/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 A__TAIL(cons(X,XS)) -> MARK(XS)
 A__TAKE(s(N),cons(X,XS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(Y)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(repItems(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> A__TAIL(mark(X))
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> A__TAKE(mark(X1),mark(X2))
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> A__ZIP(mark(X1),mark(X2))
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 1
[a__take](X1,X2) = 2.X1 + 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[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 + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2
[A__INCR](X) = X
[A__TAIL](X) = 2.X + 1
[A__TAKE](X1,X2) = X1 + 2.X2 + 2
[A__ZIP](X1,X2) = X1 + X2
[MARK](X) = 2.X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 A__TAKE(s(N),cons(X,XS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(Y)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(repItems(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> A__TAKE(mark(X1),mark(X2))
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> A__ZIP(mark(X1),mark(X2))
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[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) = X + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = X + 1
[A__TAKE](X1,X2) = 2.X2 + 2
[A__ZIP](X1,X2) = X1 + 2.X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(Y)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(repItems(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> A__ZIP(mark(X1),mark(X2))
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 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
[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 + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = X
[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
[MARK](X) = 2.X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 A__ZIP(cons(X,XS),cons(Y,YS)) -> MARK(Y)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(repItems(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> A__ZIP(mark(X1),mark(X2))
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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) = 2.X + 2
[a__take](X1,X2) = 2.X1 + X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[incr](X) = 2.X
[nil] = 0
[oddNs] = 0
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 0
[repItems](X) = 2.X + 2
[s](X) = 2.X
[tail](X) = 2.X + 2
[take](X1,X2) = 2.X1 + X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = X + 1
[A__ZIP](X1,X2) = 2.X1 + X2 + 2
[MARK](X) = 2.X + 1

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(repItems(X)) -> MARK(X)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 2
[a__take](X1,X2) = X1 + 2.X2 + 2
[a__zip](X1,X2) = X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[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) = X + 2
[take](X1,X2) = X1 + 2.X2 + 2
[zip](X1,X2) = X1 + 2.X2 + 2
[A__INCR](X) = X + 2
[MARK](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(s(X)) -> MARK(X)
 MARK(tail(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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) = 2.X + 1
[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
[incr](X) = 2.X
[nil] = 0
[oddNs] = 0
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 0
[repItems](X) = 2.X + 2
[s](X) = 2.X
[tail](X) = 2.X + 1
[take](X1,X2) = 2.X1 + X2 + 1
[zip](X1,X2) = 2.X1 + 2.X2 + 1
[A__INCR](X) = 2.X + 2
[MARK](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(s(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X1)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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) = 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
[incr](X) = 2.X
[nil] = 1
[oddNs] = 0
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 0
[repItems](X) = 2.X + 2
[s](X) = 2.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
[MARK](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(s(X)) -> MARK(X)
 MARK(take(X1,X2)) -> MARK(X2)
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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) = 2.X + 1
[a__take](X1,X2) = 2.X2 + 2
[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
[mark](X) = X
[0] = 0
[cons](X1,X2) = 2.X1 + X2
[incr](X) = 2.X
[nil] = 1
[oddNs] = 0
[pair](X1,X2) = X1 + 2.X2
[pairNs] = 0
[repItems](X) = 2.X + 2
[s](X) = 2.X
[tail](X) = 2.X + 1
[take](X1,X2) = 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 1
[MARK](X) = 2.X + 1

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(s(X)) -> MARK(X)
 MARK(zip(X1,X2)) -> MARK(X1)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 1
[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
[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 + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[MARK](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A__INCR(cons(X,XS)) -> MARK(X)
 MARK(cons(X1,X2)) -> MARK(X1)
 MARK(incr(X)) -> A__INCR(mark(X))
 MARK(incr(X)) -> MARK(X)
 MARK(pair(X1,X2)) -> MARK(X1)
 MARK(pair(X1,X2)) -> MARK(X2)
 MARK(s(X)) -> MARK(X)
 MARK(zip(X1,X2)) -> MARK(X2)
-> Rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
-> Usable rules:
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__incr(X) -> incr(X)
 a__oddNs -> a__incr(a__pairNs)
 a__oddNs -> oddNs
 a__pairNs -> cons(0,incr(oddNs))
 a__pairNs -> pairNs
 a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
 a__repItems(nil) -> nil
 a__repItems(X) -> repItems(X)
 a__tail(cons(X,XS)) -> mark(XS)
 a__tail(X) -> tail(X)
 a__take(0,XS) -> nil
 a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
 a__take(X1,X2) -> take(X1,X2)
 a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
 a__zip(nil,XS) -> nil
 a__zip(X,nil) -> nil
 a__zip(X1,X2) -> zip(X1,X2)
 mark(0) -> 0
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(incr(X)) -> a__incr(mark(X))
 mark(nil) -> nil
 mark(oddNs) -> a__oddNs
 mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
 mark(pairNs) -> a__pairNs
 mark(repItems(X)) -> a__repItems(mark(X))
 mark(s(X)) -> s(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
 mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
->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 + 1
[a__tail](X) = 2.X + 1
[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
[incr](X) = X
[nil] = 0
[oddNs] = 2
[pair](X1,X2) = 2.X1 + 2.X2
[pairNs] = 2
[repItems](X) = 2.X + 1
[s](X) = X
[tail](X) = 2.X + 1
[take](X1,X2) = 2.X1 + 2.X2 + 2
[zip](X1,X2) = 2.X1 + 2.X2 + 2
[A__INCR](X) = 2.X + 2
[MARK](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

The problem is finite.