YES

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

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


The system was reversed.

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


Applying the dependency pairs transformation.

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 5:

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

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

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

The system is trivially terminating.