NO

Problem 1: 

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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 G(X:S) -> H(X:S)
 H(d) -> C
 H(d) -> G(c)
-> Rules:
 c -> d
 g(X:S) -> h(X:S)
 h(d) -> g(c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(X:S) -> H(X:S)
 H(d) -> G(c)
->->-> Rules:
 c -> d
 g(X:S) -> h(X:S)
 h(d) -> g(c)

Problem 1: 

Infinite Processor:
-> Pairs:
 G(X:S) -> H(X:S)
 H(d) -> G(c)
-> Rules:
 c -> d
 g(X:S) -> h(X:S)
 h(d) -> g(c)
-> Pairs in cycle:
 G(c) -> H(c)
 H(c) -> H(d)
 H(d) -> G(c)

The problem is infinite.