= 7 11 3 15 10 1 ,
  6 9 6 ->= 7 11 3 15 10 6 ,
  6 9 7 ->= 7 11 3 15 10 7 ,
  6 9 8 ->= 7 11 3 15 10 8 ,
  3 9 1 ->= 15 11 3 15 10 1 ,
  3 9 6 ->= 15 11 3 15 10 6 ,
  3 9 7 ->= 15 11 3 15 10 7 ,
  3 9 8 ->= 15 11 3 15 10 8 ,
  11 9 1 ->= 12 11 3 15 10 1 ,
  11 9 6 ->= 12 11 3 15 10 6 ,
  11 9 7 ->= 12 11 3 15 10 7 ,
  11 9 8 ->= 12 11 3 15 10 8 ,
  6 3 ->= 6 ,
  6 15 ->= 7 ,
  3 9 ->= 9 ,
  3 15 ->= 15 ,
  3 16 ->= 16 ,
  11 3 ->= 11 ,
  11 15 ->= 12 ,
  17 3 ->= 17 ,
  15 12 10 ->= 9 1 ,
  15 12 11 ->= 9 6 ,
  15 12 12 ->= 9 7 ,
  15 12 13 ->= 9 8 }


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, 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, 16->15, 17->16 }, 
it remains to prove termination of the 37-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 4 ->= 4 ,
  4 5 ->= 5 ,
  4 6 ->= 6 ,
  4 7 ->= 7 ,
  8 4 ->= 8 ,
  9 4 ->= 9 ,
  9 5 ->= 10 ,
  9 6 ->= 11 ,
  9 7 ->= 12 ,
  13 4 ->= 13 ,
  5 8 4 ->= 6 10 1 14 9 4 ,
  5 8 5 ->= 6 10 1 14 9 5 ,
  5 8 6 ->= 6 10 1 14 9 6 ,
  5 8 7 ->= 6 10 1 14 9 7 ,
  1 8 4 ->= 14 10 1 14 9 4 ,
  1 8 5 ->= 14 10 1 14 9 5 ,
  1 8 6 ->= 14 10 1 14 9 6 ,
  1 8 7 ->= 14 10 1 14 9 7 ,
  10 8 4 ->= 11 10 1 14 9 4 ,
  10 8 5 ->= 11 10 1 14 9 5 ,
  10 8 6 ->= 11 10 1 14 9 6 ,
  10 8 7 ->= 11 10 1 14 9 7 ,
  5 1 ->= 5 ,
  5 14 ->= 6 ,
  1 8 ->= 8 ,
  1 14 ->= 14 ,
  1 15 ->= 15 ,
  10 1 ->= 10 ,
  10 14 ->= 11 ,
  16 1 ->= 16 ,
  14 11 9 ->= 8 4 ,
  14 11 10 ->= 8 5 ,
  14 11 11 ->= 8 6 ,
  14 11 12 ->= 8 7 }


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 36-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 3 ->= 3 ,
  3 4 ->= 4 ,
  3 5 ->= 5 ,
  3 6 ->= 6 ,
  7 3 ->= 7 ,
  8 3 ->= 8 ,
  8 4 ->= 9 ,
  8 5 ->= 10 ,
  8 6 ->= 11 ,
  12 3 ->= 12 ,
  4 7 3 ->= 5 9 1 13 8 3 ,
  4 7 4 ->= 5 9 1 13 8 4 ,
  4 7 5 ->= 5 9 1 13 8 5 ,
  4 7 6 ->= 5 9 1 13 8 6 ,
  1 7 3 ->= 13 9 1 13 8 3 ,
  1 7 4 ->= 13 9 1 13 8 4 ,
  1 7 5 ->= 13 9 1 13 8 5 ,
  1 7 6 ->= 13 9 1 13 8 6 ,
  9 7 3 ->= 10 9 1 13 8 3 ,
  9 7 4 ->= 10 9 1 13 8 4 ,
  9 7 5 ->= 10 9 1 13 8 5 ,
  9 7 6 ->= 10 9 1 13 8 6 ,
  4 1 ->= 4 ,
  4 13 ->= 5 ,
  1 7 ->= 7 ,
  1 13 ->= 13 ,
  1 14 ->= 14 ,
  9 1 ->= 9 ,
  9 13 ->= 10 ,
  15 1 ->= 15 ,
  13 10 8 ->= 7 3 ,
  13 10 9 ->= 7 4 ,
  13 10 10 ->= 7 5 ,
  13 10 11 ->= 7 6 }


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, 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 2 ->= 2 ,
  2 3 ->= 3 ,
  2 4 ->= 4 ,
  2 5 ->= 5 ,
  6 2 ->= 6 ,
  7 2 ->= 7 ,
  7 3 ->= 8 ,
  7 4 ->= 9 ,
  7 5 ->= 10 ,
  11 2 ->= 11 ,
  3 6 2 ->= 4 8 1 12 7 2 ,
  3 6 3 ->= 4 8 1 12 7 3 ,
  3 6 4 ->= 4 8 1 12 7 4 ,
  3 6 5 ->= 4 8 1 12 7 5 ,
  1 6 2 ->= 12 8 1 12 7 2 ,
  1 6 3 ->= 12 8 1 12 7 3 ,
  1 6 4 ->= 12 8 1 12 7 4 ,
  1 6 5 ->= 12 8 1 12 7 5 ,
  8 6 2 ->= 9 8 1 12 7 2 ,
  8 6 3 ->= 9 8 1 12 7 3 ,
  8 6 4 ->= 9 8 1 12 7 4 ,
  8 6 5 ->= 9 8 1 12 7 5 ,
  3 1 ->= 3 ,
  3 12 ->= 4 ,
  1 6 ->= 6 ,
  1 12 ->= 12 ,
  1 13 ->= 13 ,
  8 1 ->= 8 ,
  8 12 ->= 9 ,
  14 1 ->= 14 ,
  12 9 7 ->= 6 2 ,
  12 9 8 ->= 6 3 ,
  12 9 9 ->= 6 4 ,
  12 9 10 ->= 6 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 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, 3->1, 4->2, 5->3, 6->4, 7->5, 8->6, 9->7, 10->8, 11->9, 1->10, 12->11, 13->12, 14->13 }, 
it remains to prove termination of the 34-rule system
{ 0 0 ->= 0 ,
  0 1 ->= 1 ,
  0 2 ->= 2 ,
  0 3 ->= 3 ,
  4 0 ->= 4 ,
  5 0 ->= 5 ,
  5 1 ->= 6 ,
  5 2 ->= 7 ,
  5 3 ->= 8 ,
  9 0 ->= 9 ,
  1 4 0 ->= 2 6 10 11 5 0 ,
  1 4 1 ->= 2 6 10 11 5 1 ,
  1 4 2 ->= 2 6 10 11 5 2 ,
  1 4 3 ->= 2 6 10 11 5 3 ,
  10 4 0 ->= 11 6 10 11 5 0 ,
  10 4 1 ->= 11 6 10 11 5 1 ,
  10 4 2 ->= 11 6 10 11 5 2 ,
  10 4 3 ->= 11 6 10 11 5 3 ,
  6 4 0 ->= 7 6 10 11 5 0 ,
  6 4 1 ->= 7 6 10 11 5 1 ,
  6 4 2 ->= 7 6 10 11 5 2 ,
  6 4 3 ->= 7 6 10 11 5 3 ,
  1 10 ->= 1 ,
  1 11 ->= 2 ,
  10 4 ->= 4 ,
  10 11 ->= 11 ,
  10 12 ->= 12 ,
  6 10 ->= 6 ,
  6 11 ->= 7 ,
  13 10 ->= 13 ,
  11 7 5 ->= 4 0 ,
  11 7 6 ->= 4 1 ,
  11 7 7 ->= 4 2 ,
  11 7 8 ->= 4 3 }

The system is trivially terminating.