YES

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (2,false)->3, (2,true)->4, (3,false)->5, (0,false)->6 },
it remains to prove termination of the 19-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 4 ,
  0 -> 4 3 3 ,
  0 -> 4 3 ,
  0 -> 4 ,
  4 1 3 -> 0 1 ,
  4 1 3 -> 2 ,
  4 5 -> 2 1 ,
  4 5 -> 2 ,
  0 5 -> 4 3 5 1 ,
  0 5 -> 4 5 1 ,
  0 5 -> 2 ,
  6 1 ->= 1 3 ,
  6 ->= 3 3 3 ,
  1 ->= ,
  6 ->= ,
  3 1 3 ->= 6 1 ,
  3 5 ->= 5 1 1 ,
  6 5 ->= 3 3 5 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 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 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 16-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 4 ,
  0 -> 4 3 3 ,
  0 -> 4 3 ,
  0 -> 4 ,
  4 1 3 -> 0 1 ,
  4 1 3 -> 2 ,
  0 5 -> 4 3 5 1 ,
  0 5 -> 4 5 1 ,
  6 1 ->= 1 3 ,
  6 ->= 3 3 3 ,
  1 ->= ,
  6 ->= ,
  3 1 3 ->= 6 1 ,
  3 5 ->= 5 1 1 ,
  6 5 ->= 3 3 5 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 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, 4->2, 3->3, 5->4, 6->5 }, 
it remains to prove termination of the 14-rule system
{ 0 1 -> 2 ,
  0 -> 2 3 3 ,
  0 -> 2 3 ,
  0 -> 2 ,
  2 1 3 -> 0 1 ,
  0 4 -> 2 3 4 1 ,
  0 4 -> 2 4 1 ,
  5 1 ->= 1 3 ,
  5 ->= 3 3 3 ,
  1 ->= ,
  5 ->= ,
  3 1 3 ->= 5 1 ,
  3 4 ->= 4 1 1 ,
  5 4 ->= 3 3 4 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 1 |
| 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 0 |
 \     /
5 is interpreted by
 /     \
| 1 0 0 |
| 0 1 0 |
| 0 0 1 |
 \     /

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


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

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


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

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

The system is trivially terminating.