YES

After renaming modulo { f->0, b->1, a->2, c->3, d->4 }, 
it remains to prove termination of the 7-rule system
{ 0 0 -> 1 1 1 ,
  2 0 -> 0 2 2 ,
  1 1 -> 3 3 2 3 ,
  4 1 -> 4 2 1 ,
  3 3 -> 4 4 4 ,
  1 4 -> 4 1 ,
  3 4 4 -> 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 80 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 53 |
|  0  1 |
 \     /
2 is interpreted by
 /   \
| 1 0 |
| 0 1 |
 \   /
3 is interpreted by
 /     \
|  1 35 |
|  0  1 |
 \     /
4 is interpreted by
 /     \
|  1 23 |
|  0  1 |
 \     /

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,false)->1, (0,false)->2, (2,true)->3, (3,false)->4, (3,true)->5, (2,false)->6 },
it remains to prove termination of the 10-rule system
{ 0 1 -> 0 2 ,
  0 1 -> 0 ,
  3 4 -> 3 2 4 ,
  3 4 -> 0 4 ,
  3 4 -> 5 ,
  5 6 -> 3 4 ,
  5 6 -> 5 ,
  2 1 ->= 1 2 2 ,
  6 4 ->= 6 2 4 ,
  4 6 ->= 6 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 0 |
| 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 |
 \   /
5 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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

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

The system is trivially terminating.