NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(X:S) -> C
 F(X:S) -> F(c)
-> Rules:
 c -> b
 f(X:S) -> f(c)

Problem 1: 

Infinite Processor:
-> Pairs:
 F(X:S) -> C
 F(X:S) -> F(c)
-> Rules:
 c -> b
 f(X:S) -> f(c)
-> Pairs in cycle:
 F(X:S) -> F(c)

The problem is infinite.