YES

After renaming modulo { b->0, d->1, c->2, a->3 }, 
it remains to prove termination of the 7-rule system
{ 0 1 0 -> 2 1 0 ,
  0 3 2 -> 0 2 ,
  3 1 -> 1 2 ,
  0 0 0 -> 3 0 2 ,
  1 2 -> 0 1 ,
  1 2 -> 1 0 1 ,
  1 3 2 -> 0 0 }


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 1 |
| 0 1 |
 \   /

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


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (0,false)->2, (2,false)->3, (1,true)->4, (2,true)->5, (3,false)->6 },
it remains to prove termination of the 20-rule system
{ 0 1 2 -> 0 1 3 ,
  0 1 2 -> 4 3 ,
  0 1 2 -> 5 ,
  4 6 -> 5 1 ,
  4 6 -> 4 ,
  0 2 2 -> 5 2 6 ,
  0 2 2 -> 0 6 ,
  5 1 -> 4 2 ,
  5 1 -> 0 ,
  5 1 -> 4 2 1 ,
  5 1 -> 0 1 ,
  5 1 -> 4 ,
  5 6 1 -> 0 2 ,
  5 6 1 -> 0 ,
  2 1 2 ->= 2 1 3 ,
  1 6 ->= 3 1 ,
  2 2 2 ->= 3 2 6 ,
  3 1 ->= 1 2 ,
  3 1 ->= 1 2 1 ,
  3 6 1 ->= 2 2 }


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

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

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


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 1 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
6 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 11-rule system
{ 0 1 2 -> 0 1 3 ,
  0 2 2 -> 4 2 5 ,
  4 1 -> 0 ,
  4 1 -> 0 1 ,
  4 5 1 -> 0 2 ,
  2 1 2 ->= 2 1 3 ,
  1 5 ->= 3 1 ,
  2 2 2 ->= 3 2 5 ,
  3 1 ->= 1 2 ,
  3 1 ->= 1 2 1 ,
  3 5 1 ->= 2 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 0 |
| 0 1 0 |
| 0 0 0 |
 \     /
1 is interpreted by
 /     \
| 1 0 1 |
| 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 1 1 |
 \     /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 10-rule system
{ 0 1 2 -> 0 1 3 ,
  0 2 2 -> 4 2 5 ,
  4 1 -> 0 ,
  4 1 -> 0 1 ,
  4 5 1 -> 0 2 ,
  2 1 2 ->= 2 1 3 ,
  2 2 2 ->= 3 2 5 ,
  3 1 ->= 1 2 ,
  3 1 ->= 1 2 1 ,
  3 5 1 ->= 2 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 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 1 |
 \     /
4 is interpreted by
 /     \
| 1 0 1 |
| 0 1 0 |
| 0 0 0 |
 \     /
5 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 }, 
it remains to prove termination of the 8-rule system
{ 0 1 2 -> 0 1 3 ,
  0 2 2 -> 4 2 5 ,
  4 5 1 -> 0 2 ,
  2 1 2 ->= 2 1 3 ,
  2 2 2 ->= 3 2 5 ,
  3 1 ->= 1 2 ,
  3 1 ->= 1 2 1 ,
  3 5 1 ->= 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 0 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 1 |
 \       /
4 is interpreted by
 /       \
| 1 0 1 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 0 0 1 |
| 0 0 0 0 |
 \       /

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


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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

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

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


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 0 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 1 0 0 |
| 0 0 0 0 |
 \       /

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

The system is trivially terminating.