NO

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 2ND(cons(X:S,XS:S)) -> HEAD(XS:S)
 FROM(X:S) -> FROM(s(X:S))
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> TAKE(N:S,XS:S)
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(XS:S)
 from(X:S) -> cons(X:S,from(s(X:S)))
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S))

Problem 1: 

Infinite Processor:
-> Pairs:
 2ND(cons(X:S,XS:S)) -> HEAD(XS:S)
 FROM(X:S) -> FROM(s(X:S))
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> TAKE(N:S,XS:S)
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(XS:S)
 from(X:S) -> cons(X:S,from(s(X:S)))
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,take(N:S,XS:S))
-> Pairs in cycle:
 FROM(X:S) -> FROM(s(X:S))

The problem is infinite.