NO

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S Z:S)
(RULES
f(X:S) -> cons(X:S)
g(0) -> s(0)
g(s(X:S)) -> s(s(g(X:S)))
sel(0,cons(X:S)) -> X:S
sel(s(X:S),cons(Y:S)) -> sel(X:S,Z:S)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 f(X:S) -> cons(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 sel(0,cons(X:S)) -> X:S
 sel(s(X:S),cons(Y:S)) -> sel(X:S,Z:S)
-> The system has extra variables.

The problem is infinite.