NO

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is infinite.