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 }


The system was reversed.

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


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 2 |
| 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 0 |
| 0 1 |
 \   /
12 is interpreted by
 /   \
| 1 1 |
| 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 { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 8->6, 9->7, 10->8, 11->9, 12->10, 6->11 }, 
it remains to prove termination of the 29-rule system
{ 0 0 -> 0 ,
  0 1 -> 1 ,
  0 2 -> 2 ,
  0 3 -> 3 ,
  4 0 -> 4 ,
  4 1 -> 5 ,
  6 0 -> 6 ,
  6 1 -> 7 ,
  6 2 -> 8 ,
  6 3 -> 9 ,
  10 0 -> 10 ,
  0 0 -> 1 11 6 ,
  0 1 -> 1 11 7 ,
  0 2 -> 1 11 8 ,
  0 3 -> 1 11 9 ,
  4 0 -> 5 11 6 ,
  4 1 -> 5 11 7 ,
  4 2 -> 5 11 8 ,
  4 3 -> 5 11 9 ,
  6 0 -> 7 11 6 ,
  6 1 -> 7 11 7 ,
  6 2 -> 7 11 8 ,
  6 3 -> 7 11 9 ,
  11 8 6 -> 4 0 0 ,
  11 8 7 -> 4 0 1 ,
  11 8 8 -> 4 0 2 ,
  11 8 9 -> 4 0 3 ,
  1 5 5 11 -> 2 8 ,
  7 5 5 11 -> 8 8 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (1,true)->3, (4,true)->4, (6,true)->5, (7,true)->6, (10,true)->7, (11,false)->8, (6,false)->9, (11,true)->10, (7,false)->11, (2,false)->12, (8,false)->13, (3,false)->14, (9,false)->15, (4,false)->16, (5,false)->17, (10,false)->18 },
it remains to prove termination of the 69-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 ,
  4 1 -> 4 ,
  5 1 -> 5 ,
  5 2 -> 6 ,
  7 1 -> 7 ,
  0 1 -> 3 8 9 ,
  0 1 -> 10 9 ,
  0 1 -> 5 ,
  0 2 -> 3 8 11 ,
  0 2 -> 10 11 ,
  0 2 -> 6 ,
  0 12 -> 3 8 13 ,
  0 12 -> 10 13 ,
  0 14 -> 3 8 15 ,
  0 14 -> 10 15 ,
  4 1 -> 10 9 ,
  4 1 -> 5 ,
  4 2 -> 10 11 ,
  4 2 -> 6 ,
  4 12 -> 10 13 ,
  4 14 -> 10 15 ,
  5 1 -> 6 8 9 ,
  5 1 -> 10 9 ,
  5 2 -> 6 8 11 ,
  5 2 -> 10 11 ,
  5 12 -> 6 8 13 ,
  5 12 -> 10 13 ,
  5 14 -> 6 8 15 ,
  5 14 -> 10 15 ,
  10 13 9 -> 4 1 1 ,
  10 13 9 -> 0 1 ,
  10 13 9 -> 0 ,
  10 13 11 -> 4 1 2 ,
  10 13 11 -> 0 2 ,
  10 13 11 -> 3 ,
  10 13 13 -> 4 1 12 ,
  10 13 13 -> 0 12 ,
  10 13 15 -> 4 1 14 ,
  10 13 15 -> 0 14 ,
  1 1 ->= 1 ,
  1 2 ->= 2 ,
  1 12 ->= 12 ,
  1 14 ->= 14 ,
  16 1 ->= 16 ,
  16 2 ->= 17 ,
  9 1 ->= 9 ,
  9 2 ->= 11 ,
  9 12 ->= 13 ,
  9 14 ->= 15 ,
  18 1 ->= 18 ,
  1 1 ->= 2 8 9 ,
  1 2 ->= 2 8 11 ,
  1 12 ->= 2 8 13 ,
  1 14 ->= 2 8 15 ,
  16 1 ->= 17 8 9 ,
  16 2 ->= 17 8 11 ,
  16 12 ->= 17 8 13 ,
  16 14 ->= 17 8 15 ,
  9 1 ->= 11 8 9 ,
  9 2 ->= 11 8 11 ,
  9 12 ->= 11 8 13 ,
  9 14 ->= 11 8 15 ,
  8 13 9 ->= 16 1 1 ,
  8 13 11 ->= 16 1 2 ,
  8 13 13 ->= 16 1 12 ,
  8 13 15 ->= 16 1 14 ,
  2 17 17 8 ->= 12 13 ,
  11 17 17 8 ->= 13 13 }


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

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

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

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

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 29-rule system
{ 0 0 ->= 0 ,
  0 1 ->= 1 ,
  0 2 ->= 2 ,
  0 3 ->= 3 ,
  4 0 ->= 4 ,
  4 1 ->= 5 ,
  6 0 ->= 6 ,
  6 1 ->= 7 ,
  6 2 ->= 8 ,
  6 3 ->= 9 ,
  10 0 ->= 10 ,
  0 0 ->= 1 11 6 ,
  0 1 ->= 1 11 7 ,
  0 2 ->= 1 11 8 ,
  0 3 ->= 1 11 9 ,
  4 0 ->= 5 11 6 ,
  4 1 ->= 5 11 7 ,
  4 2 ->= 5 11 8 ,
  4 3 ->= 5 11 9 ,
  6 0 ->= 7 11 6 ,
  6 1 ->= 7 11 7 ,
  6 2 ->= 7 11 8 ,
  6 3 ->= 7 11 9 ,
  11 8 6 ->= 4 0 0 ,
  11 8 7 ->= 4 0 1 ,
  11 8 8 ->= 4 0 2 ,
  11 8 9 ->= 4 0 3 ,
  1 5 5 11 ->= 2 8 ,
  7 5 5 11 ->= 8 8 }

The system is trivially terminating.