NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S XS:S)
(RULES
2nd(cons(X:S)) -> head(XS:S)
from(X:S) -> cons(X:S)
head(cons(X:S)) -> X:S
sel(0,cons(X:S)) -> X:S
sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
take(0,XS:S) -> nil
take(s(N:S),cons(X:S)) -> cons(X:S)
)

Problem 1: 

Extra Variables Processor:
-> Rules:
 2nd(cons(X:S)) -> head(XS:S)
 from(X:S) -> cons(X:S)
 head(cons(X:S)) -> X:S
 sel(0,cons(X:S)) -> X:S
 sel(s(N:S),cons(X:S)) -> sel(N:S,XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S)) -> cons(X:S)
-> The system has extra variables.

The problem is infinite.