NO

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Infinite Processor:
-> Pairs:
 F -> F
-> Rules:
 b -> c
 f -> f
 g(b) -> c
-> Pairs in cycle:
 F -> F

The problem is infinite.