YES

After renaming modulo { a->0, b->1, d->2, c->3, f->4 }, 
it remains to prove termination of the 6-rule system
{ 0 1 -> 1 2 ,
  0 3 -> 2 2 2 ,
  1 2 -> 0 3 1 ,
  3 4 -> 2 2 3 ,
  2 2 -> 4 ,
  4 4 -> 0 }


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

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


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


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

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

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


The system was filtered by the following matrix interpretation
of type E_J with J = {1,...,2} and dimension 4:

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

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

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

The system is trivially terminating.