NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S Y:S)
(RULES
from(X:S) -> cons(X:S)
minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S)
minus(X:S,0) -> 0
quot(0,s(Y:S)) -> 0
quot(s(X:S),s(Y:S)) -> s(quot(minus(X:S,Y:S),s(Y:S)))
sel(0,cons(X:S)) -> X:S
sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
zWquot(cons(X:S),cons(Y:S)) -> cons(quot(X:S,Y:S))
zWquot(nil,XS:S) -> nil
zWquot(XS:S,nil) -> nil
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 from(X:S) -> cons(X:S)
 minus(s(X:S),s(Y:S)) -> minus(X:S,Y:S)
 minus(X:S,0) -> 0
 quot(0,s(Y:S)) -> 0
 quot(s(X:S),s(Y:S)) -> s(quot(minus(X:S,Y:S),s(Y:S)))
 sel(0,cons(X:S)) -> X:S
 sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
 zWquot(cons(X:S),cons(Y:S)) -> cons(quot(X:S,Y:S))
 zWquot(nil,XS:S) -> nil
 zWquot(XS:S,nil) -> nil
-> The system has extra variables.

The problem is infinite.