YES

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

After renaming modulo { 8->0, 1->1, 9->2, 2->3, 10->4, 4->5, 0->6, 5->7, 6->8, 3->9, 7->10, 13->11 }, 
it remains to prove termination of the 27-rule system
{ 0 1 -> 2 ,
  0 3 -> 4 ,
  1 5 6 -> 3 0 1 5 ,
  1 5 1 -> 3 0 1 7 ,
  1 5 3 -> 3 0 1 8 ,
  1 5 9 -> 3 0 1 10 ,
  7 5 6 -> 8 0 1 5 ,
  7 5 1 -> 8 0 1 7 ,
  7 5 3 -> 8 0 1 8 ,
  7 5 9 -> 8 0 1 10 ,
  2 5 6 -> 4 0 1 5 ,
  2 5 1 -> 4 0 1 7 ,
  2 5 3 -> 4 0 1 8 ,
  2 5 9 -> 4 0 1 10 ,
  1 5 -> 6 ,
  1 7 -> 1 ,
  1 8 -> 3 ,
  1 10 -> 9 ,
  7 5 -> 5 ,
  7 7 -> 7 ,
  7 8 -> 8 ,
  7 10 -> 10 ,
  2 7 -> 2 ,
  2 8 -> 4 ,
  11 7 -> 11 ,
  3 4 0 -> 6 1 7 5 ,
  8 4 0 -> 5 1 7 5 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (1,true)->3, (5,false)->4, (6,false)->5, (3,true)->6, (0,false)->7, (7,false)->8, (7,true)->9, (3,false)->10, (8,false)->11, (8,true)->12, (9,false)->13, (10,false)->14, (11,true)->15, (4,false)->16, (2,false)->17, (11,false)->18 },
it remains to prove termination of the 76-rule system
{ 0 1 -> 2 ,
  3 4 5 -> 6 7 1 4 ,
  3 4 5 -> 0 1 4 ,
  3 4 5 -> 3 4 ,
  3 4 1 -> 6 7 1 8 ,
  3 4 1 -> 0 1 8 ,
  3 4 1 -> 3 8 ,
  3 4 1 -> 9 ,
  3 4 10 -> 6 7 1 11 ,
  3 4 10 -> 0 1 11 ,
  3 4 10 -> 3 11 ,
  3 4 10 -> 12 ,
  3 4 13 -> 6 7 1 14 ,
  3 4 13 -> 0 1 14 ,
  3 4 13 -> 3 14 ,
  9 4 5 -> 12 7 1 4 ,
  9 4 5 -> 0 1 4 ,
  9 4 5 -> 3 4 ,
  9 4 1 -> 12 7 1 8 ,
  9 4 1 -> 0 1 8 ,
  9 4 1 -> 3 8 ,
  9 4 1 -> 9 ,
  9 4 10 -> 12 7 1 11 ,
  9 4 10 -> 0 1 11 ,
  9 4 10 -> 3 11 ,
  9 4 10 -> 12 ,
  9 4 13 -> 12 7 1 14 ,
  9 4 13 -> 0 1 14 ,
  9 4 13 -> 3 14 ,
  2 4 5 -> 0 1 4 ,
  2 4 5 -> 3 4 ,
  2 4 1 -> 0 1 8 ,
  2 4 1 -> 3 8 ,
  2 4 1 -> 9 ,
  2 4 10 -> 0 1 11 ,
  2 4 10 -> 3 11 ,
  2 4 10 -> 12 ,
  2 4 13 -> 0 1 14 ,
  2 4 13 -> 3 14 ,
  3 8 -> 3 ,
  3 11 -> 6 ,
  9 8 -> 9 ,
  9 11 -> 12 ,
  2 8 -> 2 ,
  15 8 -> 15 ,
  6 16 7 -> 3 8 4 ,
  6 16 7 -> 9 4 ,
  12 16 7 -> 3 8 4 ,
  12 16 7 -> 9 4 ,
  7 1 ->= 17 ,
  7 10 ->= 16 ,
  1 4 5 ->= 10 7 1 4 ,
  1 4 1 ->= 10 7 1 8 ,
  1 4 10 ->= 10 7 1 11 ,
  1 4 13 ->= 10 7 1 14 ,
  8 4 5 ->= 11 7 1 4 ,
  8 4 1 ->= 11 7 1 8 ,
  8 4 10 ->= 11 7 1 11 ,
  8 4 13 ->= 11 7 1 14 ,
  17 4 5 ->= 16 7 1 4 ,
  17 4 1 ->= 16 7 1 8 ,
  17 4 10 ->= 16 7 1 11 ,
  17 4 13 ->= 16 7 1 14 ,
  1 4 ->= 5 ,
  1 8 ->= 1 ,
  1 11 ->= 10 ,
  1 14 ->= 13 ,
  8 4 ->= 4 ,
  8 8 ->= 8 ,
  8 11 ->= 11 ,
  8 14 ->= 14 ,
  17 8 ->= 17 ,
  17 11 ->= 16 ,
  18 8 ->= 18 ,
  10 16 7 ->= 5 1 8 4 ,
  11 16 7 ->= 4 1 8 4 }


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 1 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 2 |
| 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 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
11 is interpreted by
 /   \
| 1 1 |
| 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 2 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 3->0, 8->1, 9->2, 2->3, 15->4, 7->5, 1->6, 17->7, 10->8, 16->9, 4->10, 5->11, 11->12, 13->13, 14->14, 18->15 }, 
it remains to prove termination of the 31-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 1 -> 4 ,
  5 6 ->= 7 ,
  5 8 ->= 9 ,
  6 10 11 ->= 8 5 6 10 ,
  6 10 6 ->= 8 5 6 1 ,
  6 10 8 ->= 8 5 6 12 ,
  6 10 13 ->= 8 5 6 14 ,
  1 10 11 ->= 12 5 6 10 ,
  1 10 6 ->= 12 5 6 1 ,
  1 10 8 ->= 12 5 6 12 ,
  1 10 13 ->= 12 5 6 14 ,
  7 10 11 ->= 9 5 6 10 ,
  7 10 6 ->= 9 5 6 1 ,
  7 10 8 ->= 9 5 6 12 ,
  7 10 13 ->= 9 5 6 14 ,
  6 10 ->= 11 ,
  6 1 ->= 6 ,
  6 12 ->= 8 ,
  6 14 ->= 13 ,
  1 10 ->= 10 ,
  1 1 ->= 1 ,
  1 12 ->= 12 ,
  1 14 ->= 14 ,
  7 1 ->= 7 ,
  7 12 ->= 9 ,
  15 1 ->= 15 ,
  8 9 5 ->= 11 6 1 10 ,
  12 9 5 ->= 10 6 1 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 |
 \     /

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 30-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  4 5 ->= 6 ,
  4 7 ->= 8 ,
  5 9 10 ->= 7 4 5 9 ,
  5 9 5 ->= 7 4 5 1 ,
  5 9 7 ->= 7 4 5 11 ,
  5 9 12 ->= 7 4 5 13 ,
  1 9 10 ->= 11 4 5 9 ,
  1 9 5 ->= 11 4 5 1 ,
  1 9 7 ->= 11 4 5 11 ,
  1 9 12 ->= 11 4 5 13 ,
  6 9 10 ->= 8 4 5 9 ,
  6 9 5 ->= 8 4 5 1 ,
  6 9 7 ->= 8 4 5 11 ,
  6 9 12 ->= 8 4 5 13 ,
  5 9 ->= 10 ,
  5 1 ->= 5 ,
  5 11 ->= 7 ,
  5 13 ->= 12 ,
  1 9 ->= 9 ,
  1 1 ->= 1 ,
  1 11 ->= 11 ,
  1 13 ->= 13 ,
  6 1 ->= 6 ,
  6 11 ->= 8 ,
  14 1 ->= 14 ,
  7 8 4 ->= 10 5 1 9 ,
  11 8 4 ->= 9 5 1 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 |
 \     /

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 ->= 5 ,
  3 6 ->= 7 ,
  4 8 9 ->= 6 3 4 8 ,
  4 8 4 ->= 6 3 4 1 ,
  4 8 6 ->= 6 3 4 10 ,
  4 8 11 ->= 6 3 4 12 ,
  1 8 9 ->= 10 3 4 8 ,
  1 8 4 ->= 10 3 4 1 ,
  1 8 6 ->= 10 3 4 10 ,
  1 8 11 ->= 10 3 4 12 ,
  5 8 9 ->= 7 3 4 8 ,
  5 8 4 ->= 7 3 4 1 ,
  5 8 6 ->= 7 3 4 10 ,
  5 8 11 ->= 7 3 4 12 ,
  4 8 ->= 9 ,
  4 1 ->= 4 ,
  4 10 ->= 6 ,
  4 12 ->= 11 ,
  1 8 ->= 8 ,
  1 1 ->= 1 ,
  1 10 ->= 10 ,
  1 12 ->= 12 ,
  5 1 ->= 5 ,
  5 10 ->= 7 ,
  13 1 ->= 13 ,
  6 7 3 ->= 9 4 1 8 ,
  10 7 3 ->= 8 4 1 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 |
 \     /

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 ->= 4 ,
  2 5 ->= 6 ,
  3 7 8 ->= 5 2 3 7 ,
  3 7 3 ->= 5 2 3 1 ,
  3 7 5 ->= 5 2 3 9 ,
  3 7 10 ->= 5 2 3 11 ,
  1 7 8 ->= 9 2 3 7 ,
  1 7 3 ->= 9 2 3 1 ,
  1 7 5 ->= 9 2 3 9 ,
  1 7 10 ->= 9 2 3 11 ,
  4 7 8 ->= 6 2 3 7 ,
  4 7 3 ->= 6 2 3 1 ,
  4 7 5 ->= 6 2 3 9 ,
  4 7 10 ->= 6 2 3 11 ,
  3 7 ->= 8 ,
  3 1 ->= 3 ,
  3 9 ->= 5 ,
  3 11 ->= 10 ,
  1 7 ->= 7 ,
  1 1 ->= 1 ,
  1 9 ->= 9 ,
  1 11 ->= 11 ,
  4 1 ->= 4 ,
  4 9 ->= 6 ,
  12 1 ->= 12 ,
  5 6 2 ->= 8 3 1 7 ,
  9 6 2 ->= 7 3 1 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 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 |
 \     /

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

The system is trivially terminating.