NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F -> F
-> Rules:
 f -> f

Problem 1: 

Infinite Processor:
-> Pairs:
 F -> F
-> Rules:
 f -> f
-> Pairs in cycle:
 F -> F

The problem is infinite.