YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.