NO

Problem 1: 

(VAR v_NonEmpty:S L:S N:S X:S)
(RULES
activate(n__zeros) -> zeros
activate(X:S) -> X:S
and(tt,X:S) -> activate(X:S)
length(cons(N:S,L:S)) -> s(length(activate(L:S)))
length(nil) -> 0
zeros -> cons(0,n__zeros)
zeros -> n__zeros
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__zeros) -> ZEROS
 AND(tt,X:S) -> ACTIVATE(X:S)
 LENGTH(cons(N:S,L:S)) -> ACTIVATE(L:S)
 LENGTH(cons(N:S,L:S)) -> LENGTH(activate(L:S))
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__zeros) -> ZEROS
 AND(tt,X:S) -> ACTIVATE(X:S)
 LENGTH(cons(N:S,L:S)) -> ACTIVATE(L:S)
 LENGTH(cons(N:S,L:S)) -> LENGTH(activate(L:S))
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 LENGTH(cons(N:S,L:S)) -> LENGTH(activate(L:S))
->->-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros

Problem 1: 

Narrowing Processor:
-> Pairs:
 LENGTH(cons(N:S,L:S)) -> LENGTH(activate(L:S))
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
->Narrowed Pairs:
->->Original Pair:
 LENGTH(cons(N:S,L:S)) -> LENGTH(activate(L:S))
->-> Narrowed pairs:
 LENGTH(cons(x5:S,n__zeros)) -> LENGTH(zeros)
 LENGTH(cons(x5:S,X:S)) -> LENGTH(X:S)

Problem 1: 

SCC Processor:
-> Pairs:
 LENGTH(cons(x5:S,n__zeros)) -> LENGTH(zeros)
 LENGTH(cons(x5:S,X:S)) -> LENGTH(X:S)
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 LENGTH(cons(x5:S,n__zeros)) -> LENGTH(zeros)
 LENGTH(cons(x5:S,X:S)) -> LENGTH(X:S)
->->-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros

Problem 1: 

Narrowing Processor:
-> Pairs:
 LENGTH(cons(x5:S,n__zeros)) -> LENGTH(zeros)
 LENGTH(cons(x5:S,X:S)) -> LENGTH(X:S)
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
->Narrowed Pairs:
->->Original Pair:
 LENGTH(cons(x5:S,n__zeros)) -> LENGTH(zeros)
->-> Narrowed pairs:
 LENGTH(cons(x6:S,n__zeros)) -> LENGTH(cons(0,n__zeros))
 LENGTH(cons(x6:S,n__zeros)) -> LENGTH(n__zeros)

Problem 1: 

Infinite Processor:
-> Pairs:
 LENGTH(cons(x5:S,X:S)) -> LENGTH(X:S)
 LENGTH(cons(x6:S,n__zeros)) -> LENGTH(cons(0,n__zeros))
 LENGTH(cons(x6:S,n__zeros)) -> LENGTH(n__zeros)
-> Rules:
 activate(n__zeros) -> zeros
 activate(X:S) -> X:S
 and(tt,X:S) -> activate(X:S)
 length(cons(N:S,L:S)) -> s(length(activate(L:S)))
 length(nil) -> 0
 zeros -> cons(0,n__zeros)
 zeros -> n__zeros
-> Pairs in cycle:
 LENGTH(cons(x6:S,n__zeros)) -> LENGTH(cons(0,n__zeros))

The problem is infinite.