YES

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


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 1 -> 2 2 ,
  3 2 -> 1 1 ,
  1 3 -> 1 0 3 ,
  2 -> 1 3 }


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (2,true)->2, (2,false)->3, (3,true)->4, (1,true)->5, (3,false)->6, (0,false)->7 },
it remains to prove termination of the 13-rule system
{ 0 1 1 1 -> 2 3 ,
  0 1 1 1 -> 2 ,
  4 3 -> 5 1 ,
  4 3 -> 5 ,
  5 6 -> 5 7 6 ,
  5 6 -> 0 6 ,
  5 6 -> 4 ,
  2 -> 5 6 ,
  2 -> 4 ,
  7 1 1 1 ->= 3 3 ,
  6 3 ->= 1 1 ,
  1 6 ->= 1 7 6 ,
  3 ->= 1 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 4 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 4 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 6 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 2 |
| 0 1 |
 \   /
7 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /

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

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

The system is trivially terminating.