YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.