NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S Y:S)
(RULES
add(0,X:S) -> X:S
add(s(X:S),Y:S) -> s(add(X:S,Y:S))
fib(N:S) -> sel(N:S,fib1(s(0),s(0)))
fib1(X:S,Y:S) -> cons(X:S)
sel(0,cons(X:S)) -> X:S
sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 add(0,X:S) -> X:S
 add(s(X:S),Y:S) -> s(add(X:S,Y:S))
 fib(N:S) -> sel(N:S,fib1(s(0),s(0)))
 fib1(X:S,Y:S) -> cons(X:S)
 sel(0,cons(X:S)) -> X:S
 sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
-> The system has extra variables.

The problem is infinite.