YES

After renaming modulo { b->0, d->1, c->2, a->3 }, 
it remains to prove termination of the 7-rule system
{ 0 0 1 1 0 0 -> 2 2 1 1 0 0 ,
  0 0 3 3 2 2 -> 0 0 2 2 ,
  3 3 1 1 -> 1 1 2 2 ,
  0 0 0 0 0 0 -> 3 3 0 0 2 2 ,
  1 1 2 2 -> 0 0 1 1 ,
  1 1 2 2 -> 1 1 0 0 1 1 ,
  1 1 3 3 2 2 -> 0 0 0 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 1 |
| 0 1 |
 \   /
1 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
2 is interpreted by
 /   \
| 1 1 |
| 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 6-rule system
{ 0 0 1 1 0 0 -> 2 2 1 1 0 0 ,
  3 3 1 1 -> 1 1 2 2 ,
  0 0 0 0 0 0 -> 3 3 0 0 2 2 ,
  1 1 2 2 -> 0 0 1 1 ,
  1 1 2 2 -> 1 1 0 0 1 1 ,
  1 1 3 3 2 2 -> 0 0 0 0 }


The system was reversed.

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (0,false)->1, (1,false)->2, (2,false)->3, (1,true)->4, (2,true)->5, (3,false)->6 },
it remains to prove termination of the 34-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  0 1 2 2 1 1 -> 0 2 2 3 3 ,
  0 1 2 2 1 1 -> 4 2 3 3 ,
  0 1 2 2 1 1 -> 4 3 3 ,
  0 1 2 2 1 1 -> 5 3 ,
  0 1 2 2 1 1 -> 5 ,
  4 2 6 6 -> 5 3 2 2 ,
  4 2 6 6 -> 5 2 2 ,
  4 2 6 6 -> 4 2 ,
  4 2 6 6 -> 4 ,
  0 1 1 1 1 1 -> 5 3 1 1 6 6 ,
  0 1 1 1 1 1 -> 5 1 1 6 6 ,
  0 1 1 1 1 1 -> 0 1 6 6 ,
  0 1 1 1 1 1 -> 0 6 6 ,
  5 3 2 2 -> 4 2 1 1 ,
  5 3 2 2 -> 4 1 1 ,
  5 3 2 2 -> 0 1 ,
  5 3 2 2 -> 0 ,
  5 3 2 2 -> 4 2 1 1 2 2 ,
  5 3 2 2 -> 4 1 1 2 2 ,
  5 3 2 2 -> 0 1 2 2 ,
  5 3 2 2 -> 0 2 2 ,
  5 3 2 2 -> 4 2 ,
  5 3 2 2 -> 4 ,
  5 3 6 6 2 2 -> 0 1 1 1 ,
  5 3 6 6 2 2 -> 0 1 1 ,
  5 3 6 6 2 2 -> 0 1 ,
  5 3 6 6 2 2 -> 0 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  2 2 6 6 ->= 3 3 2 2 ,
  1 1 1 1 1 1 ->= 3 3 1 1 6 6 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 6 6 2 2 ->= 1 1 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 0 |
| 0 1 |
 \   /
3 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
4 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 5->6 }, 
it remains to prove termination of the 16-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  4 2 5 5 -> 6 3 2 2 ,
  0 1 1 1 1 1 -> 6 3 1 1 5 5 ,
  6 3 2 2 -> 4 2 1 1 ,
  6 3 2 2 -> 4 1 1 ,
  6 3 2 2 -> 0 1 ,
  6 3 2 2 -> 4 2 1 1 2 2 ,
  6 3 2 2 -> 4 1 1 2 2 ,
  6 3 2 2 -> 0 1 2 2 ,
  6 3 5 5 2 2 -> 0 1 1 1 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  2 2 5 5 ->= 3 3 2 2 ,
  1 1 1 1 1 1 ->= 3 3 1 1 5 5 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 5 5 2 2 ->= 1 1 1 1 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 6->4, 5->5, 4->6 }, 
it remains to prove termination of the 15-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  0 1 1 1 1 1 -> 4 3 1 1 5 5 ,
  4 3 2 2 -> 6 2 1 1 ,
  4 3 2 2 -> 6 1 1 ,
  4 3 2 2 -> 0 1 ,
  4 3 2 2 -> 6 2 1 1 2 2 ,
  4 3 2 2 -> 6 1 1 2 2 ,
  4 3 2 2 -> 0 1 2 2 ,
  4 3 5 5 2 2 -> 0 1 1 1 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  2 2 5 5 ->= 3 3 2 2 ,
  1 1 1 1 1 1 ->= 3 3 1 1 5 5 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 5 5 2 2 ->= 1 1 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 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, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 11-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  0 1 1 1 1 1 -> 4 3 1 1 5 5 ,
  4 3 2 2 -> 0 1 ,
  4 3 2 2 -> 0 1 2 2 ,
  4 3 5 5 2 2 -> 0 1 1 1 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  2 2 5 5 ->= 3 3 2 2 ,
  1 1 1 1 1 1 ->= 3 3 1 1 5 5 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 5 5 2 2 ->= 1 1 1 1 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 10-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  0 1 1 1 1 1 -> 4 3 1 1 5 5 ,
  4 3 2 2 -> 0 1 ,
  4 3 2 2 -> 0 1 2 2 ,
  4 3 5 5 2 2 -> 0 1 1 1 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  1 1 1 1 1 1 ->= 3 3 1 1 5 5 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 5 5 2 2 ->= 1 1 1 1 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, 
it remains to prove termination of the 8-rule system
{ 0 1 2 2 1 1 -> 0 1 2 2 3 3 ,
  0 1 1 1 1 1 -> 4 3 1 1 5 5 ,
  4 3 5 5 2 2 -> 0 1 1 1 ,
  1 1 2 2 1 1 ->= 1 1 2 2 3 3 ,
  1 1 1 1 1 1 ->= 3 3 1 1 5 5 ,
  3 3 2 2 ->= 2 2 1 1 ,
  3 3 2 2 ->= 2 2 1 1 2 2 ,
  3 3 5 5 2 2 ->= 1 1 1 1 }


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 7:

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 12:

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

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

The system is trivially terminating.