YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> f(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(g(X:S)) -> F(X:S)
->->-> Rules:
 f(g(X:S)) -> f(X:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(g(X:S)) -> F(X:S)
-> Rules:
 f(g(X:S)) -> f(X:S)
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(g(X:S)) -> f(X:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.