NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(X:S) -> A
 F(X:S) -> H(a)
 G(a) -> F(b)
 H(X:S) -> G(X:S)
-> Rules:
 a -> b
 f(X:S) -> h(a)
 g(a) -> f(b)
 h(X:S) -> g(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(X:S) -> A
 F(X:S) -> H(a)
 G(a) -> F(b)
 H(X:S) -> G(X:S)
-> Rules:
 a -> b
 f(X:S) -> h(a)
 g(a) -> f(b)
 h(X:S) -> g(X:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(X:S) -> H(a)
 G(a) -> F(b)
 H(X:S) -> G(X:S)
->->-> Rules:
 a -> b
 f(X:S) -> h(a)
 g(a) -> f(b)
 h(X:S) -> g(X:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 F(X:S) -> H(a)
 G(a) -> F(b)
 H(X:S) -> G(X:S)
-> Rules:
 a -> b
 f(X:S) -> h(a)
 g(a) -> f(b)
 h(X:S) -> g(X:S)
-> Pairs in cycle:
 F(b) -> H(a)
 G(a) -> F(b)
 H(a) -> G(a)

The problem is infinite.