NO

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
f(s(x:S),y:S) -> f(y:S,x:S)
f(x:S,y:S) -> f(x:S,x:S)
)

Problem 1: 

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

Problem 1: 

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

The problem is infinite.