TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60001 ms.

The following DP Processors were used


Problem 1 remains open; application of the following processors failed [DependencyGraph (timeout)].

The following open problems remain:



Open Dependency Pair Problem 1

Dependency Pairs

a__U202#(tt, N, X, XS) → a__U203#(a__isLNat(XS), N, X, XS)mark#(U151(X1, X2)) → mark#(X1)
mark#(U142(X)) → a__U142#(mark(X))mark#(U102(X)) → mark#(X)
a__isNatural#(head(V1)) → a__isLNat#(V1)mark#(U132(X)) → mark#(X)
mark#(U131(X1, X2)) → a__U131#(mark(X1), X2)mark#(U91(X)) → a__U91#(mark(X))
mark#(U12(X1, X2, X3)) → a__U12#(mark(X1), X2, X3)mark#(U121(X)) → mark#(X)
mark#(s(X)) → mark#(X)mark#(sel(X1, X2)) → mark#(X1)
a__U31#(tt, N, XS) → a__isLNat#(XS)mark#(U203(X1, X2, X3, X4)) → mark#(X1)
mark#(U132(X)) → a__U132#(mark(X))mark#(U204(X1, X2)) → mark#(X1)
mark#(U171(X1, X2, X3)) → mark#(X1)mark#(afterNth(X1, X2)) → mark#(X1)
mark#(U52(X)) → mark#(X)a__tail#(cons(N, XS)) → a__U211#(a__isNatural(N), XS)
a__U141#(tt, V2) → a__isLNat#(V2)a__U21#(tt, X, Y) → a__U22#(a__isLNat(Y), X)
mark#(U11(X1, X2, X3)) → mark#(X1)a__U22#(tt, X) → mark#(X)
a__U181#(tt, Y) → a__U182#(a__isLNat(Y), Y)a__U12#(tt, N, XS) → mark#(XS)
a__U203#(tt, N, X, XS) → a__splitAt#(mark(N), mark(XS))mark#(U211(X1, X2)) → a__U211#(mark(X1), X2)
a__U172#(tt, N, XS) → a__head#(a__afterNth(mark(N), mark(XS)))a__U151#(tt, V2) → a__isLNat#(V2)
mark#(U111(X)) → mark#(X)a__U211#(tt, XS) → a__isLNat#(XS)
mark#(head(X)) → mark#(X)mark#(U22(X1, X2)) → mark#(X1)
mark#(splitAt(X1, X2)) → mark#(X1)mark#(isPLNat(X)) → a__isPLNat#(X)
mark#(isNatural(X)) → a__isNatural#(X)mark#(fst(X)) → a__fst#(mark(X))
a__U12#(tt, N, XS) → mark#(N)mark#(U41(X1, X2)) → mark#(X1)
mark#(U61(X)) → mark#(X)mark#(fst(X)) → mark#(X)
a__U141#(tt, V2) → a__U142#(a__isLNat(V2))mark#(U51(X1, X2)) → a__U51#(mark(X1), X2)
mark#(U221(X1, X2, X3)) → mark#(X1)a__splitAt#(s(N), cons(X, XS)) → a__isNatural#(N)
mark#(snd(X)) → mark#(X)mark#(U21(X1, X2, X3)) → a__U21#(mark(X1), X2, X3)
mark#(natsFrom(X)) → mark#(X)a__U191#(tt, XS) → mark#(XS)
mark#(U201(X1, X2, X3, X4)) → mark#(X1)a__isNatural#(head(V1)) → a__U111#(a__isLNat(V1))
mark#(U111(X)) → a__U111#(mark(X))a__U222#(tt, N, XS) → mark#(XS)
mark#(take(X1, X2)) → a__take#(mark(X1), mark(X2))a__U221#(tt, N, XS) → a__U222#(a__isLNat(XS), N, XS)
mark#(splitAt(X1, X2)) → a__splitAt#(mark(X1), mark(X2))mark#(U172(X1, X2, X3)) → mark#(X1)
mark#(U191(X1, X2)) → mark#(X1)mark#(U101(X1, X2)) → mark#(X1)
a__isLNat#(tail(V1)) → a__U91#(a__isLNat(V1))a__isLNat#(fst(V1)) → a__isPLNat#(V1)
mark#(take(X1, X2)) → mark#(X1)a__sel#(N, XS) → a__isNatural#(N)
a__U101#(tt, V2) → a__isLNat#(V2)a__isLNat#(afterNth(V1, V2)) → a__U41#(a__isNatural(V1), V2)
a__U101#(tt, V2) → a__U102#(a__isLNat(V2))a__U222#(tt, N, XS) → a__fst#(a__splitAt(mark(N), mark(XS)))
mark#(U203(X1, X2, X3, X4)) → a__U203#(mark(X1), X2, X3, X4)mark#(U41(X1, X2)) → a__U41#(mark(X1), X2)
a__isLNat#(fst(V1)) → a__U61#(a__isPLNat(V1))a__U222#(tt, N, XS) → mark#(N)
mark#(U204(X1, X2)) → a__U204#(mark(X1), X2)mark#(U131(X1, X2)) → mark#(X1)
mark#(U32(X1, X2)) → a__U32#(mark(X1), X2)a__fst#(pair(X, Y)) → a__isLNat#(X)
a__U171#(tt, N, XS) → a__U172#(a__isLNat(XS), N, XS)mark#(U31(X1, X2, X3)) → mark#(X1)
a__U172#(tt, N, XS) → a__afterNth#(mark(N), mark(XS))a__isLNat#(snd(V1)) → a__U81#(a__isPLNat(V1))
mark#(U42(X)) → a__U42#(mark(X))mark#(U211(X1, X2)) → mark#(X1)
mark#(U11(X1, X2, X3)) → a__U11#(mark(X1), X2, X3)a__U51#(tt, V2) → a__U52#(a__isLNat(V2))
a__U21#(tt, X, Y) → a__isLNat#(Y)a__U31#(tt, N, XS) → a__U32#(a__isLNat(XS), N)
a__U222#(tt, N, XS) → a__splitAt#(mark(N), mark(XS))mark#(U181(X1, X2)) → mark#(X1)
mark#(U42(X)) → mark#(X)mark#(U221(X1, X2, X3)) → a__U221#(mark(X1), X2, X3)
a__U182#(tt, Y) → mark#(Y)mark#(U172(X1, X2, X3)) → a__U172#(mark(X1), X2, X3)
mark#(sel(X1, X2)) → mark#(X2)a__isLNat#(afterNth(V1, V2)) → a__isNatural#(V1)
a__U221#(tt, N, XS) → a__isLNat#(XS)mark#(tail(X)) → a__tail#(mark(X))
mark#(U12(X1, X2, X3)) → mark#(X1)a__U201#(tt, N, X, XS) → a__U202#(a__isNatural(X), N, X, XS)
a__U172#(tt, N, XS) → mark#(N)mark#(splitAt(X1, X2)) → mark#(X2)
a__isLNat#(cons(V1, V2)) → a__U51#(a__isNatural(V1), V2)a__U41#(tt, V2) → a__isLNat#(V2)
a__isNatural#(sel(V1, V2)) → a__U131#(a__isNatural(V1), V2)mark#(sel(X1, X2)) → a__sel#(mark(X1), mark(X2))
mark#(natsFrom(X)) → a__natsFrom#(mark(X))mark#(U142(X)) → mark#(X)
mark#(pair(X1, X2)) → mark#(X2)a__natsFrom#(N) → a__U161#(a__isNatural(N), N)
a__head#(cons(N, XS)) → a__U31#(a__isNatural(N), N, XS)a__U12#(tt, N, XS) → a__splitAt#(mark(N), mark(XS))
a__isLNat#(tail(V1)) → a__isLNat#(V1)a__snd#(pair(X, Y)) → a__isLNat#(X)
a__snd#(pair(X, Y)) → a__U181#(a__isLNat(X), Y)a__U203#(tt, N, X, XS) → mark#(N)
a__U11#(tt, N, XS) → a__isLNat#(XS)mark#(cons(X1, X2)) → mark#(X1)
a__splitAt#(0, XS) → a__isLNat#(XS)a__splitAt#(s(N), cons(X, XS)) → a__U201#(a__isNatural(N), N, X, XS)
mark#(pair(X1, X2)) → mark#(X1)a__isLNat#(take(V1, V2)) → a__U101#(a__isNatural(V1), V2)
mark#(U161(X1, X2)) → a__U161#(mark(X1), X2)mark#(tail(X)) → mark#(X)
a__sel#(N, XS) → a__U171#(a__isNatural(N), N, XS)a__head#(cons(N, XS)) → a__isNatural#(N)
mark#(U32(X1, X2)) → mark#(X1)mark#(afterNth(X1, X2)) → mark#(X2)
a__isPLNat#(pair(V1, V2)) → a__U141#(a__isLNat(V1), V2)a__isPLNat#(splitAt(V1, V2)) → a__U151#(a__isNatural(V1), V2)
a__U171#(tt, N, XS) → a__isLNat#(XS)mark#(U181(X1, X2)) → a__U181#(mark(X1), X2)
a__afterNth#(N, XS) → a__isNatural#(N)mark#(U152(X)) → a__U152#(mark(X))
mark#(head(X)) → a__head#(mark(X))a__U11#(tt, N, XS) → a__U12#(a__isLNat(XS), N, XS)
mark#(U61(X)) → a__U61#(mark(X))a__tail#(cons(N, XS)) → a__isNatural#(N)
a__U151#(tt, V2) → a__U152#(a__isLNat(V2))mark#(U31(X1, X2, X3)) → a__U31#(mark(X1), X2, X3)
a__isLNat#(cons(V1, V2)) → a__isNatural#(V1)a__U32#(tt, N) → mark#(N)
a__isLNat#(take(V1, V2)) → a__isNatural#(V1)a__U172#(tt, N, XS) → mark#(XS)
mark#(U52(X)) → a__U52#(mark(X))mark#(U71(X)) → a__U71#(mark(X))
mark#(U71(X)) → mark#(X)a__U212#(tt, XS) → mark#(XS)
a__U12#(tt, N, XS) → a__snd#(a__splitAt(mark(N), mark(XS)))mark#(afterNth(X1, X2)) → a__afterNth#(mark(X1), mark(X2))
mark#(U212(X1, X2)) → a__U212#(mark(X1), X2)a__take#(N, XS) → a__isNatural#(N)
mark#(U22(X1, X2)) → a__U22#(mark(X1), X2)mark#(U141(X1, X2)) → a__U141#(mark(X1), X2)
a__U181#(tt, Y) → a__isLNat#(Y)mark#(U102(X)) → a__U102#(mark(X))
mark#(U121(X)) → a__U121#(mark(X))mark#(U81(X)) → mark#(X)
mark#(U191(X1, X2)) → a__U191#(mark(X1), X2)a__isLNat#(snd(V1)) → a__isPLNat#(V1)
a__U201#(tt, N, X, XS) → a__isNatural#(X)mark#(U202(X1, X2, X3, X4)) → a__U202#(mark(X1), X2, X3, X4)
mark#(U212(X1, X2)) → mark#(X1)a__isNatural#(s(V1)) → a__isNatural#(V1)
a__isPLNat#(splitAt(V1, V2)) → a__isNatural#(V1)a__U202#(tt, N, X, XS) → a__isLNat#(XS)
mark#(U101(X1, X2)) → a__U101#(mark(X1), X2)a__isNatural#(s(V1)) → a__U121#(a__isNatural(V1))
a__U204#(pair(YS, ZS), X) → mark#(ZS)a__isLNat#(natsFrom(V1)) → a__isNatural#(V1)
mark#(isLNat(X)) → a__isLNat#(X)a__U211#(tt, XS) → a__U212#(a__isLNat(XS), XS)
mark#(U161(X1, X2)) → mark#(X1)mark#(U182(X1, X2)) → mark#(X1)
mark#(snd(X)) → a__snd#(mark(X))mark#(U21(X1, X2, X3)) → mark#(X1)
a__U51#(tt, V2) → a__isLNat#(V2)a__U204#(pair(YS, ZS), X) → mark#(X)
mark#(U171(X1, X2, X3)) → a__U171#(mark(X1), X2, X3)mark#(U202(X1, X2, X3, X4)) → mark#(X1)
mark#(U51(X1, X2)) → mark#(X1)a__isNatural#(sel(V1, V2)) → a__isNatural#(V1)
a__splitAt#(0, XS) → a__U191#(a__isLNat(XS), XS)mark#(U222(X1, X2, X3)) → a__U222#(mark(X1), X2, X3)
a__U131#(tt, V2) → a__isLNat#(V2)a__U41#(tt, V2) → a__U42#(a__isLNat(V2))
mark#(U152(X)) → mark#(X)mark#(U151(X1, X2)) → a__U151#(mark(X1), X2)
a__U161#(tt, N) → mark#(N)a__isLNat#(natsFrom(V1)) → a__U71#(a__isNatural(V1))
a__afterNth#(N, XS) → a__U11#(a__isNatural(N), N, XS)a__U131#(tt, V2) → a__U132#(a__isLNat(V2))
mark#(U222(X1, X2, X3)) → mark#(X1)a__take#(N, XS) → a__U221#(a__isNatural(N), N, XS)
mark#(U141(X1, X2)) → mark#(X1)a__fst#(pair(X, Y)) → a__U21#(a__isLNat(X), X, Y)
mark#(U201(X1, X2, X3, X4)) → a__U201#(mark(X1), X2, X3, X4)a__U203#(tt, N, X, XS) → mark#(XS)
a__natsFrom#(N) → a__isNatural#(N)mark#(U182(X1, X2)) → a__U182#(mark(X1), X2)
mark#(take(X1, X2)) → mark#(X2)a__isPLNat#(pair(V1, V2)) → a__isLNat#(V1)
mark#(U81(X)) → a__U81#(mark(X))mark#(U91(X)) → mark#(X)
a__U203#(tt, N, X, XS) → a__U204#(a__splitAt(mark(N), mark(XS)), X)

Rewrite Rules

a__U101(tt, V2) → a__U102(a__isLNat(V2))a__U102(tt) → tt
a__U11(tt, N, XS) → a__U12(a__isLNat(XS), N, XS)a__U111(tt) → tt
a__U12(tt, N, XS) → a__snd(a__splitAt(mark(N), mark(XS)))a__U121(tt) → tt
a__U131(tt, V2) → a__U132(a__isLNat(V2))a__U132(tt) → tt
a__U141(tt, V2) → a__U142(a__isLNat(V2))a__U142(tt) → tt
a__U151(tt, V2) → a__U152(a__isLNat(V2))a__U152(tt) → tt
a__U161(tt, N) → cons(mark(N), natsFrom(s(N)))a__U171(tt, N, XS) → a__U172(a__isLNat(XS), N, XS)
a__U172(tt, N, XS) → a__head(a__afterNth(mark(N), mark(XS)))a__U181(tt, Y) → a__U182(a__isLNat(Y), Y)
a__U182(tt, Y) → mark(Y)a__U191(tt, XS) → pair(nil, mark(XS))
a__U201(tt, N, X, XS) → a__U202(a__isNatural(X), N, X, XS)a__U202(tt, N, X, XS) → a__U203(a__isLNat(XS), N, X, XS)
a__U203(tt, N, X, XS) → a__U204(a__splitAt(mark(N), mark(XS)), X)a__U204(pair(YS, ZS), X) → pair(cons(mark(X), YS), mark(ZS))
a__U21(tt, X, Y) → a__U22(a__isLNat(Y), X)a__U211(tt, XS) → a__U212(a__isLNat(XS), XS)
a__U212(tt, XS) → mark(XS)a__U22(tt, X) → mark(X)
a__U221(tt, N, XS) → a__U222(a__isLNat(XS), N, XS)a__U222(tt, N, XS) → a__fst(a__splitAt(mark(N), mark(XS)))
a__U31(tt, N, XS) → a__U32(a__isLNat(XS), N)a__U32(tt, N) → mark(N)
a__U41(tt, V2) → a__U42(a__isLNat(V2))a__U42(tt) → tt
a__U51(tt, V2) → a__U52(a__isLNat(V2))a__U52(tt) → tt
a__U61(tt) → tta__U71(tt) → tt
a__U81(tt) → tta__U91(tt) → tt
a__afterNth(N, XS) → a__U11(a__isNatural(N), N, XS)a__fst(pair(X, Y)) → a__U21(a__isLNat(X), X, Y)
a__head(cons(N, XS)) → a__U31(a__isNatural(N), N, XS)a__isLNat(nil) → tt
a__isLNat(afterNth(V1, V2)) → a__U41(a__isNatural(V1), V2)a__isLNat(cons(V1, V2)) → a__U51(a__isNatural(V1), V2)
a__isLNat(fst(V1)) → a__U61(a__isPLNat(V1))a__isLNat(natsFrom(V1)) → a__U71(a__isNatural(V1))
a__isLNat(snd(V1)) → a__U81(a__isPLNat(V1))a__isLNat(tail(V1)) → a__U91(a__isLNat(V1))
a__isLNat(take(V1, V2)) → a__U101(a__isNatural(V1), V2)a__isNatural(0) → tt
a__isNatural(head(V1)) → a__U111(a__isLNat(V1))a__isNatural(s(V1)) → a__U121(a__isNatural(V1))
a__isNatural(sel(V1, V2)) → a__U131(a__isNatural(V1), V2)a__isPLNat(pair(V1, V2)) → a__U141(a__isLNat(V1), V2)
a__isPLNat(splitAt(V1, V2)) → a__U151(a__isNatural(V1), V2)a__natsFrom(N) → a__U161(a__isNatural(N), N)
a__sel(N, XS) → a__U171(a__isNatural(N), N, XS)a__snd(pair(X, Y)) → a__U181(a__isLNat(X), Y)
a__splitAt(0, XS) → a__U191(a__isLNat(XS), XS)a__splitAt(s(N), cons(X, XS)) → a__U201(a__isNatural(N), N, X, XS)
a__tail(cons(N, XS)) → a__U211(a__isNatural(N), XS)a__take(N, XS) → a__U221(a__isNatural(N), N, XS)
mark(U101(X1, X2)) → a__U101(mark(X1), X2)mark(U102(X)) → a__U102(mark(X))
mark(isLNat(X)) → a__isLNat(X)mark(U11(X1, X2, X3)) → a__U11(mark(X1), X2, X3)
mark(U12(X1, X2, X3)) → a__U12(mark(X1), X2, X3)mark(U111(X)) → a__U111(mark(X))
mark(snd(X)) → a__snd(mark(X))mark(splitAt(X1, X2)) → a__splitAt(mark(X1), mark(X2))
mark(U121(X)) → a__U121(mark(X))mark(U131(X1, X2)) → a__U131(mark(X1), X2)
mark(U132(X)) → a__U132(mark(X))mark(U141(X1, X2)) → a__U141(mark(X1), X2)
mark(U142(X)) → a__U142(mark(X))mark(U151(X1, X2)) → a__U151(mark(X1), X2)
mark(U152(X)) → a__U152(mark(X))mark(U161(X1, X2)) → a__U161(mark(X1), X2)
mark(natsFrom(X)) → a__natsFrom(mark(X))mark(U171(X1, X2, X3)) → a__U171(mark(X1), X2, X3)
mark(U172(X1, X2, X3)) → a__U172(mark(X1), X2, X3)mark(head(X)) → a__head(mark(X))
mark(afterNth(X1, X2)) → a__afterNth(mark(X1), mark(X2))mark(U181(X1, X2)) → a__U181(mark(X1), X2)
mark(U182(X1, X2)) → a__U182(mark(X1), X2)mark(U191(X1, X2)) → a__U191(mark(X1), X2)
mark(U201(X1, X2, X3, X4)) → a__U201(mark(X1), X2, X3, X4)mark(U202(X1, X2, X3, X4)) → a__U202(mark(X1), X2, X3, X4)
mark(isNatural(X)) → a__isNatural(X)mark(U203(X1, X2, X3, X4)) → a__U203(mark(X1), X2, X3, X4)
mark(U204(X1, X2)) → a__U204(mark(X1), X2)mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2)) → a__U22(mark(X1), X2)mark(U211(X1, X2)) → a__U211(mark(X1), X2)
mark(U212(X1, X2)) → a__U212(mark(X1), X2)mark(U221(X1, X2, X3)) → a__U221(mark(X1), X2, X3)
mark(U222(X1, X2, X3)) → a__U222(mark(X1), X2, X3)mark(fst(X)) → a__fst(mark(X))
mark(U31(X1, X2, X3)) → a__U31(mark(X1), X2, X3)mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U41(X1, X2)) → a__U41(mark(X1), X2)mark(U42(X)) → a__U42(mark(X))
mark(U51(X1, X2)) → a__U51(mark(X1), X2)mark(U52(X)) → a__U52(mark(X))
mark(U61(X)) → a__U61(mark(X))mark(U71(X)) → a__U71(mark(X))
mark(U81(X)) → a__U81(mark(X))mark(U91(X)) → a__U91(mark(X))
mark(isPLNat(X)) → a__isPLNat(X)mark(tail(X)) → a__tail(mark(X))
mark(take(X1, X2)) → a__take(mark(X1), mark(X2))mark(sel(X1, X2)) → a__sel(mark(X1), mark(X2))
mark(tt) → ttmark(cons(X1, X2)) → cons(mark(X1), X2)
mark(s(X)) → s(mark(X))mark(pair(X1, X2)) → pair(mark(X1), mark(X2))
mark(nil) → nilmark(0) → 0
a__U101(X1, X2) → U101(X1, X2)a__U102(X) → U102(X)
a__isLNat(X) → isLNat(X)a__U11(X1, X2, X3) → U11(X1, X2, X3)
a__U12(X1, X2, X3) → U12(X1, X2, X3)a__U111(X) → U111(X)
a__snd(X) → snd(X)a__splitAt(X1, X2) → splitAt(X1, X2)
a__U121(X) → U121(X)a__U131(X1, X2) → U131(X1, X2)
a__U132(X) → U132(X)a__U141(X1, X2) → U141(X1, X2)
a__U142(X) → U142(X)a__U151(X1, X2) → U151(X1, X2)
a__U152(X) → U152(X)a__U161(X1, X2) → U161(X1, X2)
a__natsFrom(X) → natsFrom(X)a__U171(X1, X2, X3) → U171(X1, X2, X3)
a__U172(X1, X2, X3) → U172(X1, X2, X3)a__head(X) → head(X)
a__afterNth(X1, X2) → afterNth(X1, X2)a__U181(X1, X2) → U181(X1, X2)
a__U182(X1, X2) → U182(X1, X2)a__U191(X1, X2) → U191(X1, X2)
a__U201(X1, X2, X3, X4) → U201(X1, X2, X3, X4)a__U202(X1, X2, X3, X4) → U202(X1, X2, X3, X4)
a__isNatural(X) → isNatural(X)a__U203(X1, X2, X3, X4) → U203(X1, X2, X3, X4)
a__U204(X1, X2) → U204(X1, X2)a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2) → U22(X1, X2)a__U211(X1, X2) → U211(X1, X2)
a__U212(X1, X2) → U212(X1, X2)a__U221(X1, X2, X3) → U221(X1, X2, X3)
a__U222(X1, X2, X3) → U222(X1, X2, X3)a__fst(X) → fst(X)
a__U31(X1, X2, X3) → U31(X1, X2, X3)a__U32(X1, X2) → U32(X1, X2)
a__U41(X1, X2) → U41(X1, X2)a__U42(X) → U42(X)
a__U51(X1, X2) → U51(X1, X2)a__U52(X) → U52(X)
a__U61(X) → U61(X)a__U71(X) → U71(X)
a__U81(X) → U81(X)a__U91(X) → U91(X)
a__isPLNat(X) → isPLNat(X)a__tail(X) → tail(X)
a__take(X1, X2) → take(X1, X2)a__sel(X1, X2) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: a__U121, U111, U61, a__isPLNat, a__U41, a__U42, a__isNatural, a__U191, a__U111, isPLNat, tail, U71, U191, 0, U121, a__U32, a__U31, a__sel, a__U141, a__U142, a__take, pair, U132, U131, U42, a__U91, U41, a__fst, a__U22, a__head, a__snd, a__U21, cons, a__afterNth, a__U131, a__U132, splitAt, U142, U141, U51, s, tt, U52, a__U12, a__U11, afterNth, natsFrom, a__natsFrom, U161, U204, U203, a__U161, fst, a__U222, U211, a__U221, U212, a__U71, head, U21, U22, a__U202, a__U203, a__U204, mark, U151, U152, a__U152, a__U151, a__U212, U221, a__U211, isLNat, U222, a__U81, U31, U32, a__U51, a__U52, U181, U182, a__U182, isNatural, a__U181, a__U201, U91, a__isLNat, a__U102, a__U101, snd, U171, U172, a__U171, a__U172, a__tail, U201, U202, a__splitAt, take, U81, U11, U12, a__U61, U102, sel, nil, U101