YES

After renaming modulo { a->0, d->1, c->2, b->3 }, 
it remains to prove termination of the 6-rule system
{ 0 0 -> 1 2 ,
  0 3 -> 2 2 2 ,
  3 3 -> 0 2 2 ,
  2 2 -> 3 ,
  2 1 -> 0 0 ,
  1 1 -> 3 0 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 15 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 21 |
|  0  1 |
 \     /
2 is interpreted by
 /   \
| 1 9 |
| 0 1 |
 \   /
3 is interpreted by
 /     \
|  1 17 |
|  0  1 |
 \     /

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


The system was reversed.

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


Applying the dependency pairs transformation.

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

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

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

The system is trivially terminating.