YES

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


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (1,true)->2, (2,false)->3, (2,true)->4, (0,false)->5, (3,true)->6, (3,false)->7 },
it remains to prove termination of the 16-rule system
{ 0 1 -> 2 3 ,
  0 1 -> 4 ,
  4 -> 0 5 5 ,
  4 -> 0 5 ,
  4 -> 0 ,
  6 1 7 -> 2 5 ,
  6 1 7 -> 0 ,
  2 1 3 -> 6 1 1 7 7 ,
  2 1 3 -> 2 1 7 7 ,
  2 1 3 -> 2 7 7 ,
  2 1 3 -> 6 7 ,
  2 1 3 -> 6 ,
  5 1 ->= 1 3 ,
  3 ->= 5 5 5 ,
  7 1 7 ->= 1 5 ,
  1 1 3 ->= 7 1 1 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 2 |
| 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 0 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 6:

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

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

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

The system is trivially terminating.