YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
f(f(x:S)) -> g(f(x:S))
)

Problem 1: 

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

Problem 1: 

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

The problem is finite.