3.64/3.90	YES
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	(VAR v_NonEmpty:S N:S X:S X1:S X2:S XS:S Y:S YS:S)
3.64/3.90	(RULES
3.64/3.90	a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	a__incr(X:S) -> incr(X:S)
3.64/3.90	a__oddNs -> a__incr(a__pairNs)
3.64/3.90	a__oddNs -> oddNs
3.64/3.90	a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	a__pairNs -> pairNs
3.64/3.90	a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	a__repItems(nil) -> nil
3.64/3.90	a__repItems(X:S) -> repItems(X:S)
3.64/3.90	a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	a__tail(X:S) -> tail(X:S)
3.64/3.90	a__take(0,XS:S) -> nil
3.64/3.90	a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	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))
3.64/3.90	a__zip(nil,XS:S) -> nil
3.64/3.90	a__zip(X:S,nil) -> nil
3.64/3.90	a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	mark(0) -> 0
3.64/3.90	mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	mark(nil) -> nil
3.64/3.90	mark(oddNs) -> a__oddNs
3.64/3.90	mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	mark(pairNs) -> a__pairNs
3.64/3.90	mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	) 
3.64/3.90	(STRATEGY INNERMOST)
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Dependency Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ODDNS -> A__INCR(a__pairNs)
3.64/3.90	 A__ODDNS -> A__PAIRNS
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(oddNs) -> A__ODDNS
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(pairNs) -> A__PAIRNS
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ODDNS -> A__INCR(a__pairNs)
3.64/3.90	 A__ODDNS -> A__PAIRNS
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(oddNs) -> A__ODDNS
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(pairNs) -> A__PAIRNS
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ODDNS -> A__INCR(a__pairNs)
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(oddNs) -> A__ODDNS
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ODDNS -> A__INCR(a__pairNs)
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(oddNs) -> A__ODDNS
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 1
3.64/3.90	[a__pairNs] = 1
3.64/3.90	[a__repItems](X) = 2.X + 2
3.64/3.90	[a__tail](X) = 2.X + 1
3.64/3.90	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = 2.X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 2
3.64/3.90	[oddNs] = 1
3.64/3.90	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.90	[pairNs] = 1
3.64/3.90	[repItems](X) = 2.X + 2
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X + 1
3.64/3.90	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[A__INCR](X) = X
3.64/3.90	[A__ODDNS] = 2
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 2.X + 2
3.64/3.90	[A__TAIL](X) = 2.X
3.64/3.90	[A__TAKE](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[A__ZIP](X1,X2) = X1 + X2 + 1
3.64/3.90	[MARK](X) = 2.X
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(oddNs) -> A__ODDNS
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__REPITEMS(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 1
3.64/3.90	[a__pairNs] = 1
3.64/3.90	[a__repItems](X) = 2.X + 2
3.64/3.90	[a__tail](X) = 2.X + 1
3.64/3.90	[a__take](X1,X2) = X1 + 2.X2 + 1
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = 2.X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 0
3.64/3.90	[oddNs] = 1
3.64/3.90	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.90	[pairNs] = 1
3.64/3.90	[repItems](X) = 2.X + 2
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X + 1
3.64/3.90	[take](X1,X2) = X1 + 2.X2 + 1
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[A__INCR](X) = 2.X
3.64/3.90	[A__ODDNS] = 0
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 2.X + 1
3.64/3.90	[A__TAIL](X) = 2.X + 2
3.64/3.90	[A__TAKE](X1,X2) = 2.X1 + X2 + 2
3.64/3.90	[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[MARK](X) = 2.X
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> A__REPITEMS(mark(X:S))
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAIL(cons(X:S,XS:S)) -> MARK(XS:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 2
3.64/3.90	[a__pairNs] = 2
3.64/3.90	[a__repItems](X) = 2.X
3.64/3.90	[a__tail](X) = 2.X + 2
3.64/3.90	[a__take](X1,X2) = 2.X1 + X2 + 1
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = 2.X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 1
3.64/3.90	[oddNs] = 2
3.64/3.90	[pair](X1,X2) = 2.X1 + X2
3.64/3.90	[pairNs] = 2
3.64/3.90	[repItems](X) = 2.X
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X + 2
3.64/3.90	[take](X1,X2) = 2.X1 + X2 + 1
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[A__INCR](X) = 2.X + 1
3.64/3.90	[A__ODDNS] = 0
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 0
3.64/3.90	[A__TAIL](X) = 2.X + 2
3.64/3.90	[A__TAKE](X1,X2) = X1 + X2 + 2
3.64/3.90	[A__ZIP](X1,X2) = 2.X1 + X2 + 2
3.64/3.90	[MARK](X) = 2.X + 1
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> A__TAIL(mark(X:S))
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__TAKE(s(N:S),cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 2
3.64/3.90	[a__pairNs] = 2
3.64/3.90	[a__repItems](X) = 2.X + 2
3.64/3.90	[a__tail](X) = 2.X + 2
3.64/3.90	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 2
3.64/3.90	[oddNs] = 2
3.64/3.90	[pair](X1,X2) = X1 + 2.X2
3.64/3.90	[pairNs] = 2
3.64/3.90	[repItems](X) = 2.X + 2
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X + 2
3.64/3.90	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[A__INCR](X) = X
3.64/3.90	[A__ODDNS] = 0
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 0
3.64/3.90	[A__TAIL](X) = 0
3.64/3.90	[A__TAKE](X1,X2) = 2.X2 + 2
3.64/3.90	[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[MARK](X) = X
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> A__TAKE(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 2
3.64/3.90	[a__pairNs] = 2
3.64/3.90	[a__repItems](X) = 2.X + 2
3.64/3.90	[a__tail](X) = 2.X
3.64/3.90	[a__take](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = 2.X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 1
3.64/3.90	[oddNs] = 2
3.64/3.90	[pair](X1,X2) = 2.X1 + X2
3.64/3.90	[pairNs] = 2
3.64/3.90	[repItems](X) = 2.X + 2
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X
3.64/3.90	[take](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[A__INCR](X) = 2.X + 1
3.64/3.90	[A__ODDNS] = 0
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 0
3.64/3.90	[A__TAIL](X) = 0
3.64/3.90	[A__TAKE](X1,X2) = 0
3.64/3.90	[A__ZIP](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[MARK](X) = 2.X + 1
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Strongly Connected Components:
3.64/3.90	->->Cycle:
3.64/3.90	->->-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	->->-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	Reduction Pairs Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 A__ZIP(cons(X:S,XS:S),cons(Y:S,YS:S)) -> MARK(Y:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	-> Usable rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.90	 a__zip(nil,XS:S) -> nil
3.64/3.90	 a__zip(X:S,nil) -> nil
3.64/3.90	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.90	 mark(0) -> 0
3.64/3.90	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.90	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.90	 mark(nil) -> nil
3.64/3.90	 mark(oddNs) -> a__oddNs
3.64/3.90	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(pairNs) -> a__pairNs
3.64/3.90	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.90	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.90	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.90	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.90	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.90	->Interpretation type:
3.64/3.90	 Linear
3.64/3.90	->Coefficients:
3.64/3.90	 Natural Numbers
3.64/3.90	->Dimension:
3.64/3.90	 1
3.64/3.90	->Bound:
3.64/3.90	 2
3.64/3.90	->Interpretation:
3.64/3.90	 
3.64/3.90	[a__incr](X) = X
3.64/3.90	[a__oddNs] = 2
3.64/3.90	[a__pairNs] = 2
3.64/3.90	[a__repItems](X) = 2.X + 2
3.64/3.90	[a__tail](X) = 2.X + 2
3.64/3.90	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[a__zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[mark](X) = X
3.64/3.90	[0] = 0
3.64/3.90	[cons](X1,X2) = 2.X1 + X2
3.64/3.90	[fSNonEmpty] = 0
3.64/3.90	[incr](X) = X
3.64/3.90	[nil] = 0
3.64/3.90	[oddNs] = 2
3.64/3.90	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.90	[pairNs] = 2
3.64/3.90	[repItems](X) = 2.X + 2
3.64/3.90	[s](X) = X
3.64/3.90	[tail](X) = 2.X + 2
3.64/3.90	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.90	[zip](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.90	[A__INCR](X) = 2.X + 1
3.64/3.90	[A__ODDNS] = 0
3.64/3.90	[A__PAIRNS] = 0
3.64/3.90	[A__REPITEMS](X) = 0
3.64/3.90	[A__TAIL](X) = 0
3.64/3.90	[A__TAKE](X1,X2) = 0
3.64/3.90	[A__ZIP](X1,X2) = X2 + 2
3.64/3.90	[MARK](X) = 2.X + 1
3.64/3.90	
3.64/3.90	Problem 1: 
3.64/3.90	
3.64/3.90	SCC Processor:
3.64/3.90	-> Pairs:
3.64/3.90	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.90	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.90	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> A__ZIP(mark(X1:S),mark(X2:S))
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.90	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.90	-> Rules:
3.64/3.90	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.90	 a__incr(X:S) -> incr(X:S)
3.64/3.90	 a__oddNs -> a__incr(a__pairNs)
3.64/3.90	 a__oddNs -> oddNs
3.64/3.90	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.90	 a__pairNs -> pairNs
3.64/3.90	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.90	 a__repItems(nil) -> nil
3.64/3.90	 a__repItems(X:S) -> repItems(X:S)
3.64/3.90	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.90	 a__tail(X:S) -> tail(X:S)
3.64/3.90	 a__take(0,XS:S) -> nil
3.64/3.90	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.90	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.90	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(repItems(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X + 2
3.64/3.91	[a__tail](X) = X + 1
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = 2.X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 0
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X + 2
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = X + 1
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[A__INCR](X) = X + 1
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 1
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(tail(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X + 2
3.64/3.91	[a__tail](X) = 2.X + 2
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 2
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X + 2
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = 2.X + 2
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[A__INCR](X) = 2.X + 2
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 2
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = 2.X
3.64/3.91	[a__oddNs] = 0
3.64/3.91	[a__pairNs] = 0
3.64/3.91	[a__repItems](X) = 2.X + 2
3.64/3.91	[a__tail](X) = X + 2
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = 2.X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = 2.X
3.64/3.91	[nil] = 2
3.64/3.91	[oddNs] = 0
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 0
3.64/3.91	[repItems](X) = 2.X + 2
3.64/3.91	[s](X) = 2.X
3.64/3.91	[tail](X) = X + 2
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[A__INCR](X) = 2.X + 2
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 2
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(take(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X + 2
3.64/3.91	[a__tail](X) = X + 1
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = 2.X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 1
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X + 2
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = X + 1
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2 + 1
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[A__INCR](X) = X + 1
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 1
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X + 2
3.64/3.91	[a__tail](X) = 2.X + 2
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = 2.X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 2
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X + 2
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = 2.X + 2
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[A__INCR](X) = 2.X + 2
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 2
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(zip(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 Natural Numbers
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X
3.64/3.91	[a__tail](X) = 2.X
3.64/3.91	[a__take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[a__zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = X1 + X2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 2
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = 2.X1 + 2.X2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = 2.X
3.64/3.91	[take](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[zip](X1,X2) = 2.X1 + 2.X2 + 2
3.64/3.91	[A__INCR](X) = 2.X + 2
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 2.X + 2
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Reduction Pairs Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 A__INCR(cons(X:S,XS:S)) -> MARK(X:S)
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	-> Usable rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Interpretation type:
3.64/3.91	 Linear
3.64/3.91	->Coefficients:
3.64/3.91	 All rationals
3.64/3.91	->Dimension:
3.64/3.91	 1
3.64/3.91	->Bound:
3.64/3.91	 2
3.64/3.91	->Interpretation:
3.64/3.91	 
3.64/3.91	[a__incr](X) = X
3.64/3.91	[a__oddNs] = 2
3.64/3.91	[a__pairNs] = 2
3.64/3.91	[a__repItems](X) = 2.X + 1/2
3.64/3.91	[a__tail](X) = 2.X + 1/2
3.64/3.91	[a__take](X1,X2) = 2.X2
3.64/3.91	[a__zip](X1,X2) = X1 + 2.X2
3.64/3.91	[mark](X) = X
3.64/3.91	[0] = 0
3.64/3.91	[cons](X1,X2) = 2.X1 + 1/2.X2 + 1/2
3.64/3.91	[fSNonEmpty] = 0
3.64/3.91	[incr](X) = X
3.64/3.91	[nil] = 0
3.64/3.91	[oddNs] = 2
3.64/3.91	[pair](X1,X2) = X1 + 2.X2 + 1/2
3.64/3.91	[pairNs] = 2
3.64/3.91	[repItems](X) = 2.X + 1/2
3.64/3.91	[s](X) = X
3.64/3.91	[tail](X) = 2.X + 1/2
3.64/3.91	[take](X1,X2) = 2.X2
3.64/3.91	[zip](X1,X2) = X1 + 2.X2
3.64/3.91	[A__INCR](X) = 1/2.X + 1/2
3.64/3.91	[A__ODDNS] = 0
3.64/3.91	[A__PAIRNS] = 0
3.64/3.91	[A__REPITEMS](X) = 0
3.64/3.91	[A__TAIL](X) = 0
3.64/3.91	[A__TAKE](X1,X2) = 0
3.64/3.91	[A__ZIP](X1,X2) = 0
3.64/3.91	[MARK](X) = 1/2.X + 1/2
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> A__INCR(mark(X:S))
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	->->Cycle:
3.64/3.91	->->-> Pairs:
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	->->-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	Subterm Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 MARK(cons(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(incr(X:S)) -> MARK(X:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X1:S)
3.64/3.91	 MARK(pair(X1:S,X2:S)) -> MARK(X2:S)
3.64/3.91	 MARK(s(X:S)) -> MARK(X:S)
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Projection:
3.64/3.91	 pi(MARK) = 1
3.64/3.91	
3.64/3.91	Problem 1: 
3.64/3.91	
3.64/3.91	SCC Processor:
3.64/3.91	-> Pairs:
3.64/3.91	 Empty
3.64/3.91	-> Rules:
3.64/3.91	 a__incr(cons(X:S,XS:S)) -> cons(s(mark(X:S)),incr(XS:S))
3.64/3.91	 a__incr(X:S) -> incr(X:S)
3.64/3.91	 a__oddNs -> a__incr(a__pairNs)
3.64/3.91	 a__oddNs -> oddNs
3.64/3.91	 a__pairNs -> cons(0,incr(oddNs))
3.64/3.91	 a__pairNs -> pairNs
3.64/3.91	 a__repItems(cons(X:S,XS:S)) -> cons(mark(X:S),cons(X:S,repItems(XS:S)))
3.64/3.91	 a__repItems(nil) -> nil
3.64/3.91	 a__repItems(X:S) -> repItems(X:S)
3.64/3.91	 a__tail(cons(X:S,XS:S)) -> mark(XS:S)
3.64/3.91	 a__tail(X:S) -> tail(X:S)
3.64/3.91	 a__take(0,XS:S) -> nil
3.64/3.91	 a__take(s(N:S),cons(X:S,XS:S)) -> cons(mark(X:S),take(N:S,XS:S))
3.64/3.91	 a__take(X1:S,X2:S) -> take(X1:S,X2:S)
3.64/3.91	 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))
3.64/3.91	 a__zip(nil,XS:S) -> nil
3.64/3.91	 a__zip(X:S,nil) -> nil
3.64/3.91	 a__zip(X1:S,X2:S) -> zip(X1:S,X2:S)
3.64/3.91	 mark(0) -> 0
3.64/3.91	 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S)
3.64/3.91	 mark(incr(X:S)) -> a__incr(mark(X:S))
3.64/3.91	 mark(nil) -> nil
3.64/3.91	 mark(oddNs) -> a__oddNs
3.64/3.91	 mark(pair(X1:S,X2:S)) -> pair(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(pairNs) -> a__pairNs
3.64/3.91	 mark(repItems(X:S)) -> a__repItems(mark(X:S))
3.64/3.91	 mark(s(X:S)) -> s(mark(X:S))
3.64/3.91	 mark(tail(X:S)) -> a__tail(mark(X:S))
3.64/3.91	 mark(take(X1:S,X2:S)) -> a__take(mark(X1:S),mark(X2:S))
3.64/3.91	 mark(zip(X1:S,X2:S)) -> a__zip(mark(X1:S),mark(X2:S))
3.64/3.91	->Strongly Connected Components:
3.64/3.91	 There is no strongly connected component
3.64/3.91	
3.64/3.91	The problem is finite.
3.64/3.91	EOF