NO

Problem 1: 

(VAR v_NonEmpty:S N:S X:S X1:S X2:S XS:S Y:S YS:S)
(RULES
activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
activate(n__incr(X:S)) -> incr(X:S)
activate(n__repItems(X:S)) -> repItems(X:S)
activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
activate(X:S) -> X:S
cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
incr(X:S) -> n__incr(X:S)
oddNs -> incr(pairNs)
pairNs -> cons(0,n__incr(oddNs))
repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
repItems(nil) -> nil
repItems(X:S) -> n__repItems(X:S)
tail(cons(X:S,XS:S)) -> activate(XS:S)
take(0,XS:S) -> nil
take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
take(X1:S,X2:S) -> n__take(X1:S,X2:S)
zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
zip(nil,XS:S) -> nil
zip(X:S,nil) -> nil
zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__cons(X1:S,X2:S)) -> CONS(X1:S,X2:S)
 ACTIVATE(n__incr(X:S)) -> INCR(X:S)
 ACTIVATE(n__repItems(X:S)) -> REPITEMS(X:S)
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 ACTIVATE(n__zip(X1:S,X2:S)) -> ZIP(X1:S,X2:S)
 INCR(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 INCR(cons(X:S,XS:S)) -> CONS(s(X:S),n__incr(activate(XS:S)))
 ODDNS -> INCR(pairNs)
 ODDNS -> PAIRNS
 PAIRNS -> CONS(0,n__incr(oddNs))
 PAIRNS -> ODDNS
 REPITEMS(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 REPITEMS(cons(X:S,XS:S)) -> CONS(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 TAIL(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> CONS(X:S,n__take(N:S,activate(XS:S)))
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(XS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(YS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> CONS(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
-> Rules:
 activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
 activate(n__incr(X:S)) -> incr(X:S)
 activate(n__repItems(X:S)) -> repItems(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
 activate(X:S) -> X:S
 cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
 incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
 incr(X:S) -> n__incr(X:S)
 oddNs -> incr(pairNs)
 pairNs -> cons(0,n__incr(oddNs))
 repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 repItems(nil) -> nil
 repItems(X:S) -> n__repItems(X:S)
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
 zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
 zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__cons(X1:S,X2:S)) -> CONS(X1:S,X2:S)
 ACTIVATE(n__incr(X:S)) -> INCR(X:S)
 ACTIVATE(n__repItems(X:S)) -> REPITEMS(X:S)
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 ACTIVATE(n__zip(X1:S,X2:S)) -> ZIP(X1:S,X2:S)
 INCR(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 INCR(cons(X:S,XS:S)) -> CONS(s(X:S),n__incr(activate(XS:S)))
 ODDNS -> INCR(pairNs)
 ODDNS -> PAIRNS
 PAIRNS -> CONS(0,n__incr(oddNs))
 PAIRNS -> ODDNS
 REPITEMS(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 REPITEMS(cons(X:S,XS:S)) -> CONS(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 TAIL(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> CONS(X:S,n__take(N:S,activate(XS:S)))
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(XS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(YS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> CONS(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
-> Rules:
 activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
 activate(n__incr(X:S)) -> incr(X:S)
 activate(n__repItems(X:S)) -> repItems(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
 activate(X:S) -> X:S
 cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
 incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
 incr(X:S) -> n__incr(X:S)
 oddNs -> incr(pairNs)
 pairNs -> cons(0,n__incr(oddNs))
 repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 repItems(nil) -> nil
 repItems(X:S) -> n__repItems(X:S)
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
 zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
 zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__incr(X:S)) -> INCR(X:S)
 ACTIVATE(n__repItems(X:S)) -> REPITEMS(X:S)
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 ACTIVATE(n__zip(X1:S,X2:S)) -> ZIP(X1:S,X2:S)
 INCR(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 REPITEMS(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(XS:S)
 ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> ACTIVATE(YS:S)
->->-> Rules:
 activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
 activate(n__incr(X:S)) -> incr(X:S)
 activate(n__repItems(X:S)) -> repItems(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
 activate(X:S) -> X:S
 cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
 incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
 incr(X:S) -> n__incr(X:S)
 oddNs -> incr(pairNs)
 pairNs -> cons(0,n__incr(oddNs))
 repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 repItems(nil) -> nil
 repItems(X:S) -> n__repItems(X:S)
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
 zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
 zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)
->->Cycle:
->->-> Pairs:
 ODDNS -> PAIRNS
 PAIRNS -> ODDNS
->->-> Rules:
 activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
 activate(n__incr(X:S)) -> incr(X:S)
 activate(n__repItems(X:S)) -> repItems(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
 activate(X:S) -> X:S
 cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
 incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
 incr(X:S) -> n__incr(X:S)
 oddNs -> incr(pairNs)
 pairNs -> cons(0,n__incr(oddNs))
 repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 repItems(nil) -> nil
 repItems(X:S) -> n__repItems(X:S)
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
 zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
 zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)

Problem 1: 

Infinite Processor:
-> Pairs:
 ODDNS -> PAIRNS
 PAIRNS -> ODDNS
-> Rules:
 activate(n__cons(X1:S,X2:S)) -> cons(X1:S,X2:S)
 activate(n__incr(X:S)) -> incr(X:S)
 activate(n__repItems(X:S)) -> repItems(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(n__zip(X1:S,X2:S)) -> zip(X1:S,X2:S)
 activate(X:S) -> X:S
 cons(X1:S,X2:S) -> n__cons(X1:S,X2:S)
 incr(cons(X:S,XS:S)) -> cons(s(X:S),n__incr(activate(XS:S)))
 incr(X:S) -> n__incr(X:S)
 oddNs -> incr(pairNs)
 pairNs -> cons(0,n__incr(oddNs))
 repItems(cons(X:S,XS:S)) -> cons(X:S,n__cons(X:S,n__repItems(activate(XS:S))))
 repItems(nil) -> nil
 repItems(X:S) -> n__repItems(X:S)
 tail(cons(X:S,XS:S)) -> activate(XS:S)
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
 zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(X:S,Y:S),n__zip(activate(XS:S),activate(YS:S)))
 zip(nil,XS:S) -> nil
 zip(X:S,nil) -> nil
 zip(X1:S,X2:S) -> n__zip(X1:S,X2:S)
-> Pairs in cycle:
 ODDNS -> PAIRNS
 PAIRNS -> ODDNS

The problem is infinite.