NO

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Infinite Processor:
-> Pairs:
 F(a) -> F(a)
-> Rules:
 f(a) -> f(a)
-> Pairs in cycle:
 F(a) -> F(a)

The problem is infinite.