YES

Problem 1: 

(VAR v_NonEmpty:S N:S X:S X1:S X2:S XS:S Y:S YS:S)
(RULES
a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
a__incr(X:S) -> incr(X:S)
a__oddNs -> a__incr(a__pairNs)
a__oddNs -> oddNs
a__pairNs -> cons(0,incr(oddNs))
a__pairNs -> pairNs
a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
a__repItems(nil) -> nil
a__repItems(X:S) -> repItems(X:S)
a__tail(cons(X:S,XS:S)) -> mark(XS:S)
a__tail(X:S) -> tail(X:S)
a__take(0,XS:S) -> nil
a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
a__take(X1:S,X2:S) -> take(X1:S,X2:S)
a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
a__zip(nil,XS:S) -> nil
a__zip(X:S,nil) -> nil
a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
mark(0) -> 0
mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
mark(incr(X:S)) -> a__incr(mark(X:S))
mark(nil) -> nil
mark(oddNs) -> a__oddNs
mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
mark(pairNs) -> a__pairNs
mark(repItems(X:S)) -> a__repItems(mark(X:S))
mark(s(X:S)) -> s(mark(X:S))
mark(tail(X:S)) -> a__tail(mark(X:S))
mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ODDNS -> A__INCR(a__pairNs)
 A__ODDNS -> A__PAIRNS
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(oddNs) -> A__ODDNS
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(pairNs) -> A__PAIRNS
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ODDNS -> A__INCR(a__pairNs)
 A__ODDNS -> A__PAIRNS
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(oddNs) -> A__ODDNS
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(pairNs) -> A__PAIRNS
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ODDNS -> A__INCR(a__pairNs)
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(oddNs) -> A__ODDNS
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ODDNS -> A__INCR(a__pairNs)
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(oddNs) -> A__ODDNS
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 1
[a__pairNs] = 1
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 1
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 2
[oddNs] = 1
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 1
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = X
[A__ODDNS] = 2
[A__PAIRNS] = 0
[A__REPITEMS](X) = 2.X + 2
[A__TAIL](X) = 2.X
[A__TAKE](X1,X2) = 2.X1 + 2.X2 + 2
[A__ZIP](X1,X2) = X1 + X2 + 1
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(oddNs) -> A__ODDNS
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 1
[a__pairNs] = 1
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 1
[a__take](X1,X2) = X1 + 2.X2 + 1
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 0
[oddNs] = 1
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 1
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 1
[take](X1,X2) = X1 + 2.X2 + 1
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 2.X + 1
[A__TAIL](X) = 2.X + 2
[A__TAKE](X1,X2) = 2.X1 + X2 + 2
[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X
[a__tail](X) = 2.X + 2
[a__take](X1,X2) = 2.X1 + X2 + 1
[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 1
[oddNs] = 2
[pair](X1,X2) = 2.X1 + X2
[pairNs] = 2
[repItems](X) = 2.X
[s](X) = X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + X2 + 1
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = 2.X + 1
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 2.X + 2
[A__TAKE](X1,X2) = X1 + X2 + 2
[A__ZIP](X1,X2) = 2.X1 + X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 2
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 2
[oddNs] = 2
[pair](X1,X2) = X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = X
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 2.X2 + 2
[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X
[a__take](X1,X2) = 2.X1 + 2.X2 + 1
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 1
[oddNs] = 2
[pair](X1,X2) = 2.X1 + X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X
[take](X1,X2) = 2.X1 + 2.X2 + 1
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 1
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 2
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 0
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = 2.X + 1
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(repItems(X:S)) -> MARK(X:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = X + 1
[a__take](X1,X2) = 2.X1 + 2.X2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 0
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = X + 1
[take](X1,X2) = 2.X1 + 2.X2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = X + 1
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(tail(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 2
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 2
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = 2.X
[a__oddNs] = 0
[a__pairNs] = 0
[a__repItems](X) = 2.X + 2
[a__tail](X) = X + 2
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = 2.X
[nil] = 2
[oddNs] = 0
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 0
[repItems](X) = 2.X + 2
[s](X) = 2.X
[tail](X) = X + 2
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = X + 1
[a__take](X1,X2) = 2.X1 + 2.X2 + 1
[a__zip](X1,X2) = 2.X1 + 2.X2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 1
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = X + 1
[take](X1,X2) = 2.X1 + 2.X2 + 1
[zip](X1,X2) = 2.X1 + 2.X2
[A__INCR](X) = X + 1
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 2
[a__tail](X) = 2.X + 2
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 2
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 2
[s](X) = X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X
[a__tail](X) = 2.X
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = X1 + X2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 2
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X
[s](X) = X
[tail](X) = 2.X
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
-> Usable rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a__incr](X) = X
[a__oddNs] = 2
[a__pairNs] = 2
[a__repItems](X) = 2.X + 1/2
[a__tail](X) = 2.X + 1/2
[a__take](X1,X2) = 2.X2
[a__zip](X1,X2) = X1 + 2.X2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + 1/2.X2 + 1/2
[fSNonEmpty] = 0
[incr](X) = X
[nil] = 0
[oddNs] = 2
[pair](X1,X2) = X1 + 2.X2 + 1/2
[pairNs] = 2
[repItems](X) = 2.X + 1/2
[s](X) = X
[tail](X) = 2.X + 1/2
[take](X1,X2) = 2.X2
[zip](X1,X2) = X1 + 2.X2
[A__INCR](X) = 1/2.X + 1/2
[A__ODDNS] = 0
[A__PAIRNS] = 0
[A__REPITEMS](X) = 0
[A__TAIL](X) = 0
[A__TAKE](X1,X2) = 0
[A__ZIP](X1,X2) = 0
[MARK](X) = 1/2.X + 1/2

Problem 1: 

SCC Processor:
-> Pairs:
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> A__INCR(mark(X:S))
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
->->-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
 MARK(incr(X:S)) -> MARK(X:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
 MARK(s(X:S)) -> MARK(X:S)
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Projection:
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
 a__incr(X:S) -> incr(X:S)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
 a__repItems(nil) -> nil
 a__repItems(X:S) -> repItems(X:S)
 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
 a__tail(X:S) -> tail(X:S)
 a__take(0,XS:S) -> nil
 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
 a__zip(cons(X:S,XS:S),cons(Y:S,YS:S)) -> cons(pair(mark(X:S),mark(Y:S)),zip(XS:S,YS:S))
 a__zip(nil,XS:S) -> nil
 a__zip(X:S,nil) -> nil
 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
 mark(0) -> 0
 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
 mark(incr(X:S)) -> a__incr(mark(X:S))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
 mark(pairNs) -> a__pairNs
 mark(repItems(X:S)) -> a__repItems(mark(X:S))
 mark(s(X:S)) -> s(mark(X:S))
 mark(tail(X:S)) -> a__tail(mark(X:S))
 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.