YES

Problem 1: 

(VAR v_NonEmpty:S)
(RULES
0 -> 1
f(0) -> f(0)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 0 -> 1
 f(0) -> f(0)

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 0 -> 1
 f(0) -> f(0)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.