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


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 9 5 4 ,
  0 1 5 -> 2 9 5 5 ,
  0 1 6 -> 2 9 5 6 ,
  0 1 7 -> 2 9 5 7 ,
  4 1 4 -> 6 9 5 4 ,
  4 1 5 -> 6 9 5 5 ,
  4 1 6 -> 6 9 5 6 ,
  4 1 7 -> 6 9 5 7 ,
  8 1 4 -> 10 9 5 4 ,
  8 1 5 -> 10 9 5 5 ,
  8 1 6 -> 10 9 5 6 ,
  8 1 7 -> 10 9 5 7 ,
  12 1 4 -> 14 9 5 4 ,
  12 1 5 -> 14 9 5 5 ,
  12 1 6 -> 14 9 5 6 ,
  12 1 7 -> 14 9 5 7 ,
  1 4 -> 0 0 2 8 ,
  1 5 -> 0 0 2 9 ,
  1 6 -> 0 0 2 10 ,
  1 7 -> 0 0 2 11 ,
  5 4 -> 4 0 2 8 ,
  5 5 -> 4 0 2 9 ,
  5 6 -> 4 0 2 10 ,
  5 7 -> 4 0 2 11 ,
  9 4 -> 8 0 2 8 ,
  9 5 -> 8 0 2 9 ,
  9 6 -> 8 0 2 10 ,
  9 7 -> 8 0 2 11 ,
  13 4 -> 12 0 2 8 ,
  13 5 -> 12 0 2 9 ,
  13 6 -> 12 0 2 10 ,
  13 7 -> 12 0 2 11 ,
  2 10 8 -> 0 ,
  2 10 9 -> 1 ,
  2 10 10 -> 2 ,
  2 10 11 -> 3 ,
  6 10 8 -> 4 ,
  6 10 9 -> 5 ,
  6 10 10 -> 6 ,
  6 10 11 -> 7 ,
  10 10 8 -> 8 ,
  10 10 9 -> 9 ,
  10 10 10 -> 10 ,
  10 10 11 -> 11 ,
  14 10 8 -> 12 ,
  14 10 9 -> 13 ,
  14 10 10 -> 14 ,
  14 10 11 -> 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 5 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 3 |
| 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 3 |
| 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, 9->9, 5->10, 7->11 }, 
it remains to prove termination of the 28-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 9 10 4 ,
  0 1 10 -> 2 9 10 10 ,
  0 1 5 -> 2 9 10 5 ,
  0 1 11 -> 2 9 10 11 ,
  4 1 4 -> 5 9 10 4 ,
  4 1 10 -> 5 9 10 10 ,
  4 1 5 -> 5 9 10 5 ,
  4 1 11 -> 5 9 10 11 ,
  6 1 4 -> 7 9 10 4 ,
  6 1 10 -> 7 9 10 10 ,
  6 1 5 -> 7 9 10 5 ,
  6 1 11 -> 7 9 10 11 ,
  10 4 -> 4 0 2 6 ,
  10 10 -> 4 0 2 9 ,
  10 5 -> 4 0 2 7 ,
  9 4 -> 6 0 2 6 ,
  9 10 -> 6 0 2 9 ,
  9 5 -> 6 0 2 7 ,
  2 7 9 -> 1 }


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 27-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 9 10 4 ,
  0 1 10 -> 2 9 10 10 ,
  0 1 5 -> 2 9 10 5 ,
  0 1 11 -> 2 9 10 11 ,
  4 1 4 -> 5 9 10 4 ,
  4 1 10 -> 5 9 10 10 ,
  4 1 5 -> 5 9 10 5 ,
  4 1 11 -> 5 9 10 11 ,
  6 1 4 -> 7 9 10 4 ,
  6 1 10 -> 7 9 10 10 ,
  6 1 5 -> 7 9 10 5 ,
  6 1 11 -> 7 9 10 11 ,
  10 4 -> 4 0 2 6 ,
  10 10 -> 4 0 2 9 ,
  10 5 -> 4 0 2 7 ,
  9 4 -> 6 0 2 6 ,
  9 10 -> 6 0 2 9 ,
  9 5 -> 6 0 2 7 ,
  2 7 9 -> 1 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (2,false)->1, (2,true)->2, (4,true)->3, (0,false)->4, (6,true)->5, (8,true)->6, (1,false)->7, (4,false)->8, (9,false)->9, (10,false)->10, (9,true)->11, (10,true)->12, (5,false)->13, (11,false)->14, (6,false)->15, (7,false)->16, (3,false)->17, (8,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 10 8 ,
  0 7 8 -> 11 10 8 ,
  0 7 8 -> 12 8 ,
  0 7 8 -> 3 ,
  0 7 10 -> 2 9 10 10 ,
  0 7 10 -> 11 10 10 ,
  0 7 10 -> 12 10 ,
  0 7 10 -> 12 ,
  0 7 13 -> 2 9 10 13 ,
  0 7 13 -> 11 10 13 ,
  0 7 13 -> 12 13 ,
  0 7 14 -> 2 9 10 14 ,
  0 7 14 -> 11 10 14 ,
  0 7 14 -> 12 14 ,
  3 7 8 -> 11 10 8 ,
  3 7 8 -> 12 8 ,
  3 7 8 -> 3 ,
  3 7 10 -> 11 10 10 ,
  3 7 10 -> 12 10 ,
  3 7 10 -> 12 ,
  3 7 13 -> 11 10 13 ,
  3 7 13 -> 12 13 ,
  3 7 14 -> 11 10 14 ,
  3 7 14 -> 12 14 ,
  5 7 8 -> 11 10 8 ,
  5 7 8 -> 12 8 ,
  5 7 8 -> 3 ,
  5 7 10 -> 11 10 10 ,
  5 7 10 -> 12 10 ,
  5 7 10 -> 12 ,
  5 7 13 -> 11 10 13 ,
  5 7 13 -> 12 13 ,
  5 7 14 -> 11 10 14 ,
  5 7 14 -> 12 14 ,
  12 8 -> 3 4 1 15 ,
  12 8 -> 0 1 15 ,
  12 8 -> 2 15 ,
  12 8 -> 5 ,
  12 10 -> 3 4 1 9 ,
  12 10 -> 0 1 9 ,
  12 10 -> 2 9 ,
  12 10 -> 11 ,
  12 13 -> 3 4 1 16 ,
  12 13 -> 0 1 16 ,
  12 13 -> 2 16 ,
  11 8 -> 5 4 1 15 ,
  11 8 -> 0 1 15 ,
  11 8 -> 2 15 ,
  11 8 -> 5 ,
  11 10 -> 5 4 1 9 ,
  11 10 -> 0 1 9 ,
  11 10 -> 2 9 ,
  11 10 -> 11 ,
  11 13 -> 5 4 1 16 ,
  11 13 -> 0 1 16 ,
  11 13 -> 2 16 ,
  4 7 ->= 7 ,
  4 1 ->= 1 ,
  4 17 ->= 17 ,
  8 4 ->= 8 ,
  8 1 ->= 13 ,
  15 4 ->= 15 ,
  15 1 ->= 16 ,
  18 4 ->= 18 ,
  4 7 8 ->= 1 9 10 8 ,
  4 7 10 ->= 1 9 10 10 ,
  4 7 13 ->= 1 9 10 13 ,
  4 7 14 ->= 1 9 10 14 ,
  8 7 8 ->= 13 9 10 8 ,
  8 7 10 ->= 13 9 10 10 ,
  8 7 13 ->= 13 9 10 13 ,
  8 7 14 ->= 13 9 10 14 ,
  15 7 8 ->= 16 9 10 8 ,
  15 7 10 ->= 16 9 10 10 ,
  15 7 13 ->= 16 9 10 13 ,
  15 7 14 ->= 16 9 10 14 ,
  10 8 ->= 8 4 1 15 ,
  10 10 ->= 8 4 1 9 ,
  10 13 ->= 8 4 1 16 ,
  9 8 ->= 15 4 1 15 ,
  9 10 ->= 15 4 1 9 ,
  9 13 ->= 15 4 1 16 ,
  1 16 9 ->= 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 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 4 |
| 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 4 |
| 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 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, 17->6, 8->7, 13->8, 15->9, 16->10, 18->11, 9->12, 10->13, 14->14 }, 
it remains to prove termination of the 30-rule system
{ 0 1 -> 0 ,
  2 1 -> 2 ,
  3 1 -> 3 ,
  1 4 ->= 4 ,
  1 5 ->= 5 ,
  1 6 ->= 6 ,
  7 1 ->= 7 ,
  7 5 ->= 8 ,
  9 1 ->= 9 ,
  9 5 ->= 10 ,
  11 1 ->= 11 ,
  1 4 7 ->= 5 12 13 7 ,
  1 4 13 ->= 5 12 13 13 ,
  1 4 8 ->= 5 12 13 8 ,
  1 4 14 ->= 5 12 13 14 ,
  7 4 7 ->= 8 12 13 7 ,
  7 4 13 ->= 8 12 13 13 ,
  7 4 8 ->= 8 12 13 8 ,
  7 4 14 ->= 8 12 13 14 ,
  9 4 7 ->= 10 12 13 7 ,
  9 4 13 ->= 10 12 13 13 ,
  9 4 8 ->= 10 12 13 8 ,
  9 4 14 ->= 10 12 13 14 ,
  13 7 ->= 7 1 5 9 ,
  13 13 ->= 7 1 5 12 ,
  13 8 ->= 7 1 5 10 ,
  12 7 ->= 9 1 5 9 ,
  12 13 ->= 9 1 5 12 ,
  12 8 ->= 9 1 5 10 ,
  5 10 12 ->= 4 }


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


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 27-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 9 10 4 ,
  0 1 10 ->= 2 9 10 10 ,
  0 1 5 ->= 2 9 10 5 ,
  0 1 11 ->= 2 9 10 11 ,
  4 1 4 ->= 5 9 10 4 ,
  4 1 10 ->= 5 9 10 10 ,
  4 1 5 ->= 5 9 10 5 ,
  4 1 11 ->= 5 9 10 11 ,
  6 1 4 ->= 7 9 10 4 ,
  6 1 10 ->= 7 9 10 10 ,
  6 1 5 ->= 7 9 10 5 ,
  6 1 11 ->= 7 9 10 11 ,
  10 4 ->= 4 0 2 6 ,
  10 10 ->= 4 0 2 9 ,
  10 5 ->= 4 0 2 7 ,
  9 4 ->= 6 0 2 6 ,
  9 10 ->= 6 0 2 9 ,
  9 5 ->= 6 0 2 7 ,
  2 7 9 ->= 1 }

The system is trivially terminating.