YES

After renaming modulo { a->0, b->1, c->2, d->3, e->4, f->5 }, 
it remains to prove termination of the 9-rule system
{ 0 1 -> 1 2 0 ,
  1 2 -> 2 1 1 ,
  0 2 -> 2 0 1 ,
  0 0 -> 0 3 3 3 ,
  3 0 -> 3 3 2 ,
  0 3 3 2 -> 0 0 0 3 ,
  4 4 5 5 -> 5 5 5 4 4 ,
  4 -> 0 ,
  1 3 -> 3 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 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 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (2,false)->3, (0,false)->4, (2,true)->5, (3,true)->6, (3,false)->7, (4,true)->8, (4,false)->9, (5,false)->10 },
it remains to prove termination of the 33-rule system
{ 0 1 -> 2 3 4 ,
  0 1 -> 5 4 ,
  0 1 -> 0 ,
  5 4 -> 0 4 3 ,
  5 4 -> 0 3 ,
  5 4 -> 5 ,
  5 1 -> 0 1 3 ,
  5 1 -> 2 3 ,
  5 1 -> 5 ,
  2 1 -> 6 7 7 1 ,
  2 1 -> 6 7 1 ,
  2 1 -> 6 1 ,
  2 1 -> 2 ,
  2 7 -> 5 7 7 ,
  2 7 -> 6 7 ,
  2 7 -> 6 ,
  5 7 7 1 -> 6 1 1 1 ,
  5 7 7 1 -> 2 1 1 ,
  5 7 7 1 -> 2 1 ,
  5 7 7 1 -> 2 ,
  8 9 10 10 -> 8 9 9 ,
  8 9 10 10 -> 8 9 ,
  8 9 10 10 -> 8 ,
  6 4 -> 6 7 ,
  6 4 -> 6 ,
  4 1 ->= 1 3 4 ,
  3 4 ->= 4 4 3 ,
  3 1 ->= 4 1 3 ,
  1 1 ->= 7 7 7 1 ,
  1 7 ->= 3 7 7 ,
  3 7 7 1 ->= 7 1 1 1 ,
  9 9 10 10 ->= 10 10 9 9 9 ,
  7 4 ->= 7 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 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 1 |
| 0 1 |
 \   /
9 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
10 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, 9->8, 10->9 }, 
it remains to prove termination of the 30-rule system
{ 0 1 -> 2 3 4 ,
  0 1 -> 5 4 ,
  0 1 -> 0 ,
  5 4 -> 0 4 3 ,
  5 4 -> 0 3 ,
  5 4 -> 5 ,
  5 1 -> 0 1 3 ,
  5 1 -> 2 3 ,
  5 1 -> 5 ,
  2 1 -> 6 7 7 1 ,
  2 1 -> 6 7 1 ,
  2 1 -> 6 1 ,
  2 1 -> 2 ,
  2 7 -> 5 7 7 ,
  2 7 -> 6 7 ,
  2 7 -> 6 ,
  5 7 7 1 -> 6 1 1 1 ,
  5 7 7 1 -> 2 1 1 ,
  5 7 7 1 -> 2 1 ,
  5 7 7 1 -> 2 ,
  6 4 -> 6 7 ,
  6 4 -> 6 ,
  4 1 ->= 1 3 4 ,
  3 4 ->= 4 4 3 ,
  3 1 ->= 4 1 3 ,
  1 1 ->= 7 7 7 1 ,
  1 7 ->= 3 7 7 ,
  3 7 7 1 ->= 7 1 1 1 ,
  8 8 9 9 ->= 9 9 8 8 8 ,
  7 4 ->= 7 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 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 6->7, 8->8, 9->9 }, 
it remains to prove termination of the 24-rule system
{ 0 1 -> 2 3 4 ,
  0 1 -> 5 4 ,
  0 1 -> 0 ,
  5 4 -> 0 4 3 ,
  5 4 -> 0 3 ,
  5 4 -> 5 ,
  5 1 -> 0 1 3 ,
  5 1 -> 2 3 ,
  5 1 -> 5 ,
  2 1 -> 2 ,
  2 6 -> 5 6 6 ,
  5 6 6 1 -> 2 1 1 ,
  5 6 6 1 -> 2 1 ,
  5 6 6 1 -> 2 ,
  7 4 -> 7 6 ,
  7 4 -> 7 ,
  4 1 ->= 1 3 4 ,
  3 4 ->= 4 4 3 ,
  3 1 ->= 4 1 3 ,
  1 1 ->= 6 6 6 1 ,
  1 6 ->= 3 6 6 ,
  3 6 6 1 ->= 6 1 1 1 ,
  8 8 9 9 ->= 9 9 8 8 8 ,
  6 4 ->= 6 6 }


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 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 0 |
| 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 2 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 1 1 |
 \     /
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 1 |
| 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 |
 \     /

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


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

After renaming modulo { 5->0, 4->1, 0->2, 3->3, 1->4, 2->5, 6->6, 7->7, 8->8 }, 
it remains to prove termination of the 17-rule system
{ 0 1 -> 2 1 3 ,
  0 1 -> 2 3 ,
  0 1 -> 0 ,
  0 4 -> 2 4 3 ,
  5 4 -> 5 ,
  5 6 -> 0 6 6 ,
  0 6 6 4 -> 5 4 4 ,
  0 6 6 4 -> 5 4 ,
  0 6 6 4 -> 5 ,
  1 4 ->= 4 3 1 ,
  3 1 ->= 1 1 3 ,
  3 4 ->= 1 4 3 ,
  4 4 ->= 6 6 6 4 ,
  4 6 ->= 3 6 6 ,
  3 6 6 4 ->= 6 4 4 4 ,
  7 7 8 8 ->= 8 8 7 7 7 ,
  6 1 ->= 6 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 1 |
| 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 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 |
 \   /

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 12-rule system
{ 0 1 -> 0 ,
  0 2 -> 3 2 2 ,
  3 2 2 1 -> 0 1 1 ,
  3 2 2 1 -> 0 1 ,
  3 2 2 1 -> 0 ,
  4 1 ->= 1 5 4 ,
  5 4 ->= 4 4 5 ,
  5 1 ->= 4 1 5 ,
  1 1 ->= 2 2 2 1 ,
  1 2 ->= 5 2 2 ,
  5 2 2 1 ->= 2 1 1 1 ,
  2 4 ->= 2 2 }


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 0 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 0 0 |
| 0 1 0 0 |
 \       /
2 is interpreted by
 /       \
| 1 0 1 0 |
| 0 1 0 0 |
| 0 0 0 0 |
| 0 0 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 1 1 0 |
| 0 0 0 1 |
 \       /
5 is interpreted by
 /       \
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 2 1 |
| 0 1 0 0 |
 \       /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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


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 1 |
| 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 |
 \   /

After renaming modulo { 0->0, 1->1, 4->2, 5->3, 2->4 }, 
it remains to prove termination of the 7-rule system
{ 0 1 -> 0 ,
  2 1 ->= 1 3 2 ,
  3 2 ->= 2 2 3 ,
  3 1 ->= 2 1 3 ,
  1 1 ->= 4 4 4 1 ,
  1 4 ->= 3 4 4 ,
  3 4 4 1 ->= 4 1 1 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 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 1 |
 \     /
3 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /
4 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 0 |
 \     /

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

The system is trivially terminating.