NO

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
eq -> eq
eq -> ffalse
eq -> ttrue
inf(X:S) -> cons
length(cons) -> s
length(nil) -> 0
take(0,X:S) -> nil
take(s,cons) -> cons
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 EQ -> EQ
-> Rules:
 eq -> eq
 eq -> ffalse
 eq -> ttrue
 inf(X:S) -> cons
 length(cons) -> s
 length(nil) -> 0
 take(0,X:S) -> nil
 take(s,cons) -> cons

Problem 1: 

Infinite Processor:
-> Pairs:
 EQ -> EQ
-> Rules:
 eq -> eq
 eq -> ffalse
 eq -> ttrue
 inf(X:S) -> cons
 length(cons) -> s
 length(nil) -> 0
 take(0,X:S) -> nil
 take(s,cons) -> cons
-> Pairs in cycle:
 EQ -> EQ

The problem is infinite.