NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(x:S) -> F(f(x:S))
 F(x:S) -> F(x:S)
-> Rules:
 f(x:S) -> f(f(x:S))

Problem 1: 

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

The problem is infinite.