YES

After renaming modulo { a->0, b->1, c->2 }, 
it remains to prove termination of the 3-rule system
{ 0 -> ,
  0 0 -> 0 1 2 ,
  2 1 -> 0 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 48-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 0 -> 0 1 6 8 ,
  0 0 1 -> 0 1 6 9 ,
  0 0 2 -> 0 1 6 10 ,
  0 0 3 -> 0 1 6 11 ,
  4 0 0 -> 4 1 6 8 ,
  4 0 1 -> 4 1 6 9 ,
  4 0 2 -> 4 1 6 10 ,
  4 0 3 -> 4 1 6 11 ,
  8 0 0 -> 8 1 6 8 ,
  8 0 1 -> 8 1 6 9 ,
  8 0 2 -> 8 1 6 10 ,
  8 0 3 -> 8 1 6 11 ,
  12 0 0 -> 12 1 6 8 ,
  12 0 1 -> 12 1 6 9 ,
  12 0 2 -> 12 1 6 10 ,
  12 0 3 -> 12 1 6 11 ,
  2 9 4 -> 0 2 8 0 ,
  2 9 5 -> 0 2 8 1 ,
  2 9 6 -> 0 2 8 2 ,
  2 9 7 -> 0 2 8 3 ,
  6 9 4 -> 4 2 8 0 ,
  6 9 5 -> 4 2 8 1 ,
  6 9 6 -> 4 2 8 2 ,
  6 9 7 -> 4 2 8 3 ,
  10 9 4 -> 8 2 8 0 ,
  10 9 5 -> 8 2 8 1 ,
  10 9 6 -> 8 2 8 2 ,
  10 9 7 -> 8 2 8 3 ,
  14 9 4 -> 12 2 8 0 ,
  14 9 5 -> 12 2 8 1 ,
  14 9 6 -> 12 2 8 2 ,
  14 9 7 -> 12 2 8 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 2 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 3 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 2 |
| 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 0 |
| 0 1 |
 \   /
15 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


Applying the dependency pairs transformation.

After renaming modulo { (5,true)->0, (5,false)->1, (1,false)->2, (6,false)->3, (2,false)->4, (6,true)->5, (3,false)->6, (4,false)->7, (7,true)->8, (0,true)->9, (8,true)->10, (3,true)->11, (7,false)->12, (0,false)->13, (8,false)->14 },
it remains to prove termination of the 46-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 2 -> 5 4 ,
  0 1 6 -> 0 2 3 7 ,
  0 1 6 -> 5 7 ,
  8 1 2 -> 8 2 3 4 ,
  8 1 2 -> 5 4 ,
  8 1 6 -> 8 2 3 7 ,
  8 1 6 -> 5 7 ,
  9 1 2 -> 9 2 3 4 ,
  9 1 2 -> 5 4 ,
  9 1 6 -> 9 2 3 7 ,
  9 1 6 -> 5 7 ,
  10 1 2 -> 10 2 3 4 ,
  10 1 2 -> 5 4 ,
  10 1 6 -> 10 2 3 7 ,
  10 1 6 -> 5 7 ,
  11 4 12 -> 0 6 13 1 ,
  11 4 12 -> 11 13 1 ,
  11 4 12 -> 9 1 ,
  11 4 12 -> 0 ,
  11 4 3 -> 0 6 13 6 ,
  11 4 3 -> 11 13 6 ,
  11 4 3 -> 9 6 ,
  11 4 3 -> 11 ,
  5 4 12 -> 8 6 13 1 ,
  5 4 12 -> 11 13 1 ,
  5 4 12 -> 9 1 ,
  5 4 12 -> 0 ,
  5 4 3 -> 8 6 13 6 ,
  5 4 3 -> 11 13 6 ,
  5 4 3 -> 9 6 ,
  5 4 3 -> 11 ,
  13 2 ->= 4 ,
  13 6 ->= 7 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 6 ->= 1 2 3 7 ,
  12 1 2 ->= 12 2 3 4 ,
  12 1 6 ->= 12 2 3 7 ,
  13 1 2 ->= 13 2 3 4 ,
  13 1 6 ->= 13 2 3 7 ,
  14 1 2 ->= 14 2 3 4 ,
  14 1 6 ->= 14 2 3 7 ,
  6 4 12 ->= 1 6 13 1 ,
  6 4 3 ->= 1 6 13 6 ,
  3 4 12 ->= 12 6 13 1 ,
  3 4 3 ->= 12 6 13 6 }


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 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 0 |
| 0 1 |
 \   /
8 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 is interpreted by
 /   \
| 1 1 |
| 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 |
 \   /

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, 14->14 }, 
it remains to prove termination of the 44-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 2 -> 5 4 ,
  0 1 6 -> 0 2 3 7 ,
  0 1 6 -> 5 7 ,
  8 1 2 -> 8 2 3 4 ,
  8 1 2 -> 5 4 ,
  8 1 6 -> 8 2 3 7 ,
  8 1 6 -> 5 7 ,
  9 1 2 -> 9 2 3 4 ,
  9 1 2 -> 5 4 ,
  9 1 6 -> 9 2 3 7 ,
  9 1 6 -> 5 7 ,
  10 1 2 -> 10 2 3 4 ,
  10 1 6 -> 10 2 3 7 ,
  11 4 12 -> 0 6 13 1 ,
  11 4 12 -> 11 13 1 ,
  11 4 12 -> 9 1 ,
  11 4 12 -> 0 ,
  11 4 3 -> 0 6 13 6 ,
  11 4 3 -> 11 13 6 ,
  11 4 3 -> 9 6 ,
  11 4 3 -> 11 ,
  5 4 12 -> 8 6 13 1 ,
  5 4 12 -> 11 13 1 ,
  5 4 12 -> 9 1 ,
  5 4 12 -> 0 ,
  5 4 3 -> 8 6 13 6 ,
  5 4 3 -> 11 13 6 ,
  5 4 3 -> 9 6 ,
  5 4 3 -> 11 ,
  13 2 ->= 4 ,
  13 6 ->= 7 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 6 ->= 1 2 3 7 ,
  12 1 2 ->= 12 2 3 4 ,
  12 1 6 ->= 12 2 3 7 ,
  13 1 2 ->= 13 2 3 4 ,
  13 1 6 ->= 13 2 3 7 ,
  14 1 2 ->= 14 2 3 4 ,
  14 1 6 ->= 14 2 3 7 ,
  6 4 12 ->= 1 6 13 1 ,
  6 4 3 ->= 1 6 13 6 ,
  3 4 12 ->= 12 6 13 1 ,
  3 4 3 ->= 12 6 13 6 }


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 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 1 |
| 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 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 0 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 7->6, 8->7, 9->8, 10->9, 13->10, 12->11, 14->12 }, 
it remains to prove termination of the 22-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 1 2 -> 7 2 3 4 ,
  7 1 5 -> 7 2 3 6 ,
  8 1 2 -> 8 2 3 4 ,
  8 1 5 -> 8 2 3 6 ,
  9 1 2 -> 9 2 3 4 ,
  9 1 5 -> 9 2 3 6 ,
  10 2 ->= 4 ,
  10 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  11 1 2 ->= 11 2 3 4 ,
  11 1 5 ->= 11 2 3 6 ,
  10 1 2 ->= 10 2 3 4 ,
  10 1 5 ->= 10 2 3 6 ,
  12 1 2 ->= 12 2 3 4 ,
  12 1 5 ->= 12 2 3 6 ,
  5 4 11 ->= 1 5 10 1 ,
  5 4 3 ->= 1 5 10 5 ,
  3 4 11 ->= 11 5 10 1 ,
  3 4 3 ->= 11 5 10 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
12 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9, 11->10, 12->11 }, 
it remains to prove termination of the 20-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 1 2 -> 7 2 3 4 ,
  7 1 5 -> 7 2 3 6 ,
  8 1 2 -> 8 2 3 4 ,
  8 1 5 -> 8 2 3 6 ,
  9 2 ->= 4 ,
  9 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  10 1 2 ->= 10 2 3 4 ,
  10 1 5 ->= 10 2 3 6 ,
  9 1 2 ->= 9 2 3 4 ,
  9 1 5 ->= 9 2 3 6 ,
  11 1 2 ->= 11 2 3 4 ,
  11 1 5 ->= 11 2 3 6 ,
  5 4 10 ->= 1 5 9 1 ,
  5 4 3 ->= 1 5 9 5 ,
  3 4 10 ->= 10 5 9 1 ,
  3 4 3 ->= 10 5 9 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
11 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9, 11->10 }, 
it remains to prove termination of the 18-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 1 2 -> 7 2 3 4 ,
  7 1 5 -> 7 2 3 6 ,
  8 2 ->= 4 ,
  8 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  9 1 2 ->= 9 2 3 4 ,
  9 1 5 ->= 9 2 3 6 ,
  8 1 2 ->= 8 2 3 4 ,
  8 1 5 ->= 8 2 3 6 ,
  10 1 2 ->= 10 2 3 4 ,
  10 1 5 ->= 10 2 3 6 ,
  5 4 9 ->= 1 5 8 1 ,
  5 4 3 ->= 1 5 8 5 ,
  3 4 9 ->= 9 5 8 1 ,
  3 4 3 ->= 9 5 8 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
10 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

After renaming modulo { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 8->7, 9->8, 10->9 }, 
it remains to prove termination of the 16-rule system
{ 0 1 2 -> 0 2 3 4 ,
  0 1 5 -> 0 2 3 6 ,
  7 2 ->= 4 ,
  7 5 ->= 6 ,
  1 1 2 ->= 1 2 3 4 ,
  1 1 5 ->= 1 2 3 6 ,
  8 1 2 ->= 8 2 3 4 ,
  8 1 5 ->= 8 2 3 6 ,
  7 1 2 ->= 7 2 3 4 ,
  7 1 5 ->= 7 2 3 6 ,
  9 1 2 ->= 9 2 3 4 ,
  9 1 5 ->= 9 2 3 6 ,
  5 4 8 ->= 1 5 7 1 ,
  5 4 3 ->= 1 5 7 5 ,
  3 4 8 ->= 8 5 7 1 ,
  3 4 3 ->= 8 5 7 5 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

0 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
1 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 1 |
| 0 0 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 1 0 0 |
 \       /
3 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
4 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
 \       /
6 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
7 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
8 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /
9 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
 \       /

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

The system is trivially terminating.