MAYBE Time: 1.840169 TRS: { a__fst X -> fst X, a__fst pair(X, Y) -> a__U21(a__and(a__isLNat X, isLNat Y), X), a__splitAt(X1, X2) -> splitAt(X1, X2), a__splitAt(s N, cons(X, XS)) -> a__U81(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt(0(), XS) -> a__U71(a__isLNat XS, XS), mark tt() -> tt(), mark cons(X1, X2) -> cons(mark X1, X2), mark natsFrom X -> a__natsFrom mark X, mark s X -> s mark X, mark pair(X1, X2) -> pair(mark X1, mark X2), mark nil() -> nil(), mark isLNat X -> a__isLNat X, mark afterNth(X1, X2) -> a__afterNth(mark X1, mark X2), mark fst X -> a__fst mark X, mark snd X -> a__snd mark X, mark tail X -> a__tail mark X, mark take(X1, X2) -> a__take(mark X1, mark X2), mark 0() -> 0(), mark head X -> a__head mark X, mark sel(X1, X2) -> a__sel(mark X1, mark X2), mark splitAt(X1, X2) -> a__splitAt(mark X1, mark X2), mark and(X1, X2) -> a__and(mark X1, X2), mark isNatural X -> a__isNatural X, mark U101(X1, X2, X3) -> a__U101(mark X1, X2, X3), mark U11(X1, X2, X3) -> a__U11(mark X1, X2, X3), mark U21(X1, X2) -> a__U21(mark X1, X2), mark U31(X1, X2) -> a__U31(mark X1, X2), mark U41(X1, X2) -> a__U41(mark X1, X2), mark U51(X1, X2, X3) -> a__U51(mark X1, X2, X3), mark U61(X1, X2) -> a__U61(mark X1, X2), mark U71(X1, X2) -> a__U71(mark X1, X2), mark U81(X1, X2, X3, X4) -> a__U81(mark X1, X2, X3, X4), mark U82(X1, X2) -> a__U82(mark X1, X2), mark U91(X1, X2) -> a__U91(mark X1, X2), mark isPLNat X -> a__isPLNat X, a__U101(X1, X2, X3) -> U101(X1, X2, X3), a__U101(tt(), N, XS) -> a__fst a__splitAt(mark N, mark XS), a__snd X -> snd X, a__snd pair(X, Y) -> a__U61(a__and(a__isLNat X, isLNat Y), Y), a__U11(X1, X2, X3) -> U11(X1, X2, X3), a__U11(tt(), N, XS) -> a__snd a__splitAt(mark N, mark XS), a__U21(X1, X2) -> U21(X1, X2), a__U21(tt(), X) -> mark X, a__U31(X1, X2) -> U31(X1, X2), a__U31(tt(), N) -> mark N, a__U41(X1, X2) -> U41(X1, X2), a__U41(tt(), N) -> cons(mark N, natsFrom s N), a__head X -> head X, a__head cons(N, XS) -> a__U31(a__and(a__isNatural N, isLNat XS), N), a__afterNth(N, XS) -> a__U11(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth(X1, X2) -> afterNth(X1, X2), a__U51(X1, X2, X3) -> U51(X1, X2, X3), a__U51(tt(), N, XS) -> a__head a__afterNth(mark N, mark XS), a__U61(X1, X2) -> U61(X1, X2), a__U61(tt(), Y) -> mark Y, a__U71(X1, X2) -> U71(X1, X2), a__U71(tt(), XS) -> pair(nil(), mark XS), a__U82(X1, X2) -> U82(X1, X2), a__U82(pair(YS, ZS), X) -> pair(cons(mark X, YS), mark ZS), a__U81(X1, X2, X3, X4) -> U81(X1, X2, X3, X4), a__U81(tt(), N, X, XS) -> a__U82(a__splitAt(mark N, mark XS), X), a__U91(X1, X2) -> U91(X1, X2), a__U91(tt(), XS) -> mark XS, a__and(X1, X2) -> and(X1, X2), a__and(tt(), X) -> mark X, a__isNatural X -> isNatural X, a__isNatural s V1 -> a__isNatural V1, a__isNatural 0() -> tt(), a__isNatural head V1 -> a__isLNat V1, a__isNatural sel(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat X -> isLNat X, a__isLNat cons(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat natsFrom V1 -> a__isNatural V1, a__isLNat nil() -> tt(), a__isLNat afterNth(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat fst V1 -> a__isPLNat V1, a__isLNat snd V1 -> a__isPLNat V1, a__isLNat tail V1 -> a__isLNat V1, a__isLNat take(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isPLNat X -> isPLNat X, a__isPLNat pair(V1, V2) -> a__and(a__isLNat V1, isLNat V2), a__isPLNat splitAt(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__natsFrom N -> a__U41(a__isNatural N, N), a__natsFrom X -> natsFrom X, a__sel(N, XS) -> a__U51(a__and(a__isNatural N, isLNat XS), N, XS), a__sel(X1, X2) -> sel(X1, X2), a__tail X -> tail X, a__tail cons(N, XS) -> a__U91(a__and(a__isNatural N, isLNat XS), XS), a__take(N, XS) -> a__U101(a__and(a__isNatural N, isLNat XS), N, XS), a__take(X1, X2) -> take(X1, X2)} DP: DP: { a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X), a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__fst# pair(X, Y) -> a__isLNat# X, a__splitAt#(s N, cons(X, XS)) -> a__U81#(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt#(s N, cons(X, XS)) -> a__and#(a__isNatural N, and(isNatural X, isLNat XS)), a__splitAt#(s N, cons(X, XS)) -> a__isNatural# N, a__splitAt#(0(), XS) -> a__U71#(a__isLNat XS, XS), a__splitAt#(0(), XS) -> a__isLNat# XS, mark# cons(X1, X2) -> mark# X1, mark# natsFrom X -> mark# X, mark# natsFrom X -> a__natsFrom# mark X, mark# s X -> mark# X, mark# pair(X1, X2) -> mark# X1, mark# pair(X1, X2) -> mark# X2, mark# isLNat X -> a__isLNat# X, mark# afterNth(X1, X2) -> mark# X1, mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2), mark# fst X -> a__fst# mark X, mark# fst X -> mark# X, mark# snd X -> mark# X, mark# snd X -> a__snd# mark X, mark# tail X -> mark# X, mark# tail X -> a__tail# mark X, mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> a__take#(mark X1, mark X2), mark# head X -> mark# X, mark# head X -> a__head# mark X, mark# sel(X1, X2) -> mark# X1, mark# sel(X1, X2) -> mark# X2, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2), mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), mark# splitAt(X1, X2) -> mark# X1, mark# splitAt(X1, X2) -> mark# X2, mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> a__and#(mark X1, X2), mark# isNatural X -> a__isNatural# X, mark# U101(X1, X2, X3) -> mark# X1, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3), mark# U11(X1, X2, X3) -> mark# X1, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3), mark# U21(X1, X2) -> mark# X1, mark# U21(X1, X2) -> a__U21#(mark X1, X2), mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> a__U31#(mark X1, X2), mark# U41(X1, X2) -> mark# X1, mark# U41(X1, X2) -> a__U41#(mark X1, X2), mark# U51(X1, X2, X3) -> mark# X1, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3), mark# U61(X1, X2) -> mark# X1, mark# U61(X1, X2) -> a__U61#(mark X1, X2), mark# U71(X1, X2) -> mark# X1, mark# U71(X1, X2) -> a__U71#(mark X1, X2), mark# U81(X1, X2, X3, X4) -> mark# X1, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4), mark# U82(X1, X2) -> mark# X1, mark# U82(X1, X2) -> a__U82#(mark X1, X2), mark# U91(X1, X2) -> mark# X1, mark# U91(X1, X2) -> a__U91#(mark X1, X2), mark# isPLNat X -> a__isPLNat# X, a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__U101#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U101#(tt(), N, XS) -> mark# N, a__U101#(tt(), N, XS) -> mark# XS, a__snd# pair(X, Y) -> a__U61#(a__and(a__isLNat X, isLNat Y), Y), a__snd# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__snd# pair(X, Y) -> a__isLNat# X, a__U11#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U11#(tt(), N, XS) -> mark# N, a__U11#(tt(), N, XS) -> mark# XS, a__U11#(tt(), N, XS) -> a__snd# a__splitAt(mark N, mark XS), a__U21#(tt(), X) -> mark# X, a__U31#(tt(), N) -> mark# N, a__U41#(tt(), N) -> mark# N, a__head# cons(N, XS) -> a__U31#(a__and(a__isNatural N, isLNat XS), N), a__head# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__head# cons(N, XS) -> a__isNatural# N, a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__afterNth#(N, XS) -> a__isNatural# N, a__U51#(tt(), N, XS) -> mark# N, a__U51#(tt(), N, XS) -> mark# XS, a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__U61#(tt(), Y) -> mark# Y, a__U71#(tt(), XS) -> mark# XS, a__U82#(pair(YS, ZS), X) -> mark# X, a__U82#(pair(YS, ZS), X) -> mark# ZS, a__U81#(tt(), N, X, XS) -> a__splitAt#(mark N, mark XS), a__U81#(tt(), N, X, XS) -> mark# N, a__U81#(tt(), N, X, XS) -> mark# XS, a__U81#(tt(), N, X, XS) -> a__U82#(a__splitAt(mark N, mark XS), X), a__U91#(tt(), XS) -> mark# XS, a__and#(tt(), X) -> mark# X, a__isNatural# s V1 -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isNatural# sel(V1, V2) -> a__isNatural# V1, a__isLNat# cons(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isLNat# natsFrom V1 -> a__isNatural# V1, a__isLNat# afterNth(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isLNat# fst V1 -> a__isPLNat# V1, a__isLNat# snd V1 -> a__isPLNat# V1, a__isLNat# tail V1 -> a__isLNat# V1, a__isLNat# take(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isPLNat# pair(V1, V2) -> a__and#(a__isLNat V1, isLNat V2), a__isPLNat# pair(V1, V2) -> a__isLNat# V1, a__isPLNat# splitAt(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__natsFrom# N -> a__U41#(a__isNatural N, N), a__natsFrom# N -> a__isNatural# N, a__sel#(N, XS) -> a__U51#(a__and(a__isNatural N, isLNat XS), N, XS), a__sel#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__sel#(N, XS) -> a__isNatural# N, a__tail# cons(N, XS) -> a__U91#(a__and(a__isNatural N, isLNat XS), XS), a__tail# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__tail# cons(N, XS) -> a__isNatural# N, a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__take#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__take#(N, XS) -> a__isNatural# N} TRS: { a__fst X -> fst X, a__fst pair(X, Y) -> a__U21(a__and(a__isLNat X, isLNat Y), X), a__splitAt(X1, X2) -> splitAt(X1, X2), a__splitAt(s N, cons(X, XS)) -> a__U81(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt(0(), XS) -> a__U71(a__isLNat XS, XS), mark tt() -> tt(), mark cons(X1, X2) -> cons(mark X1, X2), mark natsFrom X -> a__natsFrom mark X, mark s X -> s mark X, mark pair(X1, X2) -> pair(mark X1, mark X2), mark nil() -> nil(), mark isLNat X -> a__isLNat X, mark afterNth(X1, X2) -> a__afterNth(mark X1, mark X2), mark fst X -> a__fst mark X, mark snd X -> a__snd mark X, mark tail X -> a__tail mark X, mark take(X1, X2) -> a__take(mark X1, mark X2), mark 0() -> 0(), mark head X -> a__head mark X, mark sel(X1, X2) -> a__sel(mark X1, mark X2), mark splitAt(X1, X2) -> a__splitAt(mark X1, mark X2), mark and(X1, X2) -> a__and(mark X1, X2), mark isNatural X -> a__isNatural X, mark U101(X1, X2, X3) -> a__U101(mark X1, X2, X3), mark U11(X1, X2, X3) -> a__U11(mark X1, X2, X3), mark U21(X1, X2) -> a__U21(mark X1, X2), mark U31(X1, X2) -> a__U31(mark X1, X2), mark U41(X1, X2) -> a__U41(mark X1, X2), mark U51(X1, X2, X3) -> a__U51(mark X1, X2, X3), mark U61(X1, X2) -> a__U61(mark X1, X2), mark U71(X1, X2) -> a__U71(mark X1, X2), mark U81(X1, X2, X3, X4) -> a__U81(mark X1, X2, X3, X4), mark U82(X1, X2) -> a__U82(mark X1, X2), mark U91(X1, X2) -> a__U91(mark X1, X2), mark isPLNat X -> a__isPLNat X, a__U101(X1, X2, X3) -> U101(X1, X2, X3), a__U101(tt(), N, XS) -> a__fst a__splitAt(mark N, mark XS), a__snd X -> snd X, a__snd pair(X, Y) -> a__U61(a__and(a__isLNat X, isLNat Y), Y), a__U11(X1, X2, X3) -> U11(X1, X2, X3), a__U11(tt(), N, XS) -> a__snd a__splitAt(mark N, mark XS), a__U21(X1, X2) -> U21(X1, X2), a__U21(tt(), X) -> mark X, a__U31(X1, X2) -> U31(X1, X2), a__U31(tt(), N) -> mark N, a__U41(X1, X2) -> U41(X1, X2), a__U41(tt(), N) -> cons(mark N, natsFrom s N), a__head X -> head X, a__head cons(N, XS) -> a__U31(a__and(a__isNatural N, isLNat XS), N), a__afterNth(N, XS) -> a__U11(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth(X1, X2) -> afterNth(X1, X2), a__U51(X1, X2, X3) -> U51(X1, X2, X3), a__U51(tt(), N, XS) -> a__head a__afterNth(mark N, mark XS), a__U61(X1, X2) -> U61(X1, X2), a__U61(tt(), Y) -> mark Y, a__U71(X1, X2) -> U71(X1, X2), a__U71(tt(), XS) -> pair(nil(), mark XS), a__U82(X1, X2) -> U82(X1, X2), a__U82(pair(YS, ZS), X) -> pair(cons(mark X, YS), mark ZS), a__U81(X1, X2, X3, X4) -> U81(X1, X2, X3, X4), a__U81(tt(), N, X, XS) -> a__U82(a__splitAt(mark N, mark XS), X), a__U91(X1, X2) -> U91(X1, X2), a__U91(tt(), XS) -> mark XS, a__and(X1, X2) -> and(X1, X2), a__and(tt(), X) -> mark X, a__isNatural X -> isNatural X, a__isNatural s V1 -> a__isNatural V1, a__isNatural 0() -> tt(), a__isNatural head V1 -> a__isLNat V1, a__isNatural sel(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat X -> isLNat X, a__isLNat cons(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat natsFrom V1 -> a__isNatural V1, a__isLNat nil() -> tt(), a__isLNat afterNth(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat fst V1 -> a__isPLNat V1, a__isLNat snd V1 -> a__isPLNat V1, a__isLNat tail V1 -> a__isLNat V1, a__isLNat take(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isPLNat X -> isPLNat X, a__isPLNat pair(V1, V2) -> a__and(a__isLNat V1, isLNat V2), a__isPLNat splitAt(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__natsFrom N -> a__U41(a__isNatural N, N), a__natsFrom X -> natsFrom X, a__sel(N, XS) -> a__U51(a__and(a__isNatural N, isLNat XS), N, XS), a__sel(X1, X2) -> sel(X1, X2), a__tail X -> tail X, a__tail cons(N, XS) -> a__U91(a__and(a__isNatural N, isLNat XS), XS), a__take(N, XS) -> a__U101(a__and(a__isNatural N, isLNat XS), N, XS), a__take(X1, X2) -> take(X1, X2)} EDG: { (a__natsFrom# N -> a__U41#(a__isNatural N, N), a__U41#(tt(), N) -> mark# N) (a__U61#(tt(), Y) -> mark# Y, mark# isPLNat X -> a__isPLNat# X) (a__U61#(tt(), Y) -> mark# Y, mark# U91(X1, X2) -> a__U91#(mark X1, X2)) (a__U61#(tt(), Y) -> mark# Y, mark# U91(X1, X2) -> mark# X1) (a__U61#(tt(), Y) -> mark# Y, mark# U82(X1, X2) -> a__U82#(mark X1, X2)) (a__U61#(tt(), Y) -> mark# Y, mark# U82(X1, X2) -> mark# X1) (a__U61#(tt(), Y) -> mark# Y, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4)) (a__U61#(tt(), Y) -> mark# Y, mark# U81(X1, X2, X3, X4) -> mark# X1) (a__U61#(tt(), Y) -> mark# Y, mark# U71(X1, X2) -> a__U71#(mark X1, X2)) (a__U61#(tt(), Y) -> mark# Y, mark# U71(X1, X2) -> mark# X1) (a__U61#(tt(), Y) -> mark# Y, mark# U61(X1, X2) -> a__U61#(mark X1, X2)) (a__U61#(tt(), Y) -> mark# Y, mark# U61(X1, X2) -> mark# X1) (a__U61#(tt(), Y) -> mark# Y, mark# U51(X1, X2, X3) -> a__U51#(mark X1, 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a__and#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# isNatural X -> a__isNatural# X) (mark# sel(X1, X2) -> mark# X2, mark# U101(X1, X2, X3) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3)) (mark# sel(X1, X2) -> mark# X2, mark# U11(X1, X2, X3) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3)) (mark# sel(X1, X2) -> mark# X2, mark# U21(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U21(X1, X2) -> a__U21#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U31(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U31(X1, X2) -> a__U31#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U41(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U41(X1, X2) -> a__U41#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U51(X1, X2, X3) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3)) (mark# sel(X1, X2) -> mark# X2, mark# U61(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U61(X1, X2) -> a__U61#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U71(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U71(X1, X2) -> a__U71#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U81(X1, X2, X3, X4) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4)) (mark# sel(X1, X2) -> mark# X2, mark# U82(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U82(X1, X2) -> a__U82#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# U91(X1, X2) -> mark# X1) (mark# sel(X1, X2) -> mark# X2, mark# U91(X1, X2) -> a__U91#(mark X1, X2)) (mark# sel(X1, X2) -> mark# X2, mark# isPLNat X -> a__isPLNat# X) (mark# afterNth(X1, X2) -> mark# X2, mark# cons(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# natsFrom X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# natsFrom X -> a__natsFrom# mark X) (mark# afterNth(X1, X2) -> mark# X2, mark# s X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# pair(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# pair(X1, X2) -> mark# X2) (mark# afterNth(X1, X2) -> mark# X2, mark# isLNat X -> a__isLNat# X) (mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> mark# X2) (mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# fst X -> a__fst# mark X) (mark# afterNth(X1, X2) -> mark# X2, mark# fst X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# snd X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# snd X -> a__snd# mark X) (mark# afterNth(X1, X2) -> mark# X2, mark# tail X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# tail X -> a__tail# mark X) (mark# afterNth(X1, X2) -> mark# X2, mark# take(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# take(X1, X2) -> mark# X2) (mark# afterNth(X1, X2) -> mark# X2, mark# take(X1, X2) -> a__take#(mark X1, mark X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# head X -> mark# X) (mark# afterNth(X1, X2) -> mark# X2, mark# head X -> a__head# mark X) (mark# afterNth(X1, X2) -> mark# X2, mark# sel(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# sel(X1, X2) -> mark# X2) (mark# afterNth(X1, X2) -> mark# X2, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# splitAt(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# splitAt(X1, X2) -> mark# X2) (mark# afterNth(X1, X2) -> mark# X2, mark# and(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# and(X1, X2) -> a__and#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# isNatural X -> a__isNatural# X) (mark# afterNth(X1, X2) -> mark# X2, mark# U101(X1, X2, X3) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3)) (mark# afterNth(X1, X2) -> mark# X2, mark# U11(X1, X2, X3) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3)) (mark# afterNth(X1, X2) -> mark# X2, mark# U21(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U21(X1, X2) -> a__U21#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U31(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U31(X1, X2) -> a__U31#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U41(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U41(X1, X2) -> a__U41#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U51(X1, X2, X3) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3)) (mark# afterNth(X1, X2) -> mark# X2, mark# U61(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U61(X1, X2) -> a__U61#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U71(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U71(X1, X2) -> a__U71#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U81(X1, X2, X3, X4) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4)) (mark# afterNth(X1, X2) -> mark# X2, mark# U82(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U82(X1, X2) -> a__U82#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# U91(X1, X2) -> mark# X1) (mark# afterNth(X1, X2) -> mark# X2, mark# U91(X1, X2) -> a__U91#(mark X1, X2)) (mark# afterNth(X1, X2) -> mark# X2, mark# isPLNat X -> a__isPLNat# X) (a__U91#(tt(), XS) -> mark# XS, mark# cons(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# natsFrom X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# natsFrom X -> a__natsFrom# mark X) (a__U91#(tt(), XS) -> mark# XS, mark# s X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# pair(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# pair(X1, X2) -> mark# X2) (a__U91#(tt(), XS) -> mark# XS, mark# isLNat X -> a__isLNat# X) (a__U91#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> mark# X2) (a__U91#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2)) (a__U91#(tt(), XS) -> mark# XS, mark# fst X -> a__fst# mark X) (a__U91#(tt(), XS) -> mark# XS, mark# fst X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# snd X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# snd X -> a__snd# mark X) (a__U91#(tt(), XS) -> mark# XS, mark# tail X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# tail X -> a__tail# mark X) (a__U91#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> mark# X2) (a__U91#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> a__take#(mark X1, mark X2)) (a__U91#(tt(), XS) -> mark# XS, mark# head X -> mark# X) (a__U91#(tt(), XS) -> mark# XS, mark# head X -> a__head# mark X) (a__U91#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> mark# X2) (a__U91#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2)) (a__U91#(tt(), XS) -> mark# XS, mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2)) (a__U91#(tt(), XS) -> mark# XS, mark# splitAt(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# splitAt(X1, X2) -> mark# X2) (a__U91#(tt(), XS) -> mark# XS, mark# and(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# and(X1, X2) -> a__and#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# isNatural X -> a__isNatural# X) (a__U91#(tt(), XS) -> mark# XS, mark# U101(X1, X2, X3) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3)) (a__U91#(tt(), XS) -> mark# XS, mark# U11(X1, X2, X3) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3)) (a__U91#(tt(), XS) -> mark# XS, mark# U21(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U21(X1, X2) -> a__U21#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U31(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U31(X1, X2) -> a__U31#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U41(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U41(X1, X2) -> a__U41#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U51(X1, X2, X3) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3)) (a__U91#(tt(), XS) -> mark# XS, mark# U61(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U61(X1, X2) -> a__U61#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U71(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U71(X1, X2) -> a__U71#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U81(X1, X2, X3, X4) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4)) (a__U91#(tt(), XS) -> mark# XS, mark# U82(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U82(X1, X2) -> a__U82#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# U91(X1, X2) -> mark# X1) (a__U91#(tt(), XS) -> mark# XS, mark# U91(X1, X2) -> a__U91#(mark X1, X2)) (a__U91#(tt(), XS) -> mark# XS, mark# isPLNat X -> a__isPLNat# X) (a__U71#(tt(), XS) -> mark# XS, mark# cons(X1, X2) -> mark# X1) (a__U71#(tt(), XS) -> mark# XS, mark# natsFrom X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# natsFrom X -> a__natsFrom# mark X) (a__U71#(tt(), XS) -> mark# XS, mark# s X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# pair(X1, X2) -> mark# X1) (a__U71#(tt(), XS) -> mark# XS, mark# pair(X1, X2) -> mark# X2) (a__U71#(tt(), XS) -> mark# XS, mark# isLNat X -> a__isLNat# X) (a__U71#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> mark# X1) (a__U71#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> mark# X2) (a__U71#(tt(), XS) -> mark# XS, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2)) (a__U71#(tt(), XS) -> mark# XS, mark# fst X -> a__fst# mark X) (a__U71#(tt(), XS) -> mark# XS, mark# fst X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# snd X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# snd X -> a__snd# mark X) (a__U71#(tt(), XS) -> mark# XS, mark# tail X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# tail X -> a__tail# mark X) (a__U71#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> mark# X1) (a__U71#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> mark# X2) (a__U71#(tt(), XS) -> mark# XS, mark# take(X1, X2) -> a__take#(mark X1, mark X2)) (a__U71#(tt(), XS) -> mark# XS, mark# head X -> mark# X) (a__U71#(tt(), XS) -> mark# XS, mark# head X -> a__head# mark X) (a__U71#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> mark# X1) (a__U71#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> mark# X2) (a__U71#(tt(), XS) -> mark# XS, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2)) (a__U71#(tt(), XS) -> mark# XS, mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2)) (a__U71#(tt(), XS) -> mark# 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and(isNatural X, isLNat XS)), N, X, XS), a__U81#(tt(), N, X, XS) -> a__U82#(a__splitAt(mark N, mark XS), X)) (a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__isNatural# s V1 -> a__isNatural# V1) (a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1) (a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__isNatural# V1) (a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isNatural# s V1 -> a__isNatural# V1) (a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1) (a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__isNatural# V1) (a__isLNat# snd V1 -> a__isPLNat# V1, a__isPLNat# pair(V1, V2) -> a__and#(a__isLNat V1, isLNat V2)) (a__isLNat# snd V1 -> a__isPLNat# V1, a__isPLNat# pair(V1, V2) -> a__isLNat# V1) (a__isLNat# snd V1 -> a__isPLNat# V1, a__isPLNat# splitAt(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isLNat# snd V1 -> a__isPLNat# V1, a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1) (a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isNatural# s V1 -> a__isNatural# V1) (a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1) (a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__isNatural# V1) (a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isNatural# s V1 -> a__isNatural# V1) (a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1) (a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isNatural# sel(V1, V2) -> a__isNatural# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# cons(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# cons(V1, V2) -> a__isNatural# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# natsFrom V1 -> a__isNatural# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# afterNth(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# afterNth(V1, V2) -> a__isNatural# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# fst V1 -> a__isPLNat# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# snd V1 -> a__isPLNat# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# tail V1 -> a__isLNat# V1) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# take(V1, V2) -> a__and#(a__isNatural V1, isLNat V2)) (a__isNatural# head V1 -> a__isLNat# V1, a__isLNat# take(V1, V2) -> a__isNatural# V1) (a__take#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__and#(tt(), X) -> mark# X) (a__sel#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__and#(tt(), X) -> mark# X) (a__isPLNat# pair(V1, V2) -> a__and#(a__isLNat V1, isLNat V2), a__and#(tt(), X) -> mark# X) (a__isLNat# afterNth(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__and#(tt(), X) -> mark# X) (a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__and#(tt(), X) -> mark# X) (a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS)) (a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__afterNth#(N, XS) -> a__and#(a__isNatural N, isLNat XS)) (a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__afterNth#(N, XS) -> a__isNatural# N) (a__head# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__and#(tt(), X) -> mark# X) (a__snd# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__and#(tt(), X) -> mark# X) (mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), a__splitAt#(s N, cons(X, XS)) -> a__U81#(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS)) (mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), a__splitAt#(s N, cons(X, XS)) -> a__and#(a__isNatural N, and(isNatural X, isLNat XS))) (mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), a__splitAt#(s N, cons(X, XS)) -> a__isNatural# N) (mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), a__splitAt#(0(), XS) -> a__U71#(a__isLNat XS, XS)) (mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), a__splitAt#(0(), XS) -> a__isLNat# XS) (mark# take(X1, X2) -> a__take#(mark X1, mark X2), a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS)) (mark# take(X1, X2) -> a__take#(mark X1, mark X2), a__take#(N, XS) -> a__and#(a__isNatural N, isLNat XS)) (mark# take(X1, X2) -> a__take#(mark X1, mark X2), a__take#(N, XS) -> a__isNatural# N) (a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__and#(tt(), X) -> mark# X) (mark# tail X -> a__tail# mark X, a__tail# cons(N, XS) -> a__U91#(a__and(a__isNatural N, isLNat XS), XS)) (mark# tail X -> a__tail# mark X, a__tail# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS)) (mark# tail X -> a__tail# mark X, a__tail# cons(N, XS) -> a__isNatural# N) (mark# fst X -> a__fst# mark X, a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X)) (mark# fst X -> a__fst# mark X, a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y)) (mark# fst X -> a__fst# mark X, a__fst# pair(X, Y) -> a__isLNat# X) (a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS)) (a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__U101#(tt(), N, XS) -> a__splitAt#(mark N, mark XS)) (a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__U101#(tt(), N, XS) -> mark# N) (a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__U101#(tt(), N, XS) -> mark# XS) (a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__U11#(tt(), N, XS) -> a__splitAt#(mark N, mark XS)) (a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__U11#(tt(), N, XS) -> mark# N) (a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__U11#(tt(), N, XS) -> mark# XS) (a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__U11#(tt(), N, XS) -> a__snd# a__splitAt(mark N, mark XS)) (a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__head# cons(N, XS) -> a__U31#(a__and(a__isNatural N, isLNat XS), N)) (a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__head# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS)) (a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__head# cons(N, XS) -> a__isNatural# N) (a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X)) (a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y)) (a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__fst# pair(X, Y) -> a__isLNat# X) (a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X), a__U21#(tt(), X) -> mark# X) (a__splitAt#(s N, cons(X, XS)) -> a__and#(a__isNatural N, and(isNatural X, isLNat XS)), a__and#(tt(), X) -> mark# X) (a__head# cons(N, XS) -> a__U31#(a__and(a__isNatural N, isLNat XS), N), a__U31#(tt(), N) -> mark# N) } STATUS: arrows: 0.824532 SCCS (1): Scc: { a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X), a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__fst# pair(X, Y) -> a__isLNat# X, a__splitAt#(s N, cons(X, XS)) -> a__U81#(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt#(s N, cons(X, XS)) -> a__and#(a__isNatural N, and(isNatural X, isLNat XS)), a__splitAt#(s N, cons(X, XS)) -> a__isNatural# N, a__splitAt#(0(), XS) -> a__U71#(a__isLNat XS, XS), a__splitAt#(0(), XS) -> a__isLNat# XS, mark# cons(X1, X2) -> mark# X1, mark# natsFrom X -> mark# X, mark# natsFrom X -> a__natsFrom# mark X, mark# s X -> mark# X, mark# pair(X1, X2) -> mark# X1, mark# pair(X1, X2) -> mark# X2, mark# isLNat X -> a__isLNat# X, mark# afterNth(X1, X2) -> mark# X1, mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2), mark# fst X -> a__fst# mark X, mark# fst X -> mark# X, mark# snd X -> mark# X, mark# snd X -> a__snd# mark X, mark# tail X -> mark# X, mark# tail X -> a__tail# mark X, mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> a__take#(mark X1, mark X2), mark# head X -> mark# X, mark# head X -> a__head# mark X, mark# sel(X1, X2) -> mark# X1, mark# sel(X1, X2) -> mark# X2, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2), mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), mark# splitAt(X1, X2) -> mark# X1, mark# splitAt(X1, X2) -> mark# X2, mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> a__and#(mark X1, X2), mark# isNatural X -> a__isNatural# X, mark# U101(X1, X2, X3) -> mark# X1, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3), mark# U11(X1, X2, X3) -> mark# X1, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3), mark# U21(X1, X2) -> mark# X1, mark# U21(X1, X2) -> a__U21#(mark X1, X2), mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> a__U31#(mark X1, X2), mark# U41(X1, X2) -> mark# X1, mark# U41(X1, X2) -> a__U41#(mark X1, X2), mark# U51(X1, X2, X3) -> mark# X1, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3), mark# U61(X1, X2) -> mark# X1, mark# U61(X1, X2) -> a__U61#(mark X1, X2), mark# U71(X1, X2) -> mark# X1, mark# U71(X1, X2) -> a__U71#(mark X1, X2), mark# U81(X1, X2, X3, X4) -> mark# X1, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4), mark# U82(X1, X2) -> mark# X1, mark# U82(X1, X2) -> a__U82#(mark X1, X2), mark# U91(X1, X2) -> mark# X1, mark# U91(X1, X2) -> a__U91#(mark X1, X2), mark# isPLNat X -> a__isPLNat# X, a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__U101#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U101#(tt(), N, XS) -> mark# N, a__U101#(tt(), N, XS) -> mark# XS, a__snd# pair(X, Y) -> a__U61#(a__and(a__isLNat X, isLNat Y), Y), a__snd# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__snd# pair(X, Y) -> a__isLNat# X, a__U11#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U11#(tt(), N, XS) -> mark# N, a__U11#(tt(), N, XS) -> mark# XS, a__U11#(tt(), N, XS) -> a__snd# a__splitAt(mark N, mark XS), a__U21#(tt(), X) -> mark# X, a__U31#(tt(), N) -> mark# N, a__U41#(tt(), N) -> mark# N, a__head# cons(N, XS) -> a__U31#(a__and(a__isNatural N, isLNat XS), N), a__head# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__head# cons(N, XS) -> a__isNatural# N, a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__afterNth#(N, XS) -> a__isNatural# N, a__U51#(tt(), N, XS) -> mark# N, a__U51#(tt(), N, XS) -> mark# XS, a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__U61#(tt(), Y) -> mark# Y, a__U71#(tt(), XS) -> mark# XS, a__U82#(pair(YS, ZS), X) -> mark# X, a__U82#(pair(YS, ZS), X) -> mark# ZS, a__U81#(tt(), N, X, XS) -> a__splitAt#(mark N, mark XS), a__U81#(tt(), N, X, XS) -> mark# N, a__U81#(tt(), N, X, XS) -> mark# XS, a__U81#(tt(), N, X, XS) -> a__U82#(a__splitAt(mark N, mark XS), X), a__U91#(tt(), XS) -> mark# XS, a__and#(tt(), X) -> mark# X, a__isNatural# s V1 -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isNatural# sel(V1, V2) -> a__isNatural# V1, a__isLNat# cons(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isLNat# natsFrom V1 -> a__isNatural# V1, a__isLNat# afterNth(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isLNat# fst V1 -> a__isPLNat# V1, a__isLNat# snd V1 -> a__isPLNat# V1, a__isLNat# tail V1 -> a__isLNat# V1, a__isLNat# take(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isPLNat# pair(V1, V2) -> a__and#(a__isLNat V1, isLNat V2), a__isPLNat# pair(V1, V2) -> a__isLNat# V1, a__isPLNat# splitAt(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__natsFrom# N -> a__U41#(a__isNatural N, N), a__natsFrom# N -> a__isNatural# N, a__sel#(N, XS) -> a__U51#(a__and(a__isNatural N, isLNat XS), N, XS), a__sel#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__sel#(N, XS) -> a__isNatural# N, a__tail# cons(N, XS) -> a__U91#(a__and(a__isNatural N, isLNat XS), XS), a__tail# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__tail# cons(N, XS) -> a__isNatural# N, a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__take#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__take#(N, XS) -> a__isNatural# N} SCC (124): Strict: { a__fst# pair(X, Y) -> a__U21#(a__and(a__isLNat X, isLNat Y), X), a__fst# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__fst# pair(X, Y) -> a__isLNat# X, a__splitAt#(s N, cons(X, XS)) -> a__U81#(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt#(s N, cons(X, XS)) -> a__and#(a__isNatural N, and(isNatural X, isLNat XS)), a__splitAt#(s N, cons(X, XS)) -> a__isNatural# N, a__splitAt#(0(), XS) -> a__U71#(a__isLNat XS, XS), a__splitAt#(0(), XS) -> a__isLNat# XS, mark# cons(X1, X2) -> mark# X1, mark# natsFrom X -> mark# X, mark# natsFrom X -> a__natsFrom# mark X, mark# s X -> mark# X, mark# pair(X1, X2) -> mark# X1, mark# pair(X1, X2) -> mark# X2, mark# isLNat X -> a__isLNat# X, mark# afterNth(X1, X2) -> mark# X1, mark# afterNth(X1, X2) -> mark# X2, mark# afterNth(X1, X2) -> a__afterNth#(mark X1, mark X2), mark# fst X -> a__fst# mark X, mark# fst X -> mark# X, mark# snd X -> mark# X, mark# snd X -> a__snd# mark X, mark# tail X -> mark# X, mark# tail X -> a__tail# mark X, mark# take(X1, X2) -> mark# X1, mark# take(X1, X2) -> mark# X2, mark# take(X1, X2) -> a__take#(mark X1, mark X2), mark# head X -> mark# X, mark# head X -> a__head# mark X, mark# sel(X1, X2) -> mark# X1, mark# sel(X1, X2) -> mark# X2, mark# sel(X1, X2) -> a__sel#(mark X1, mark X2), mark# splitAt(X1, X2) -> a__splitAt#(mark X1, mark X2), mark# splitAt(X1, X2) -> mark# X1, mark# splitAt(X1, X2) -> mark# X2, mark# and(X1, X2) -> mark# X1, mark# and(X1, X2) -> a__and#(mark X1, X2), mark# isNatural X -> a__isNatural# X, mark# U101(X1, X2, X3) -> mark# X1, mark# U101(X1, X2, X3) -> a__U101#(mark X1, X2, X3), mark# U11(X1, X2, X3) -> mark# X1, mark# U11(X1, X2, X3) -> a__U11#(mark X1, X2, X3), mark# U21(X1, X2) -> mark# X1, mark# U21(X1, X2) -> a__U21#(mark X1, X2), mark# U31(X1, X2) -> mark# X1, mark# U31(X1, X2) -> a__U31#(mark X1, X2), mark# U41(X1, X2) -> mark# X1, mark# U41(X1, X2) -> a__U41#(mark X1, X2), mark# U51(X1, X2, X3) -> mark# X1, mark# U51(X1, X2, X3) -> a__U51#(mark X1, X2, X3), mark# U61(X1, X2) -> mark# X1, mark# U61(X1, X2) -> a__U61#(mark X1, X2), mark# U71(X1, X2) -> mark# X1, mark# U71(X1, X2) -> a__U71#(mark X1, X2), mark# U81(X1, X2, X3, X4) -> mark# X1, mark# U81(X1, X2, X3, X4) -> a__U81#(mark X1, X2, X3, X4), mark# U82(X1, X2) -> mark# X1, mark# U82(X1, X2) -> a__U82#(mark X1, X2), mark# U91(X1, X2) -> mark# X1, mark# U91(X1, X2) -> a__U91#(mark X1, X2), mark# isPLNat X -> a__isPLNat# X, a__U101#(tt(), N, XS) -> a__fst# a__splitAt(mark N, mark XS), a__U101#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U101#(tt(), N, XS) -> mark# N, a__U101#(tt(), N, XS) -> mark# XS, a__snd# pair(X, Y) -> a__U61#(a__and(a__isLNat X, isLNat Y), Y), a__snd# pair(X, Y) -> a__and#(a__isLNat X, isLNat Y), a__snd# pair(X, Y) -> a__isLNat# X, a__U11#(tt(), N, XS) -> a__splitAt#(mark N, mark XS), a__U11#(tt(), N, XS) -> mark# N, a__U11#(tt(), N, XS) -> mark# XS, a__U11#(tt(), N, XS) -> a__snd# a__splitAt(mark N, mark XS), a__U21#(tt(), X) -> mark# X, a__U31#(tt(), N) -> mark# N, a__U41#(tt(), N) -> mark# N, a__head# cons(N, XS) -> a__U31#(a__and(a__isNatural N, isLNat XS), N), a__head# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__head# cons(N, XS) -> a__isNatural# N, a__afterNth#(N, XS) -> a__U11#(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__afterNth#(N, XS) -> a__isNatural# N, a__U51#(tt(), N, XS) -> mark# N, a__U51#(tt(), N, XS) -> mark# XS, a__U51#(tt(), N, XS) -> a__head# a__afterNth(mark N, mark XS), a__U51#(tt(), N, XS) -> a__afterNth#(mark N, mark XS), a__U61#(tt(), Y) -> mark# Y, a__U71#(tt(), XS) -> mark# XS, a__U82#(pair(YS, ZS), X) -> mark# X, a__U82#(pair(YS, ZS), X) -> mark# ZS, a__U81#(tt(), N, X, XS) -> a__splitAt#(mark N, mark XS), a__U81#(tt(), N, X, XS) -> mark# N, a__U81#(tt(), N, X, XS) -> mark# XS, a__U81#(tt(), N, X, XS) -> a__U82#(a__splitAt(mark N, mark XS), X), a__U91#(tt(), XS) -> mark# XS, a__and#(tt(), X) -> mark# X, a__isNatural# s V1 -> a__isNatural# V1, a__isNatural# head V1 -> a__isLNat# V1, a__isNatural# sel(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isNatural# sel(V1, V2) -> a__isNatural# V1, a__isLNat# cons(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# cons(V1, V2) -> a__isNatural# V1, a__isLNat# natsFrom V1 -> a__isNatural# V1, a__isLNat# afterNth(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# afterNth(V1, V2) -> a__isNatural# V1, a__isLNat# fst V1 -> a__isPLNat# V1, a__isLNat# snd V1 -> a__isPLNat# V1, a__isLNat# tail V1 -> a__isLNat# V1, a__isLNat# take(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isLNat# take(V1, V2) -> a__isNatural# V1, a__isPLNat# pair(V1, V2) -> a__and#(a__isLNat V1, isLNat V2), a__isPLNat# pair(V1, V2) -> a__isLNat# V1, a__isPLNat# splitAt(V1, V2) -> a__and#(a__isNatural V1, isLNat V2), a__isPLNat# splitAt(V1, V2) -> a__isNatural# V1, a__natsFrom# N -> a__U41#(a__isNatural N, N), a__natsFrom# N -> a__isNatural# N, a__sel#(N, XS) -> a__U51#(a__and(a__isNatural N, isLNat XS), N, XS), a__sel#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__sel#(N, XS) -> a__isNatural# N, a__tail# cons(N, XS) -> a__U91#(a__and(a__isNatural N, isLNat XS), XS), a__tail# cons(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__tail# cons(N, XS) -> a__isNatural# N, a__take#(N, XS) -> a__U101#(a__and(a__isNatural N, isLNat XS), N, XS), a__take#(N, XS) -> a__and#(a__isNatural N, isLNat XS), a__take#(N, XS) -> a__isNatural# N} Weak: { a__fst X -> fst X, a__fst pair(X, Y) -> a__U21(a__and(a__isLNat X, isLNat Y), X), a__splitAt(X1, X2) -> splitAt(X1, X2), a__splitAt(s N, cons(X, XS)) -> a__U81(a__and(a__isNatural N, and(isNatural X, isLNat XS)), N, X, XS), a__splitAt(0(), XS) -> a__U71(a__isLNat XS, XS), mark tt() -> tt(), mark cons(X1, X2) -> cons(mark X1, X2), mark natsFrom X -> a__natsFrom mark X, mark s X -> s mark X, mark pair(X1, X2) -> pair(mark X1, mark X2), mark nil() -> nil(), mark isLNat X -> a__isLNat X, mark afterNth(X1, X2) -> a__afterNth(mark X1, mark X2), mark fst X -> a__fst mark X, mark snd X -> a__snd mark X, mark tail X -> a__tail mark X, mark take(X1, X2) -> a__take(mark X1, mark X2), mark 0() -> 0(), mark head X -> a__head mark X, mark sel(X1, X2) -> a__sel(mark X1, mark X2), mark splitAt(X1, X2) -> a__splitAt(mark X1, mark X2), mark and(X1, X2) -> a__and(mark X1, X2), mark isNatural X -> a__isNatural X, mark U101(X1, X2, X3) -> a__U101(mark X1, X2, X3), mark U11(X1, X2, X3) -> a__U11(mark X1, X2, X3), mark U21(X1, X2) -> a__U21(mark X1, X2), mark U31(X1, X2) -> a__U31(mark X1, X2), mark U41(X1, X2) -> a__U41(mark X1, X2), mark U51(X1, X2, X3) -> a__U51(mark X1, X2, X3), mark U61(X1, X2) -> a__U61(mark X1, X2), mark U71(X1, X2) -> a__U71(mark X1, X2), mark U81(X1, X2, X3, X4) -> a__U81(mark X1, X2, X3, X4), mark U82(X1, X2) -> a__U82(mark X1, X2), mark U91(X1, X2) -> a__U91(mark X1, X2), mark isPLNat X -> a__isPLNat X, a__U101(X1, X2, X3) -> U101(X1, X2, X3), a__U101(tt(), N, XS) -> a__fst a__splitAt(mark N, mark XS), a__snd X -> snd X, a__snd pair(X, Y) -> a__U61(a__and(a__isLNat X, isLNat Y), Y), a__U11(X1, X2, X3) -> U11(X1, X2, X3), a__U11(tt(), N, XS) -> a__snd a__splitAt(mark N, mark XS), a__U21(X1, X2) -> U21(X1, X2), a__U21(tt(), X) -> mark X, a__U31(X1, X2) -> U31(X1, X2), a__U31(tt(), N) -> mark N, a__U41(X1, X2) -> U41(X1, X2), a__U41(tt(), N) -> cons(mark N, natsFrom s N), a__head X -> head X, a__head cons(N, XS) -> a__U31(a__and(a__isNatural N, isLNat XS), N), a__afterNth(N, XS) -> a__U11(a__and(a__isNatural N, isLNat XS), N, XS), a__afterNth(X1, X2) -> afterNth(X1, X2), a__U51(X1, X2, X3) -> U51(X1, X2, X3), a__U51(tt(), N, XS) -> a__head a__afterNth(mark N, mark XS), a__U61(X1, X2) -> U61(X1, X2), a__U61(tt(), Y) -> mark Y, a__U71(X1, X2) -> U71(X1, X2), a__U71(tt(), XS) -> pair(nil(), mark XS), a__U82(X1, X2) -> U82(X1, X2), a__U82(pair(YS, ZS), X) -> pair(cons(mark X, YS), mark ZS), a__U81(X1, X2, X3, X4) -> U81(X1, X2, X3, X4), a__U81(tt(), N, X, XS) -> a__U82(a__splitAt(mark N, mark XS), X), a__U91(X1, X2) -> U91(X1, X2), a__U91(tt(), XS) -> mark XS, a__and(X1, X2) -> and(X1, X2), a__and(tt(), X) -> mark X, a__isNatural X -> isNatural X, a__isNatural s V1 -> a__isNatural V1, a__isNatural 0() -> tt(), a__isNatural head V1 -> a__isLNat V1, a__isNatural sel(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat X -> isLNat X, a__isLNat cons(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat natsFrom V1 -> a__isNatural V1, a__isLNat nil() -> tt(), a__isLNat afterNth(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isLNat fst V1 -> a__isPLNat V1, a__isLNat snd V1 -> a__isPLNat V1, a__isLNat tail V1 -> a__isLNat V1, a__isLNat take(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__isPLNat X -> isPLNat X, a__isPLNat pair(V1, V2) -> a__and(a__isLNat V1, isLNat V2), a__isPLNat splitAt(V1, V2) -> a__and(a__isNatural V1, isLNat V2), a__natsFrom N -> a__U41(a__isNatural N, N), a__natsFrom X -> natsFrom X, a__sel(N, XS) -> a__U51(a__and(a__isNatural N, isLNat XS), N, XS), a__sel(X1, X2) -> sel(X1, X2), a__tail X -> tail X, a__tail cons(N, XS) -> a__U91(a__and(a__isNatural N, isLNat XS), XS), a__take(N, XS) -> a__U101(a__and(a__isNatural N, isLNat XS), N, XS), a__take(X1, X2) -> take(X1, X2)} Open