YES
(VAR X)
(RULES 
f(s(X),X) -> f(X,a(X))
f(X,c(X)) -> f(s(X),X)
f(X,X) -> c(X)
)

The TRS is an overlay system and all critical pairs are trivial, thus termination of innermost rewriting is equivalent to termination of rewriting.

Proving termination of innermost rewriting for koen:

-> Dependency pairs:
nF_f(s(X),X) -> nF_f(X,a(X))
nF_f(X,c(X)) -> nF_f(s(X),X)

-> Proof of termination for koen_1:
Termination proved: No cycles in dependency graph.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in DG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.