YES

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
c -> d
f(f(X:S)) -> c
h(X:S) -> c
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(X:S)) -> C
 H(X:S) -> C
-> Rules:
 c -> d
 f(f(X:S)) -> c
 h(X:S) -> c

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(X:S)) -> C
 H(X:S) -> C
-> Rules:
 c -> d
 f(f(X:S)) -> c
 h(X:S) -> c
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.