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 ,
  1 -> 0 0 2 ,
  2 2 -> 1 }


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, (1,4)->12, (2,4)->13 },
it remains to prove termination of the 60-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 7 3 ,
  0 1 4 -> 2 7 4 ,
  0 1 5 -> 2 7 5 ,
  0 1 12 -> 2 7 12 ,
  3 1 3 -> 5 7 3 ,
  3 1 4 -> 5 7 4 ,
  3 1 5 -> 5 7 5 ,
  3 1 12 -> 5 7 12 ,
  6 1 3 -> 8 7 3 ,
  6 1 4 -> 8 7 4 ,
  6 1 5 -> 8 7 5 ,
  6 1 12 -> 8 7 12 ,
  9 1 3 -> 11 7 3 ,
  9 1 4 -> 11 7 4 ,
  9 1 5 -> 11 7 5 ,
  9 1 12 -> 11 7 12 ,
  1 3 -> 0 0 2 6 ,
  1 4 -> 0 0 2 7 ,
  1 5 -> 0 0 2 8 ,
  1 12 -> 0 0 2 13 ,
  4 3 -> 3 0 2 6 ,
  4 4 -> 3 0 2 7 ,
  4 5 -> 3 0 2 8 ,
  4 12 -> 3 0 2 13 ,
  7 3 -> 6 0 2 6 ,
  7 4 -> 6 0 2 7 ,
  7 5 -> 6 0 2 8 ,
  7 12 -> 6 0 2 13 ,
  10 3 -> 9 0 2 6 ,
  10 4 -> 9 0 2 7 ,
  10 5 -> 9 0 2 8 ,
  10 12 -> 9 0 2 13 ,
  2 8 6 -> 1 3 ,
  2 8 7 -> 1 4 ,
  2 8 8 -> 1 5 ,
  2 8 13 -> 1 12 ,
  5 8 6 -> 4 3 ,
  5 8 7 -> 4 4 ,
  5 8 8 -> 4 5 ,
  5 8 13 -> 4 12 ,
  8 8 6 -> 7 3 ,
  8 8 7 -> 7 4 ,
  8 8 8 -> 7 5 ,
  8 8 13 -> 7 12 ,
  11 8 6 -> 10 3 ,
  11 8 7 -> 10 4 ,
  11 8 8 -> 10 5 ,
  11 8 13 -> 10 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 4 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 2 |
| 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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5, 8->6, 9->7, 7->8, 4->9, 12->10, 13->11 }, 
it remains to prove termination of the 32-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 8 3 ,
  0 1 9 -> 2 8 9 ,
  0 1 4 -> 2 8 4 ,
  0 1 10 -> 2 8 10 ,
  3 1 3 -> 4 8 3 ,
  3 1 9 -> 4 8 9 ,
  3 1 4 -> 4 8 4 ,
  3 1 10 -> 4 8 10 ,
  5 1 3 -> 6 8 3 ,
  5 1 9 -> 6 8 9 ,
  5 1 4 -> 6 8 4 ,
  5 1 10 -> 6 8 10 ,
  9 3 -> 3 0 2 5 ,
  9 9 -> 3 0 2 8 ,
  9 4 -> 3 0 2 6 ,
  9 10 -> 3 0 2 11 ,
  8 3 -> 5 0 2 5 ,
  8 9 -> 5 0 2 8 ,
  8 4 -> 5 0 2 6 ,
  8 10 -> 5 0 2 11 ,
  2 6 5 -> 1 3 ,
  2 6 8 -> 1 9 ,
  2 6 6 -> 1 4 ,
  2 6 11 -> 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 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 31-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 8 3 ,
  0 1 9 -> 2 8 9 ,
  0 1 4 -> 2 8 4 ,
  0 1 10 -> 2 8 10 ,
  3 1 3 -> 4 8 3 ,
  3 1 9 -> 4 8 9 ,
  3 1 4 -> 4 8 4 ,
  3 1 10 -> 4 8 10 ,
  5 1 3 -> 6 8 3 ,
  5 1 9 -> 6 8 9 ,
  5 1 4 -> 6 8 4 ,
  5 1 10 -> 6 8 10 ,
  9 3 -> 3 0 2 5 ,
  9 9 -> 3 0 2 8 ,
  9 4 -> 3 0 2 6 ,
  9 10 -> 3 0 2 11 ,
  8 3 -> 5 0 2 5 ,
  8 9 -> 5 0 2 8 ,
  8 4 -> 5 0 2 6 ,
  8 10 -> 5 0 2 11 ,
  2 6 5 -> 1 3 ,
  2 6 8 -> 1 9 ,
  2 6 6 -> 1 4 ,
  2 6 11 -> 1 10 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (2,false)->1, (2,true)->2, (3,true)->3, (0,false)->4, (5,true)->5, (7,true)->6, (1,false)->7, (3,false)->8, (8,false)->9, (8,true)->10, (9,false)->11, (9,true)->12, (4,false)->13, (10,false)->14, (5,false)->15, (6,false)->16, (11,false)->17, (7,false)->18 },
it remains to prove termination of the 87-rule system
{ 0 1 -> 2 ,
  3 4 -> 3 ,
  5 4 -> 5 ,
  6 4 -> 6 ,
  0 7 8 -> 2 9 8 ,
  0 7 8 -> 10 8 ,
  0 7 8 -> 3 ,
  0 7 11 -> 2 9 11 ,
  0 7 11 -> 10 11 ,
  0 7 11 -> 12 ,
  0 7 13 -> 2 9 13 ,
  0 7 13 -> 10 13 ,
  0 7 14 -> 2 9 14 ,
  0 7 14 -> 10 14 ,
  3 7 8 -> 10 8 ,
  3 7 8 -> 3 ,
  3 7 11 -> 10 11 ,
  3 7 11 -> 12 ,
  3 7 13 -> 10 13 ,
  3 7 14 -> 10 14 ,
  5 7 8 -> 10 8 ,
  5 7 8 -> 3 ,
  5 7 11 -> 10 11 ,
  5 7 11 -> 12 ,
  5 7 13 -> 10 13 ,
  5 7 14 -> 10 14 ,
  12 8 -> 3 4 1 15 ,
  12 8 -> 0 1 15 ,
  12 8 -> 2 15 ,
  12 8 -> 5 ,
  12 11 -> 3 4 1 9 ,
  12 11 -> 0 1 9 ,
  12 11 -> 2 9 ,
  12 11 -> 10 ,
  12 13 -> 3 4 1 16 ,
  12 13 -> 0 1 16 ,
  12 13 -> 2 16 ,
  12 14 -> 3 4 1 17 ,
  12 14 -> 0 1 17 ,
  12 14 -> 2 17 ,
  10 8 -> 5 4 1 15 ,
  10 8 -> 0 1 15 ,
  10 8 -> 2 15 ,
  10 8 -> 5 ,
  10 11 -> 5 4 1 9 ,
  10 11 -> 0 1 9 ,
  10 11 -> 2 9 ,
  10 11 -> 10 ,
  10 13 -> 5 4 1 16 ,
  10 13 -> 0 1 16 ,
  10 13 -> 2 16 ,
  10 14 -> 5 4 1 17 ,
  10 14 -> 0 1 17 ,
  10 14 -> 2 17 ,
  2 16 15 -> 3 ,
  2 16 9 -> 12 ,
  4 7 ->= 7 ,
  4 1 ->= 1 ,
  8 4 ->= 8 ,
  8 1 ->= 13 ,
  15 4 ->= 15 ,
  15 1 ->= 16 ,
  18 4 ->= 18 ,
  4 7 8 ->= 1 9 8 ,
  4 7 11 ->= 1 9 11 ,
  4 7 13 ->= 1 9 13 ,
  4 7 14 ->= 1 9 14 ,
  8 7 8 ->= 13 9 8 ,
  8 7 11 ->= 13 9 11 ,
  8 7 13 ->= 13 9 13 ,
  8 7 14 ->= 13 9 14 ,
  15 7 8 ->= 16 9 8 ,
  15 7 11 ->= 16 9 11 ,
  15 7 13 ->= 16 9 13 ,
  15 7 14 ->= 16 9 14 ,
  11 8 ->= 8 4 1 15 ,
  11 11 ->= 8 4 1 9 ,
  11 13 ->= 8 4 1 16 ,
  11 14 ->= 8 4 1 17 ,
  9 8 ->= 15 4 1 15 ,
  9 11 ->= 15 4 1 9 ,
  9 13 ->= 15 4 1 16 ,
  9 14 ->= 15 4 1 17 ,
  1 16 15 ->= 7 8 ,
  1 16 9 ->= 7 11 ,
  1 16 16 ->= 7 13 ,
  1 16 17 ->= 7 14 }


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 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 1 |
| 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 2 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
13 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
14 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
16 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
17 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
18 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

After renaming modulo { 3->0, 4->1, 5->2, 6->3, 7->4, 1->5, 8->6, 13->7, 15->8, 16->9, 18->10, 9->11, 11->12, 14->13, 17->14 }, 
it remains to prove termination of the 34-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  6 1 ->= 6 ,
  6 5 ->= 7 ,
  8 1 ->= 8 ,
  8 5 ->= 9 ,
  10 1 ->= 10 ,
  1 4 6 ->= 5 11 6 ,
  1 4 12 ->= 5 11 12 ,
  1 4 7 ->= 5 11 7 ,
  1 4 13 ->= 5 11 13 ,
  6 4 6 ->= 7 11 6 ,
  6 4 12 ->= 7 11 12 ,
  6 4 7 ->= 7 11 7 ,
  6 4 13 ->= 7 11 13 ,
  8 4 6 ->= 9 11 6 ,
  8 4 12 ->= 9 11 12 ,
  8 4 7 ->= 9 11 7 ,
  8 4 13 ->= 9 11 13 ,
  12 6 ->= 6 1 5 8 ,
  12 12 ->= 6 1 5 11 ,
  12 7 ->= 6 1 5 9 ,
  12 13 ->= 6 1 5 14 ,
  11 6 ->= 8 1 5 8 ,
  11 12 ->= 8 1 5 11 ,
  11 7 ->= 8 1 5 9 ,
  11 13 ->= 8 1 5 14 ,
  5 9 8 ->= 4 6 ,
  5 9 11 ->= 4 12 ,
  5 9 9 ->= 4 7 ,
  5 9 14 ->= 4 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 |
 \     /
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 33-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  1 3 ->= 3 ,
  1 4 ->= 4 ,
  5 1 ->= 5 ,
  5 4 ->= 6 ,
  7 1 ->= 7 ,
  7 4 ->= 8 ,
  9 1 ->= 9 ,
  1 3 5 ->= 4 10 5 ,
  1 3 11 ->= 4 10 11 ,
  1 3 6 ->= 4 10 6 ,
  1 3 12 ->= 4 10 12 ,
  5 3 5 ->= 6 10 5 ,
  5 3 11 ->= 6 10 11 ,
  5 3 6 ->= 6 10 6 ,
  5 3 12 ->= 6 10 12 ,
  7 3 5 ->= 8 10 5 ,
  7 3 11 ->= 8 10 11 ,
  7 3 6 ->= 8 10 6 ,
  7 3 12 ->= 8 10 12 ,
  11 5 ->= 5 1 4 7 ,
  11 11 ->= 5 1 4 10 ,
  11 6 ->= 5 1 4 8 ,
  11 12 ->= 5 1 4 13 ,
  10 5 ->= 7 1 4 7 ,
  10 11 ->= 7 1 4 10 ,
  10 6 ->= 7 1 4 8 ,
  10 12 ->= 7 1 4 13 ,
  4 8 7 ->= 3 5 ,
  4 8 10 ->= 3 11 ,
  4 8 8 ->= 3 6 ,
  4 8 13 ->= 3 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 |
 \     /
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 32-rule system
{ 0 1 -> 0 ,
  1 2 ->= 2 ,
  1 3 ->= 3 ,
  4 1 ->= 4 ,
  4 3 ->= 5 ,
  6 1 ->= 6 ,
  6 3 ->= 7 ,
  8 1 ->= 8 ,
  1 2 4 ->= 3 9 4 ,
  1 2 10 ->= 3 9 10 ,
  1 2 5 ->= 3 9 5 ,
  1 2 11 ->= 3 9 11 ,
  4 2 4 ->= 5 9 4 ,
  4 2 10 ->= 5 9 10 ,
  4 2 5 ->= 5 9 5 ,
  4 2 11 ->= 5 9 11 ,
  6 2 4 ->= 7 9 4 ,
  6 2 10 ->= 7 9 10 ,
  6 2 5 ->= 7 9 5 ,
  6 2 11 ->= 7 9 11 ,
  10 4 ->= 4 1 3 6 ,
  10 10 ->= 4 1 3 9 ,
  10 5 ->= 4 1 3 7 ,
  10 11 ->= 4 1 3 12 ,
  9 4 ->= 6 1 3 6 ,
  9 10 ->= 6 1 3 9 ,
  9 5 ->= 6 1 3 7 ,
  9 11 ->= 6 1 3 12 ,
  3 7 6 ->= 2 4 ,
  3 7 9 ->= 2 10 ,
  3 7 7 ->= 2 5 ,
  3 7 12 ->= 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 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 { 1->0, 2->1, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 31-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 8 3 ,
  0 1 9 ->= 2 8 9 ,
  0 1 4 ->= 2 8 4 ,
  0 1 10 ->= 2 8 10 ,
  3 1 3 ->= 4 8 3 ,
  3 1 9 ->= 4 8 9 ,
  3 1 4 ->= 4 8 4 ,
  3 1 10 ->= 4 8 10 ,
  5 1 3 ->= 6 8 3 ,
  5 1 9 ->= 6 8 9 ,
  5 1 4 ->= 6 8 4 ,
  5 1 10 ->= 6 8 10 ,
  9 3 ->= 3 0 2 5 ,
  9 9 ->= 3 0 2 8 ,
  9 4 ->= 3 0 2 6 ,
  9 10 ->= 3 0 2 11 ,
  8 3 ->= 5 0 2 5 ,
  8 9 ->= 5 0 2 8 ,
  8 4 ->= 5 0 2 6 ,
  8 10 ->= 5 0 2 11 ,
  2 6 5 ->= 1 3 ,
  2 6 8 ->= 1 9 ,
  2 6 6 ->= 1 4 ,
  2 6 11 ->= 1 10 }

The system is trivially terminating.