YES

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


Applying the dependency pairs transformation.

After renaming modulo { (0,true)->0, (1,true)->1, (2,false)->2, (1,false)->3, (3,false)->4, (2,true)->5, (0,false)->6, (4,false)->7 },
it remains to prove termination of the 17-rule system
{ 0 -> 1 2 3 4 ,
  0 -> 5 3 4 ,
  0 -> 1 4 ,
  5 6 -> 0 3 4 2 ,
  5 6 -> 1 4 2 ,
  5 6 -> 5 ,
  1 4 -> 5 ,
  5 2 -> 5 ,
  1 7 -> 0 7 7 ,
  1 6 -> 0 3 ,
  1 6 -> 1 ,
  6 ->= 3 2 3 4 ,
  2 6 ->= 6 3 4 2 ,
  3 4 ->= 2 ,
  2 2 ->= 2 ,
  3 7 ->= 6 7 7 ,
  3 6 ->= 6 3 }


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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, 
it remains to prove termination of the 16-rule system
{ 0 -> 1 2 3 4 ,
  0 -> 5 3 4 ,
  0 -> 1 4 ,
  5 6 -> 0 3 4 2 ,
  5 6 -> 1 4 2 ,
  5 6 -> 5 ,
  1 4 -> 5 ,
  5 2 -> 5 ,
  1 6 -> 0 3 ,
  1 6 -> 1 ,
  6 ->= 3 2 3 4 ,
  2 6 ->= 6 3 4 2 ,
  3 4 ->= 2 ,
  2 2 ->= 2 ,
  3 7 ->= 6 7 7 ,
  3 6 ->= 6 3 }


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

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

After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, 
it remains to prove termination of the 9-rule system
{ 0 -> 1 2 3 4 ,
  0 -> 5 3 4 ,
  0 -> 1 4 ,
  1 4 -> 5 ,
  5 2 -> 5 ,
  2 6 ->= 6 3 4 2 ,
  3 4 ->= 2 ,
  2 2 ->= 2 ,
  3 6 ->= 6 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 |
 \   /
6 is interpreted by
 /   \
| 1 1 |
| 0 1 |
 \   /

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


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 |
 \   /

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


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

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

The system is trivially terminating.