YES

After renaming modulo { a->0, b->1, d->2, c->3, f->4 }, 
it remains to prove termination of the 7-rule system
{ 0 0 -> 1 1 1 ,
  0 -> 2 3 2 ,
  1 1 1 -> 0 4 ,
  1 1 -> 3 3 3 ,
  3 3 -> 2 2 2 ,
  3 2 2 -> 4 ,
  4 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 39 |
|  0  1 |
 \     /
1 is interpreted by
 /     \
|  1 26 |
|  0  1 |
 \     /
2 is interpreted by
 /     \
|  1 11 |
|  0  1 |
 \     /
3 is interpreted by
 /     \
|  1 17 |
|  0  1 |
 \     /
4 is interpreted by
 /     \
|  1 39 |
|  0  1 |
 \     /

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


Applying sparse 2-untiling [Hofbauer/Geser/Waldmann, FSCD 2019].

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

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

The system is trivially terminating.