YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x:S),y:S,y:S) -> F(y:S,x:S,s(x:S))
-> Rules:
 f(s(x:S),y:S,y:S) -> f(y:S,x:S,s(x:S))
 g(x:S,y:S) -> x:S
 g(x:S,y:S) -> y:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x:S),y:S,y:S) -> F(y:S,x:S,s(x:S))
->->-> Rules:
 f(s(x:S),y:S,y:S) -> f(y:S,x:S,s(x:S))
 g(x:S,y:S) -> x:S
 g(x:S,y:S) -> y:S

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 F(s(x:S),y:S,y:S) -> F(y:S,x:S,s(x:S))
-> Rules:
 f(s(x:S),y:S,y:S) -> f(y:S,x:S,s(x:S))
 g(x:S,y:S) -> x:S
 g(x:S,y:S) -> y:S
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[s](X) = 2.X + 2
[F](X1,X2,X3) = 2.X1 + 2.X2 + X3

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(s(x:S),y:S,y:S) -> f(y:S,x:S,s(x:S))
 g(x:S,y:S) -> x:S
 g(x:S,y:S) -> y:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.