NO

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
f(X:S) -> g(h(f(X:S)))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(X:S) -> F(X:S)
-> Rules:
 f(X:S) -> g(h(f(X:S)))

Problem 1: 

Infinite Processor:
-> Pairs:
 F(X:S) -> F(X:S)
-> Rules:
 f(X:S) -> g(h(f(X:S)))
-> Pairs in cycle:
 F(X:S) -> F(X:S)

The problem is infinite.