YES

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
b -> a
f(a) -> g(a)
g(b) -> f(b)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 G(b) -> F(b)
-> Rules:
 b -> a
 f(a) -> g(a)
 g(b) -> f(b)

Problem 1: 

SCC Processor:
-> Pairs:
 G(b) -> F(b)
-> Rules:
 b -> a
 f(a) -> g(a)
 g(b) -> f(b)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.