YES
(VAR X)
(RULES 
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(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 nestrec:

-> Dependency pairs:
nF_f(g(X)) -> nF_f(f(X))
nF_f(g(X)) -> nF_f(X)

-> Proof of termination for nestrec_1:
-> -> Dependency pairs in cycle:
nF_f(g(X)) -> nF_f(f(X))
nF_f(g(X)) -> nF_f(X)

UsableRules:
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))

Polynomial Interpretation:

[f](X) = X
[g](X) = X + 1
[h](X) = 0
[nF_f](X) = X

TIME: 4.5158e-2

-> -> Dependency pairs in cycle:
nF_f(g(X)) -> nF_f(f(X))

UsableRules:
f(g(X)) -> g(f(f(X)))
f(h(X)) -> h(g(X))

Polynomial Interpretation:

[f](X) = X
[g](X) = X + 1
[h](X) = 0
[nF_f](X) = X

TIME: 4.0816e-2


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.