TIMEOUT

The TRS could not be proven terminating. The proof attempt took 60002 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

mark#(fst(X)) → active#(fst(mark(X)))active#(U132(tt)) → mark#(tt)
active#(U211(tt, XS)) → isLNat#(XS)mark#(U61(X)) → U61#(mark(X))
mark#(U51(X1, X2)) → U51#(mark(X1), X2)mark#(U102(X)) → mark#(X)
U221#(X1, active(X2), X3) → U221#(X1, X2, X3)mark#(take(X1, X2)) → active#(take(mark(X1), mark(X2)))
U132#(mark(X)) → U132#(X)active#(U191(tt, XS)) → pair#(nil, XS)
U91#(active(X)) → U91#(X)active#(head(cons(N, XS))) → mark#(U31(isNatural(N), N, XS))
U51#(mark(X1), X2) → U51#(X1, X2)active#(U221(tt, N, XS)) → isLNat#(XS)
U152#(active(X)) → U152#(X)mark#(U121(X)) → mark#(X)
mark#(U152(X)) → U152#(mark(X))mark#(s(X)) → mark#(X)
active#(U21(tt, X, Y)) → isLNat#(Y)afterNth#(active(X1), X2) → afterNth#(X1, X2)
mark#(U31(X1, X2, X3)) → active#(U31(mark(X1), X2, X3))U81#(mark(X)) → U81#(X)
active#(splitAt(s(N), cons(X, XS))) → mark#(U201(isNatural(N), N, X, XS))mark#(U142(X)) → U142#(mark(X))
splitAt#(X1, mark(X2)) → splitAt#(X1, X2)mark#(U52(X)) → mark#(X)
mark#(U91(X)) → U91#(mark(X))mark#(U42(X)) → active#(U42(mark(X)))
U172#(mark(X1), X2, X3) → U172#(X1, X2, X3)U203#(mark(X1), X2, X3, X4) → U203#(X1, X2, X3, X4)
mark#(U151(X1, X2)) → U151#(mark(X1), X2)U12#(X1, active(X2), X3) → U12#(X1, X2, X3)
active#(isLNat(cons(V1, V2))) → isNatural#(V1)U12#(X1, X2, mark(X3)) → U12#(X1, X2, X3)
U141#(X1, active(X2)) → U141#(X1, X2)active#(U42(tt)) → mark#(tt)
mark#(U11(X1, X2, X3)) → mark#(X1)active#(isLNat(afterNth(V1, V2))) → isNatural#(V1)
U221#(active(X1), X2, X3) → U221#(X1, X2, X3)natsFrom#(mark(X)) → natsFrom#(X)
U31#(active(X1), X2, X3) → U31#(X1, X2, X3)U191#(X1, mark(X2)) → U191#(X1, X2)
mark#(U111(X)) → mark#(X)active#(take(N, XS)) → isNatural#(N)
active#(splitAt(0, XS)) → isLNat#(XS)active#(U151(tt, V2)) → mark#(U152(isLNat(V2)))
mark#(U211(X1, X2)) → active#(U211(mark(X1), X2))active#(U12(tt, N, XS)) → mark#(snd(splitAt(N, XS)))
mark#(U22(X1, X2)) → mark#(X1)mark#(splitAt(X1, X2)) → mark#(X1)
isNatural#(mark(X)) → isNatural#(X)active#(fst(pair(X, Y))) → U21#(isLNat(X), X, Y)
mark#(isNatural(X)) → isNatural#(X)isPLNat#(active(X)) → isPLNat#(X)
U11#(active(X1), X2, X3) → U11#(X1, X2, X3)mark#(U61(X)) → mark#(X)
U191#(mark(X1), X2) → U191#(X1, X2)U12#(X1, X2, active(X3)) → U12#(X1, X2, X3)
active#(U91(tt)) → mark#(tt)U141#(active(X1), X2) → U141#(X1, X2)
active#(U41(tt, V2)) → isLNat#(V2)mark#(natsFrom(X)) → mark#(X)
cons#(active(X1), X2) → cons#(X1, X2)mark#(afterNth(X1, X2)) → active#(afterNth(mark(X1), mark(X2)))
mark#(U201(X1, X2, X3, X4)) → mark#(X1)U172#(X1, X2, active(X3)) → U172#(X1, X2, X3)
active#(U172(tt, N, XS)) → afterNth#(N, XS)active#(U151(tt, V2)) → U152#(isLNat(V2))
mark#(U191(X1, X2)) → mark#(X1)mark#(U101(X1, X2)) → mark#(X1)
active#(U222(tt, N, XS)) → splitAt#(N, XS)active#(isPLNat(splitAt(V1, V2))) → mark#(U151(isNatural(V1), V2))
active#(snd(pair(X, Y))) → mark#(U181(isLNat(X), Y))U181#(X1, active(X2)) → U181#(X1, X2)
afterNth#(X1, mark(X2)) → afterNth#(X1, X2)isNatural#(active(X)) → isNatural#(X)
mark#(U11(X1, X2, X3)) → active#(U11(mark(X1), X2, X3))active#(head(cons(N, XS))) → isNatural#(N)
mark#(tail(X)) → active#(tail(mark(X)))mark#(U191(X1, X2)) → U191#(mark(X1), X2)
U202#(X1, mark(X2), X3, X4) → U202#(X1, X2, X3, X4)mark#(isLNat(X)) → active#(isLNat(X))
mark#(natsFrom(X)) → active#(natsFrom(mark(X)))U71#(mark(X)) → U71#(X)
active#(splitAt(s(N), cons(X, XS))) → isNatural#(N)isPLNat#(mark(X)) → isPLNat#(X)
U41#(X1, mark(X2)) → U41#(X1, X2)mark#(isPLNat(X)) → isPLNat#(X)
mark#(U171(X1, X2, X3)) → active#(U171(mark(X1), X2, X3))active#(natsFrom(N)) → isNatural#(N)
take#(X1, mark(X2)) → take#(X1, X2)mark#(splitAt(X1, X2)) → active#(splitAt(mark(X1), mark(X2)))
U131#(X1, mark(X2)) → U131#(X1, X2)mark#(U31(X1, X2, X3)) → mark#(X1)
U171#(X1, X2, active(X3)) → U171#(X1, X2, X3)active#(U191(tt, XS)) → mark#(pair(nil, XS))
U203#(X1, X2, X3, active(X4)) → U203#(X1, X2, X3, X4)active#(U101(tt, V2)) → U102#(isLNat(V2))
active#(U203(tt, N, X, XS)) → splitAt#(N, XS)U121#(active(X)) → U121#(X)
mark#(U211(X1, X2)) → mark#(X1)mark#(U161(X1, X2)) → U161#(mark(X1), X2)
sel#(mark(X1), X2) → sel#(X1, X2)active#(U152(tt)) → mark#(tt)
mark#(head(X)) → active#(head(mark(X)))active#(U51(tt, V2)) → isLNat#(V2)
active#(isLNat(take(V1, V2))) → mark#(U101(isNatural(V1), V2))U12#(X1, mark(X2), X3) → U12#(X1, X2, X3)
mark#(U181(X1, X2)) → mark#(X1)U221#(X1, X2, active(X3)) → U221#(X1, X2, X3)
mark#(U42(X)) → mark#(X)active#(isLNat(fst(V1))) → isPLNat#(V1)
U222#(X1, active(X2), X3) → U222#(X1, X2, X3)splitAt#(active(X1), X2) → splitAt#(X1, X2)
active#(U61(tt)) → mark#(tt)mark#(nil) → active#(nil)
mark#(U61(X)) → active#(U61(mark(X)))U172#(X1, mark(X2), X3) → U172#(X1, X2, X3)
take#(X1, active(X2)) → take#(X1, X2)U31#(X1, X2, mark(X3)) → U31#(X1, X2, X3)
mark#(isNatural(X)) → active#(isNatural(X))U101#(mark(X1), X2) → U101#(X1, X2)
U41#(mark(X1), X2) → U41#(X1, X2)U202#(X1, X2, mark(X3), X4) → U202#(X1, X2, X3, X4)
U101#(X1, active(X2)) → U101#(X1, X2)mark#(cons(X1, X2)) → cons#(mark(X1), X2)
mark#(U22(X1, X2)) → active#(U22(mark(X1), X2))mark#(U172(X1, X2, X3)) → U172#(mark(X1), X2, X3)
U151#(X1, active(X2)) → U151#(X1, X2)natsFrom#(active(X)) → natsFrom#(X)
U212#(active(X1), X2) → U212#(X1, X2)mark#(U32(X1, X2)) → active#(U32(mark(X1), X2))
active#(U31(tt, N, XS)) → U32#(isLNat(XS), N)mark#(splitAt(X1, X2)) → mark#(X2)
active#(U71(tt)) → mark#(tt)active#(U181(tt, Y)) → mark#(U182(isLNat(Y), Y))
U203#(X1, mark(X2), X3, X4) → U203#(X1, X2, X3, X4)active#(isLNat(natsFrom(V1))) → U71#(isNatural(V1))
mark#(U21(X1, X2, X3)) → U21#(mark(X1), X2, X3)active#(U31(tt, N, XS)) → mark#(U32(isLNat(XS), N))
s#(mark(X)) → s#(X)U204#(mark(X1), X2) → U204#(X1, X2)
mark#(U202(X1, X2, X3, X4)) → active#(U202(mark(X1), X2, X3, X4))U32#(active(X1), X2) → U32#(X1, X2)
active#(U222(tt, N, XS)) → mark#(fst(splitAt(N, XS)))U52#(mark(X)) → U52#(X)
active#(tail(cons(N, XS))) → mark#(U211(isNatural(N), XS))active#(U51(tt, V2)) → U52#(isLNat(V2))
mark#(U142(X)) → mark#(X)U81#(active(X)) → U81#(X)
splitAt#(mark(X1), X2) → splitAt#(X1, X2)active#(U161(tt, N)) → natsFrom#(s(N))
active#(natsFrom(N)) → U161#(isNatural(N), N)active#(isLNat(fst(V1))) → mark#(U61(isPLNat(V1)))
mark#(U181(X1, X2)) → U181#(mark(X1), X2)mark#(U22(X1, X2)) → U22#(mark(X1), X2)
active#(isLNat(take(V1, V2))) → isNatural#(V1)active#(isLNat(natsFrom(V1))) → isNatural#(V1)
mark#(U31(X1, X2, X3)) → U31#(mark(X1), X2, X3)mark#(U221(X1, X2, X3)) → active#(U221(mark(X1), X2, X3))
U131#(active(X1), X2) → U131#(X1, X2)U201#(X1, mark(X2), X3, X4) → U201#(X1, X2, X3, X4)
active#(sel(N, XS)) → mark#(U171(isNatural(N), N, XS))U12#(mark(X1), X2, X3) → U12#(X1, X2, X3)
mark#(cons(X1, X2)) → mark#(X1)U203#(X1, X2, X3, mark(X4)) → U203#(X1, X2, X3, X4)
pair#(X1, mark(X2)) → pair#(X1, X2)active#(tail(cons(N, XS))) → isNatural#(N)
U21#(mark(X1), X2, X3) → U21#(X1, X2, X3)mark#(U51(X1, X2)) → active#(U51(mark(X1), X2))
active#(isLNat(nil)) → mark#(tt)U201#(X1, X2, X3, active(X4)) → U201#(X1, X2, X3, X4)
mark#(U101(X1, X2)) → U101#(mark(X1), X2)U61#(active(X)) → U61#(X)
mark#(U32(X1, X2)) → mark#(X1)U211#(mark(X1), X2) → U211#(X1, X2)
active#(U32(tt, N)) → mark#(N)U151#(active(X1), X2) → U151#(X1, X2)
U51#(X1, active(X2)) → U51#(X1, X2)U181#(X1, mark(X2)) → U181#(X1, X2)
U151#(mark(X1), X2) → U151#(X1, X2)active#(U121(tt)) → mark#(tt)
active#(U211(tt, XS)) → mark#(U212(isLNat(XS), XS))U22#(mark(X1), X2) → U22#(X1, X2)
mark#(tail(X)) → tail#(mark(X))active#(isNatural(0)) → mark#(tt)
mark#(splitAt(X1, X2)) → splitAt#(mark(X1), mark(X2))active#(U12(tt, N, XS)) → snd#(splitAt(N, XS))
mark#(U152(X)) → active#(U152(mark(X)))U12#(active(X1), X2, X3) → U12#(X1, X2, X3)
U142#(mark(X)) → U142#(X)U222#(active(X1), X2, X3) → U222#(X1, X2, X3)
splitAt#(X1, active(X2)) → splitAt#(X1, X2)active#(U22(tt, X)) → mark#(X)
mark#(0) → active#(0)active#(U161(tt, N)) → cons#(N, natsFrom(s(N)))
U61#(mark(X)) → U61#(X)U221#(X1, mark(X2), X3) → U221#(X1, X2, X3)
active#(U101(tt, V2)) → mark#(U102(isLNat(V2)))U201#(mark(X1), X2, X3, X4) → U201#(X1, X2, X3, X4)
mark#(U71(X)) → active#(U71(mark(X)))U211#(X1, mark(X2)) → U211#(X1, X2)
mark#(U203(X1, X2, X3, X4)) → U203#(mark(X1), X2, X3, X4)active#(U31(tt, N, XS)) → isLNat#(XS)
U11#(X1, X2, active(X3)) → U11#(X1, X2, X3)U201#(X1, X2, active(X3), X4) → U201#(X1, X2, X3, X4)
mark#(U71(X)) → mark#(X)U182#(X1, mark(X2)) → U182#(X1, X2)
U204#(X1, mark(X2)) → U204#(X1, X2)mark#(fst(X)) → fst#(mark(X))
mark#(U41(X1, X2)) → active#(U41(mark(X1), X2))U42#(mark(X)) → U42#(X)
active#(isNatural(head(V1))) → mark#(U111(isLNat(V1)))active#(U201(tt, N, X, XS)) → mark#(U202(isNatural(X), N, X, XS))
active#(U171(tt, N, XS)) → isLNat#(XS)mark#(U81(X)) → mark#(X)
active#(isLNat(natsFrom(V1))) → mark#(U71(isNatural(V1)))mark#(U201(X1, X2, X3, X4)) → active#(U201(mark(X1), X2, X3, X4))
mark#(U132(X)) → U132#(mark(X))mark#(U172(X1, X2, X3)) → active#(U172(mark(X1), X2, X3))
active#(U81(tt)) → mark#(tt)U131#(X1, active(X2)) → U131#(X1, X2)
mark#(U41(X1, X2)) → U41#(mark(X1), X2)sel#(active(X1), X2) → sel#(X1, X2)
mark#(U161(X1, X2)) → mark#(X1)active#(isLNat(cons(V1, V2))) → mark#(U51(isNatural(V1), V2))
U21#(X1, active(X2), X3) → U21#(X1, X2, X3)U181#(mark(X1), X2) → U181#(X1, X2)
mark#(U182(X1, X2)) → mark#(X1)mark#(afterNth(X1, X2)) → afterNth#(mark(X1), mark(X2))
mark#(U21(X1, X2, X3)) → mark#(X1)active#(U41(tt, V2)) → mark#(U42(isLNat(V2)))
mark#(U102(X)) → U102#(mark(X))U22#(X1, mark(X2)) → U22#(X1, X2)
U182#(active(X1), X2) → U182#(X1, X2)U201#(X1, X2, mark(X3), X4) → U201#(X1, X2, X3, X4)
U202#(mark(X1), X2, X3, X4) → U202#(X1, X2, X3, X4)mark#(U182(X1, X2)) → U182#(mark(X1), X2)
active#(U141(tt, V2)) → isLNat#(V2)tail#(active(X)) → tail#(X)
active#(U172(tt, N, XS)) → head#(afterNth(N, XS))U201#(X1, X2, X3, mark(X4)) → U201#(X1, X2, X3, X4)
U121#(mark(X)) → U121#(X)U191#(active(X1), X2) → U191#(X1, X2)
active#(isLNat(tail(V1))) → mark#(U91(isLNat(V1)))mark#(U212(X1, X2)) → active#(U212(mark(X1), X2))
active#(U182(tt, Y)) → mark#(Y)U222#(X1, X2, mark(X3)) → U222#(X1, X2, X3)
active#(isLNat(tail(V1))) → isLNat#(V1)mark#(take(X1, X2)) → mark#(X2)
mark#(natsFrom(X)) → natsFrom#(mark(X))mark#(U21(X1, X2, X3)) → active#(U21(mark(X1), X2, X3))
U212#(X1, mark(X2)) → U212#(X1, X2)active#(U203(tt, N, X, XS)) → mark#(U204(splitAt(N, XS), X))
mark#(pair(X1, X2)) → active#(pair(mark(X1), mark(X2)))U161#(X1, active(X2)) → U161#(X1, X2)
active#(U101(tt, V2)) → isLNat#(V2)active#(isNatural(sel(V1, V2))) → U131#(isNatural(V1), V2)
active#(isNatural(head(V1))) → U111#(isLNat(V1))mark#(U151(X1, X2)) → mark#(X1)
U203#(X1, X2, mark(X3), X4) → U203#(X1, X2, X3, X4)U31#(X1, active(X2), X3) → U31#(X1, X2, X3)
mark#(U11(X1, X2, X3)) → U11#(mark(X1), X2, X3)U171#(X1, X2, mark(X3)) → U171#(X1, X2, X3)
mark#(U132(X)) → mark#(X)active#(natsFrom(N)) → mark#(U161(isNatural(N), N))
active#(U181(tt, Y)) → isLNat#(Y)mark#(snd(X)) → active#(snd(mark(X)))
mark#(U111(X)) → active#(U111(mark(X)))mark#(U12(X1, X2, X3)) → active#(U12(mark(X1), X2, X3))
active#(afterNth(N, XS)) → U11#(isNatural(N), N, XS)active#(isPLNat(pair(V1, V2))) → isLNat#(V1)
mark#(sel(X1, X2)) → mark#(X1)mark#(U203(X1, X2, X3, X4)) → mark#(X1)
U204#(X1, active(X2)) → U204#(X1, X2)mark#(U81(X)) → active#(U81(mark(X)))
active#(isNatural(s(V1))) → U121#(isNatural(V1))mark#(U204(X1, X2)) → mark#(X1)
mark#(U171(X1, X2, X3)) → mark#(X1)active#(splitAt(0, XS)) → U191#(isLNat(XS), XS)
mark#(afterNth(X1, X2)) → mark#(X1)active#(isLNat(cons(V1, V2))) → U51#(isNatural(V1), V2)
active#(U204(pair(YS, ZS), X)) → pair#(cons(X, YS), ZS)U211#(active(X1), X2) → U211#(X1, X2)
active#(U161(tt, N)) → s#(N)active#(isPLNat(pair(V1, V2))) → U141#(isLNat(V1), V2)
active#(isNatural(s(V1))) → mark#(U121(isNatural(V1)))U172#(active(X1), X2, X3) → U172#(X1, X2, X3)
active#(U204(pair(YS, ZS), X)) → cons#(X, YS)active#(isPLNat(splitAt(V1, V2))) → U151#(isNatural(V1), V2)
active#(U172(tt, N, XS)) → mark#(head(afterNth(N, XS)))active#(U151(tt, V2)) → isLNat#(V2)
head#(active(X)) → head#(X)mark#(U71(X)) → U71#(mark(X))
active#(isLNat(tail(V1))) → U91#(isLNat(V1))active#(isNatural(sel(V1, V2))) → isNatural#(V1)
mark#(U182(X1, X2)) → active#(U182(mark(X1), X2))isLNat#(active(X)) → isLNat#(X)
U201#(X1, active(X2), X3, X4) → U201#(X1, X2, X3, X4)U202#(X1, X2, X3, active(X4)) → U202#(X1, X2, X3, X4)
active#(isLNat(afterNth(V1, V2))) → U41#(isNatural(V1), V2)mark#(head(X)) → mark#(X)
U32#(X1, active(X2)) → U32#(X1, X2)active#(U11(tt, N, XS)) → mark#(U12(isLNat(XS), N, XS))
U41#(X1, active(X2)) → U41#(X1, X2)mark#(U41(X1, X2)) → mark#(X1)
cons#(X1, mark(X2)) → cons#(X1, X2)U171#(X1, active(X2), X3) → U171#(X1, X2, X3)
active#(U201(tt, N, X, XS)) → isNatural#(X)mark#(fst(X)) → mark#(X)
active#(U221(tt, N, XS)) → U222#(isLNat(XS), N, XS)active#(sel(N, XS)) → isNatural#(N)
snd#(mark(X)) → snd#(X)active#(U202(tt, N, X, XS)) → U203#(isLNat(XS), N, X, XS)
mark#(U221(X1, X2, X3)) → mark#(X1)mark#(U131(X1, X2)) → active#(U131(mark(X1), X2))
pair#(X1, active(X2)) → pair#(X1, X2)mark#(snd(X)) → mark#(X)
U51#(X1, mark(X2)) → U51#(X1, X2)U31#(X1, X2, active(X3)) → U31#(X1, X2, X3)
active#(sel(N, XS)) → U171#(isNatural(N), N, XS)active#(U41(tt, V2)) → U42#(isLNat(V2))
mark#(U172(X1, X2, X3)) → mark#(X1)mark#(U204(X1, X2)) → U204#(mark(X1), X2)
U152#(mark(X)) → U152#(X)mark#(take(X1, X2)) → mark#(X1)
active#(U111(tt)) → mark#(tt)U212#(X1, active(X2)) → U212#(X1, X2)
active#(splitAt(0, XS)) → mark#(U191(isLNat(XS), XS))U71#(active(X)) → U71#(X)
mark#(s(X)) → s#(mark(X))U182#(mark(X1), X2) → U182#(X1, X2)
active#(U202(tt, N, X, XS)) → isLNat#(XS)active#(isLNat(fst(V1))) → U61#(isPLNat(V1))
active#(afterNth(N, XS)) → isNatural#(N)U52#(active(X)) → U52#(X)
U171#(X1, mark(X2), X3) → U171#(X1, X2, X3)U172#(X1, active(X2), X3) → U172#(X1, X2, X3)
U202#(X1, X2, active(X3), X4) → U202#(X1, X2, X3, X4)afterNth#(mark(X1), X2) → afterNth#(X1, X2)
mark#(U131(X1, X2)) → mark#(X1)active#(U21(tt, X, Y)) → U22#(isLNat(Y), X)
mark#(sel(X1, X2)) → sel#(mark(X1), mark(X2))U21#(X1, mark(X2), X3) → U21#(X1, X2, X3)
mark#(U131(X1, X2)) → U131#(mark(X1), X2)U11#(mark(X1), X2, X3) → U11#(X1, X2, X3)
tail#(mark(X)) → tail#(X)mark#(sel(X1, X2)) → active#(sel(mark(X1), mark(X2)))
active#(U221(tt, N, XS)) → mark#(U222(isLNat(XS), N, XS))cons#(X1, active(X2)) → cons#(X1, X2)
active#(U161(tt, N)) → mark#(cons(N, natsFrom(s(N))))U101#(X1, mark(X2)) → U101#(X1, X2)
active#(snd(pair(X, Y))) → isLNat#(X)active#(U201(tt, N, X, XS)) → U202#(isNatural(X), N, X, XS)
active#(U52(tt)) → mark#(tt)active#(isLNat(afterNth(V1, V2))) → mark#(U41(isNatural(V1), V2))
active#(isPLNat(pair(V1, V2))) → mark#(U141(isLNat(V1), V2))take#(mark(X1), X2) → take#(X1, X2)
active#(afterNth(N, XS)) → mark#(U11(isNatural(N), N, XS))U221#(mark(X1), X2, X3) → U221#(X1, X2, X3)
active#(U142(tt)) → mark#(tt)mark#(pair(X1, X2)) → pair#(mark(X1), mark(X2))
mark#(U211(X1, X2)) → U211#(mark(X1), X2)active#(U203(tt, N, X, XS)) → U204#(splitAt(N, XS), X)
mark#(U204(X1, X2)) → active#(U204(mark(X1), X2))U11#(X1, X2, mark(X3)) → U11#(X1, X2, X3)
mark#(U142(X)) → active#(U142(mark(X)))U202#(X1, X2, X3, mark(X4)) → U202#(X1, X2, X3, X4)
mark#(sel(X1, X2)) → mark#(X2)fst#(mark(X)) → fst#(X)
active#(U211(tt, XS)) → U212#(isLNat(XS), XS)active#(isPLNat(splitAt(V1, V2))) → isNatural#(V1)
afterNth#(X1, active(X2)) → afterNth#(X1, X2)mark#(U12(X1, X2, X3)) → mark#(X1)
active#(head(cons(N, XS))) → U31#(isNatural(N), N, XS)U212#(mark(X1), X2) → U212#(X1, X2)
U171#(mark(X1), X2, X3) → U171#(X1, X2, X3)active#(isNatural(sel(V1, V2))) → mark#(U131(isNatural(V1), V2))
mark#(isLNat(X)) → isLNat#(X)isLNat#(mark(X)) → isLNat#(X)
mark#(head(X)) → head#(mark(X))mark#(take(X1, X2)) → take#(mark(X1), mark(X2))
U91#(mark(X)) → U91#(X)active#(fst(pair(X, Y))) → isLNat#(X)
U171#(active(X1), X2, X3) → U171#(X1, X2, X3)U31#(X1, mark(X2), X3) → U31#(X1, X2, X3)
mark#(U101(X1, X2)) → active#(U101(mark(X1), X2))mark#(pair(X1, X2)) → mark#(X2)
U21#(X1, X2, active(X3)) → U21#(X1, X2, X3)U172#(X1, X2, mark(X3)) → U172#(X1, X2, X3)
active#(U222(tt, N, XS)) → fst#(splitAt(N, XS))U102#(mark(X)) → U102#(X)
active#(U204(pair(YS, ZS), X)) → mark#(pair(cons(X, YS), ZS))active#(U212(tt, XS)) → mark#(XS)
active#(isLNat(take(V1, V2))) → U101#(isNatural(V1), V2)mark#(U42(X)) → U42#(mark(X))
U22#(active(X1), X2) → U22#(X1, X2)mark#(U91(X)) → active#(U91(mark(X)))
active#(U51(tt, V2)) → mark#(U52(isLNat(V2)))U11#(X1, active(X2), X3) → U11#(X1, X2, X3)
mark#(U161(X1, X2)) → active#(U161(mark(X1), X2))mark#(U222(X1, X2, X3)) → active#(U222(mark(X1), X2, X3))
fst#(active(X)) → fst#(X)U41#(active(X1), X2) → U41#(X1, X2)
sel#(X1, mark(X2)) → sel#(X1, X2)U222#(X1, X2, active(X3)) → U222#(X1, X2, X3)
mark#(U181(X1, X2)) → active#(U181(mark(X1), X2))active#(U141(tt, V2)) → mark#(U142(isLNat(V2)))
mark#(pair(X1, X2)) → mark#(X1)sel#(X1, active(X2)) → sel#(X1, X2)
active#(U171(tt, N, XS)) → mark#(U172(isLNat(XS), N, XS))U21#(active(X1), X2, X3) → U21#(X1, X2, X3)
active#(U11(tt, N, XS)) → U12#(isLNat(XS), N, XS)mark#(tail(X)) → mark#(X)
mark#(U102(X)) → active#(U102(mark(X)))U161#(X1, mark(X2)) → U161#(X1, X2)
mark#(afterNth(X1, X2)) → mark#(X2)mark#(U222(X1, X2, X3)) → U222#(mark(X1), X2, X3)
mark#(U132(X)) → active#(U132(mark(X)))mark#(U111(X)) → U111#(mark(X))
pair#(mark(X1), X2) → pair#(X1, X2)active#(U171(tt, N, XS)) → U172#(isLNat(XS), N, XS)
mark#(tt) → active#(tt)cons#(mark(X1), X2) → cons#(X1, X2)
active#(take(N, XS)) → mark#(U221(isNatural(N), N, XS))U101#(active(X1), X2) → U101#(X1, X2)
U203#(active(X1), X2, X3, X4) → U203#(X1, X2, X3, X4)U111#(mark(X)) → U111#(X)
U22#(X1, active(X2)) → U22#(X1, X2)mark#(U52(X)) → active#(U52(mark(X)))
U201#(active(X1), X2, X3, X4) → U201#(X1, X2, X3, X4)U221#(X1, X2, mark(X3)) → U221#(X1, X2, X3)
U21#(X1, X2, mark(X3)) → U21#(X1, X2, X3)mark#(U141(X1, X2)) → active#(U141(mark(X1), X2))
active#(isLNat(snd(V1))) → mark#(U81(isPLNat(V1)))active#(U21(tt, X, Y)) → mark#(U22(isLNat(Y), X))
active#(isLNat(snd(V1))) → U81#(isPLNat(V1))active#(U181(tt, Y)) → U182#(isLNat(Y), Y)
U203#(X1, active(X2), X3, X4) → U203#(X1, X2, X3, X4)U181#(active(X1), X2) → U181#(X1, X2)
mark#(s(X)) → active#(s(mark(X)))head#(mark(X)) → head#(X)
active#(U131(tt, V2)) → U132#(isLNat(V2))active#(take(N, XS)) → U221#(isNatural(N), N, XS)
active#(splitAt(s(N), cons(X, XS))) → U201#(isNatural(N), N, X, XS)mark#(U12(X1, X2, X3)) → U12#(mark(X1), X2, X3)
snd#(active(X)) → snd#(X)mark#(U141(X1, X2)) → U141#(mark(X1), X2)
U141#(X1, mark(X2)) → U141#(X1, X2)mark#(U201(X1, X2, X3, X4)) → U201#(mark(X1), X2, X3, X4)
active#(isNatural(s(V1))) → isNatural#(V1)U132#(active(X)) → U132#(X)
active#(U102(tt)) → mark#(tt)mark#(U121(X)) → U121#(mark(X))
mark#(cons(X1, X2)) → active#(cons(mark(X1), X2))mark#(snd(X)) → snd#(mark(X))
active#(U12(tt, N, XS)) → splitAt#(N, XS)U42#(active(X)) → U42#(X)
U191#(X1, active(X2)) → U191#(X1, X2)mark#(U52(X)) → U52#(mark(X))
mark#(U212(X1, X2)) → mark#(X1)U131#(mark(X1), X2) → U131#(X1, X2)
U151#(X1, mark(X2)) → U151#(X1, X2)pair#(active(X1), X2) → pair#(X1, X2)
mark#(U212(X1, X2)) → U212#(mark(X1), X2)U142#(active(X)) → U142#(X)
mark#(U32(X1, X2)) → U32#(mark(X1), X2)active#(isNatural(head(V1))) → isLNat#(V1)
mark#(U121(X)) → active#(U121(mark(X)))U182#(X1, active(X2)) → U182#(X1, X2)
U203#(X1, X2, active(X3), X4) → U203#(X1, X2, X3, X4)U202#(X1, active(X2), X3, X4) → U202#(X1, X2, X3, X4)
U222#(mark(X1), X2, X3) → U222#(X1, X2, X3)active#(U131(tt, V2)) → mark#(U132(isLNat(V2)))
active#(U11(tt, N, XS)) → isLNat#(XS)U161#(mark(X1), X2) → U161#(X1, X2)
mark#(U171(X1, X2, X3)) → U171#(mark(X1), X2, X3)mark#(U202(X1, X2, X3, X4)) → mark#(X1)
U51#(active(X1), X2) → U51#(X1, X2)mark#(U203(X1, X2, X3, X4)) → active#(U203(mark(X1), X2, X3, X4))
mark#(U81(X)) → U81#(mark(X))mark#(U221(X1, X2, X3)) → U221#(mark(X1), X2, X3)
mark#(U51(X1, X2)) → mark#(X1)mark#(U151(X1, X2)) → active#(U151(mark(X1), X2))
U32#(X1, mark(X2)) → U32#(X1, X2)active#(isLNat(snd(V1))) → isPLNat#(V1)
U102#(active(X)) → U102#(X)mark#(isPLNat(X)) → active#(isPLNat(X))
U211#(X1, active(X2)) → U211#(X1, X2)active#(U141(tt, V2)) → U142#(isLNat(V2))
mark#(U152(X)) → mark#(X)active#(U131(tt, V2)) → isLNat#(V2)
U161#(active(X1), X2) → U161#(X1, X2)active#(snd(pair(X, Y))) → U181#(isLNat(X), Y)
mark#(U222(X1, X2, X3)) → mark#(X1)mark#(U191(X1, X2)) → active#(U191(mark(X1), X2))
mark#(U141(X1, X2)) → mark#(X1)active#(fst(pair(X, Y))) → mark#(U21(isLNat(X), X, Y))
U204#(active(X1), X2) → U204#(X1, X2)mark#(U202(X1, X2, X3, X4)) → U202#(mark(X1), X2, X3, X4)
U111#(active(X)) → U111#(X)U141#(mark(X1), X2) → U141#(X1, X2)
U222#(X1, mark(X2), X3) → U222#(X1, X2, X3)U32#(mark(X1), X2) → U32#(X1, X2)
U11#(X1, mark(X2), X3) → U11#(X1, X2, X3)active#(tail(cons(N, XS))) → U211#(isNatural(N), XS)
s#(active(X)) → s#(X)U202#(active(X1), X2, X3, X4) → U202#(X1, X2, X3, X4)
active#(U202(tt, N, X, XS)) → mark#(U203(isLNat(XS), N, X, XS))U31#(mark(X1), X2, X3) → U31#(X1, X2, X3)
mark#(U91(X)) → mark#(X)take#(active(X1), X2) → take#(X1, X2)

Rewrite Rules

active(U101(tt, V2)) → mark(U102(isLNat(V2)))active(U102(tt)) → mark(tt)
active(U11(tt, N, XS)) → mark(U12(isLNat(XS), N, XS))active(U111(tt)) → mark(tt)
active(U12(tt, N, XS)) → mark(snd(splitAt(N, XS)))active(U121(tt)) → mark(tt)
active(U131(tt, V2)) → mark(U132(isLNat(V2)))active(U132(tt)) → mark(tt)
active(U141(tt, V2)) → mark(U142(isLNat(V2)))active(U142(tt)) → mark(tt)
active(U151(tt, V2)) → mark(U152(isLNat(V2)))active(U152(tt)) → mark(tt)
active(U161(tt, N)) → mark(cons(N, natsFrom(s(N))))active(U171(tt, N, XS)) → mark(U172(isLNat(XS), N, XS))
active(U172(tt, N, XS)) → mark(head(afterNth(N, XS)))active(U181(tt, Y)) → mark(U182(isLNat(Y), Y))
active(U182(tt, Y)) → mark(Y)active(U191(tt, XS)) → mark(pair(nil, XS))
active(U201(tt, N, X, XS)) → mark(U202(isNatural(X), N, X, XS))active(U202(tt, N, X, XS)) → mark(U203(isLNat(XS), N, X, XS))
active(U203(tt, N, X, XS)) → mark(U204(splitAt(N, XS), X))active(U204(pair(YS, ZS), X)) → mark(pair(cons(X, YS), ZS))
active(U21(tt, X, Y)) → mark(U22(isLNat(Y), X))active(U211(tt, XS)) → mark(U212(isLNat(XS), XS))
active(U212(tt, XS)) → mark(XS)active(U22(tt, X)) → mark(X)
active(U221(tt, N, XS)) → mark(U222(isLNat(XS), N, XS))active(U222(tt, N, XS)) → mark(fst(splitAt(N, XS)))
active(U31(tt, N, XS)) → mark(U32(isLNat(XS), N))active(U32(tt, N)) → mark(N)
active(U41(tt, V2)) → mark(U42(isLNat(V2)))active(U42(tt)) → mark(tt)
active(U51(tt, V2)) → mark(U52(isLNat(V2)))active(U52(tt)) → mark(tt)
active(U61(tt)) → mark(tt)active(U71(tt)) → mark(tt)
active(U81(tt)) → mark(tt)active(U91(tt)) → mark(tt)
active(afterNth(N, XS)) → mark(U11(isNatural(N), N, XS))active(fst(pair(X, Y))) → mark(U21(isLNat(X), X, Y))
active(head(cons(N, XS))) → mark(U31(isNatural(N), N, XS))active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(V1, V2))) → mark(U41(isNatural(V1), V2))active(isLNat(cons(V1, V2))) → mark(U51(isNatural(V1), V2))
active(isLNat(fst(V1))) → mark(U61(isPLNat(V1)))active(isLNat(natsFrom(V1))) → mark(U71(isNatural(V1)))
active(isLNat(snd(V1))) → mark(U81(isPLNat(V1)))active(isLNat(tail(V1))) → mark(U91(isLNat(V1)))
active(isLNat(take(V1, V2))) → mark(U101(isNatural(V1), V2))active(isNatural(0)) → mark(tt)
active(isNatural(head(V1))) → mark(U111(isLNat(V1)))active(isNatural(s(V1))) → mark(U121(isNatural(V1)))
active(isNatural(sel(V1, V2))) → mark(U131(isNatural(V1), V2))active(isPLNat(pair(V1, V2))) → mark(U141(isLNat(V1), V2))
active(isPLNat(splitAt(V1, V2))) → mark(U151(isNatural(V1), V2))active(natsFrom(N)) → mark(U161(isNatural(N), N))
active(sel(N, XS)) → mark(U171(isNatural(N), N, XS))active(snd(pair(X, Y))) → mark(U181(isLNat(X), Y))
active(splitAt(0, XS)) → mark(U191(isLNat(XS), XS))active(splitAt(s(N), cons(X, XS))) → mark(U201(isNatural(N), N, X, XS))
active(tail(cons(N, XS))) → mark(U211(isNatural(N), XS))active(take(N, XS)) → mark(U221(isNatural(N), N, XS))
mark(U101(X1, X2)) → active(U101(mark(X1), X2))mark(tt) → active(tt)
mark(U102(X)) → active(U102(mark(X)))mark(isLNat(X)) → active(isLNat(X))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))mark(U12(X1, X2, X3)) → active(U12(mark(X1), X2, X3))
mark(U111(X)) → active(U111(mark(X)))mark(snd(X)) → active(snd(mark(X)))
mark(splitAt(X1, X2)) → active(splitAt(mark(X1), mark(X2)))mark(U121(X)) → active(U121(mark(X)))
mark(U131(X1, X2)) → active(U131(mark(X1), X2))mark(U132(X)) → active(U132(mark(X)))
mark(U141(X1, X2)) → active(U141(mark(X1), X2))mark(U142(X)) → active(U142(mark(X)))
mark(U151(X1, X2)) → active(U151(mark(X1), X2))mark(U152(X)) → active(U152(mark(X)))
mark(U161(X1, X2)) → active(U161(mark(X1), X2))mark(cons(X1, X2)) → active(cons(mark(X1), X2))
mark(natsFrom(X)) → active(natsFrom(mark(X)))mark(s(X)) → active(s(mark(X)))
mark(U171(X1, X2, X3)) → active(U171(mark(X1), X2, X3))mark(U172(X1, X2, X3)) → active(U172(mark(X1), X2, X3))
mark(head(X)) → active(head(mark(X)))mark(afterNth(X1, X2)) → active(afterNth(mark(X1), mark(X2)))
mark(U181(X1, X2)) → active(U181(mark(X1), X2))mark(U182(X1, X2)) → active(U182(mark(X1), X2))
mark(U191(X1, X2)) → active(U191(mark(X1), X2))mark(pair(X1, X2)) → active(pair(mark(X1), mark(X2)))
mark(nil) → active(nil)mark(U201(X1, X2, X3, X4)) → active(U201(mark(X1), X2, X3, X4))
mark(U202(X1, X2, X3, X4)) → active(U202(mark(X1), X2, X3, X4))mark(isNatural(X)) → active(isNatural(X))
mark(U203(X1, X2, X3, X4)) → active(U203(mark(X1), X2, X3, X4))mark(U204(X1, X2)) → active(U204(mark(X1), X2))
mark(U21(X1, X2, X3)) → active(U21(mark(X1), X2, X3))mark(U22(X1, X2)) → active(U22(mark(X1), X2))
mark(U211(X1, X2)) → active(U211(mark(X1), X2))mark(U212(X1, X2)) → active(U212(mark(X1), X2))
mark(U221(X1, X2, X3)) → active(U221(mark(X1), X2, X3))mark(U222(X1, X2, X3)) → active(U222(mark(X1), X2, X3))
mark(fst(X)) → active(fst(mark(X)))mark(U31(X1, X2, X3)) → active(U31(mark(X1), X2, X3))
mark(U32(X1, X2)) → active(U32(mark(X1), X2))mark(U41(X1, X2)) → active(U41(mark(X1), X2))
mark(U42(X)) → active(U42(mark(X)))mark(U51(X1, X2)) → active(U51(mark(X1), X2))
mark(U52(X)) → active(U52(mark(X)))mark(U61(X)) → active(U61(mark(X)))
mark(U71(X)) → active(U71(mark(X)))mark(U81(X)) → active(U81(mark(X)))
mark(U91(X)) → active(U91(mark(X)))mark(isPLNat(X)) → active(isPLNat(X))
mark(tail(X)) → active(tail(mark(X)))mark(take(X1, X2)) → active(take(mark(X1), mark(X2)))
mark(0) → active(0)mark(sel(X1, X2)) → active(sel(mark(X1), mark(X2)))
U101(mark(X1), X2) → U101(X1, X2)U101(X1, mark(X2)) → U101(X1, X2)
U101(active(X1), X2) → U101(X1, X2)U101(X1, active(X2)) → U101(X1, X2)
U102(mark(X)) → U102(X)U102(active(X)) → U102(X)
isLNat(mark(X)) → isLNat(X)isLNat(active(X)) → isLNat(X)
U11(mark(X1), X2, X3) → U11(X1, X2, X3)U11(X1, mark(X2), X3) → U11(X1, X2, X3)
U11(X1, X2, mark(X3)) → U11(X1, X2, X3)U11(active(X1), X2, X3) → U11(X1, X2, X3)
U11(X1, active(X2), X3) → U11(X1, X2, X3)U11(X1, X2, active(X3)) → U11(X1, X2, X3)
U12(mark(X1), X2, X3) → U12(X1, X2, X3)U12(X1, mark(X2), X3) → U12(X1, X2, X3)
U12(X1, X2, mark(X3)) → U12(X1, X2, X3)U12(active(X1), X2, X3) → U12(X1, X2, X3)
U12(X1, active(X2), X3) → U12(X1, X2, X3)U12(X1, X2, active(X3)) → U12(X1, X2, X3)
U111(mark(X)) → U111(X)U111(active(X)) → U111(X)
snd(mark(X)) → snd(X)snd(active(X)) → snd(X)
splitAt(mark(X1), X2) → splitAt(X1, X2)splitAt(X1, mark(X2)) → splitAt(X1, X2)
splitAt(active(X1), X2) → splitAt(X1, X2)splitAt(X1, active(X2)) → splitAt(X1, X2)
U121(mark(X)) → U121(X)U121(active(X)) → U121(X)
U131(mark(X1), X2) → U131(X1, X2)U131(X1, mark(X2)) → U131(X1, X2)
U131(active(X1), X2) → U131(X1, X2)U131(X1, active(X2)) → U131(X1, X2)
U132(mark(X)) → U132(X)U132(active(X)) → U132(X)
U141(mark(X1), X2) → U141(X1, X2)U141(X1, mark(X2)) → U141(X1, X2)
U141(active(X1), X2) → U141(X1, X2)U141(X1, active(X2)) → U141(X1, X2)
U142(mark(X)) → U142(X)U142(active(X)) → U142(X)
U151(mark(X1), X2) → U151(X1, X2)U151(X1, mark(X2)) → U151(X1, X2)
U151(active(X1), X2) → U151(X1, X2)U151(X1, active(X2)) → U151(X1, X2)
U152(mark(X)) → U152(X)U152(active(X)) → U152(X)
U161(mark(X1), X2) → U161(X1, X2)U161(X1, mark(X2)) → U161(X1, X2)
U161(active(X1), X2) → U161(X1, X2)U161(X1, active(X2)) → U161(X1, X2)
cons(mark(X1), X2) → cons(X1, X2)cons(X1, mark(X2)) → cons(X1, X2)
cons(active(X1), X2) → cons(X1, X2)cons(X1, active(X2)) → cons(X1, X2)
natsFrom(mark(X)) → natsFrom(X)natsFrom(active(X)) → natsFrom(X)
s(mark(X)) → s(X)s(active(X)) → s(X)
U171(mark(X1), X2, X3) → U171(X1, X2, X3)U171(X1, mark(X2), X3) → U171(X1, X2, X3)
U171(X1, X2, mark(X3)) → U171(X1, X2, X3)U171(active(X1), X2, X3) → U171(X1, X2, X3)
U171(X1, active(X2), X3) → U171(X1, X2, X3)U171(X1, X2, active(X3)) → U171(X1, X2, X3)
U172(mark(X1), X2, X3) → U172(X1, X2, X3)U172(X1, mark(X2), X3) → U172(X1, X2, X3)
U172(X1, X2, mark(X3)) → U172(X1, X2, X3)U172(active(X1), X2, X3) → U172(X1, X2, X3)
U172(X1, active(X2), X3) → U172(X1, X2, X3)U172(X1, X2, active(X3)) → U172(X1, X2, X3)
head(mark(X)) → head(X)head(active(X)) → head(X)
afterNth(mark(X1), X2) → afterNth(X1, X2)afterNth(X1, mark(X2)) → afterNth(X1, X2)
afterNth(active(X1), X2) → afterNth(X1, X2)afterNth(X1, active(X2)) → afterNth(X1, X2)
U181(mark(X1), X2) → U181(X1, X2)U181(X1, mark(X2)) → U181(X1, X2)
U181(active(X1), X2) → U181(X1, X2)U181(X1, active(X2)) → U181(X1, X2)
U182(mark(X1), X2) → U182(X1, X2)U182(X1, mark(X2)) → U182(X1, X2)
U182(active(X1), X2) → U182(X1, X2)U182(X1, active(X2)) → U182(X1, X2)
U191(mark(X1), X2) → U191(X1, X2)U191(X1, mark(X2)) → U191(X1, X2)
U191(active(X1), X2) → U191(X1, X2)U191(X1, active(X2)) → U191(X1, X2)
pair(mark(X1), X2) → pair(X1, X2)pair(X1, mark(X2)) → pair(X1, X2)
pair(active(X1), X2) → pair(X1, X2)pair(X1, active(X2)) → pair(X1, X2)
U201(mark(X1), X2, X3, X4) → U201(X1, X2, X3, X4)U201(X1, mark(X2), X3, X4) → U201(X1, X2, X3, X4)
U201(X1, X2, mark(X3), X4) → U201(X1, X2, X3, X4)U201(X1, X2, X3, mark(X4)) → U201(X1, X2, X3, X4)
U201(active(X1), X2, X3, X4) → U201(X1, X2, X3, X4)U201(X1, active(X2), X3, X4) → U201(X1, X2, X3, X4)
U201(X1, X2, active(X3), X4) → U201(X1, X2, X3, X4)U201(X1, X2, X3, active(X4)) → U201(X1, X2, X3, X4)
U202(mark(X1), X2, X3, X4) → U202(X1, X2, X3, X4)U202(X1, mark(X2), X3, X4) → U202(X1, X2, X3, X4)
U202(X1, X2, mark(X3), X4) → U202(X1, X2, X3, X4)U202(X1, X2, X3, mark(X4)) → U202(X1, X2, X3, X4)
U202(active(X1), X2, X3, X4) → U202(X1, X2, X3, X4)U202(X1, active(X2), X3, X4) → U202(X1, X2, X3, X4)
U202(X1, X2, active(X3), X4) → U202(X1, X2, X3, X4)U202(X1, X2, X3, active(X4)) → U202(X1, X2, X3, X4)
isNatural(mark(X)) → isNatural(X)isNatural(active(X)) → isNatural(X)
U203(mark(X1), X2, X3, X4) → U203(X1, X2, X3, X4)U203(X1, mark(X2), X3, X4) → U203(X1, X2, X3, X4)
U203(X1, X2, mark(X3), X4) → U203(X1, X2, X3, X4)U203(X1, X2, X3, mark(X4)) → U203(X1, X2, X3, X4)
U203(active(X1), X2, X3, X4) → U203(X1, X2, X3, X4)U203(X1, active(X2), X3, X4) → U203(X1, X2, X3, X4)
U203(X1, X2, active(X3), X4) → U203(X1, X2, X3, X4)U203(X1, X2, X3, active(X4)) → U203(X1, X2, X3, X4)
U204(mark(X1), X2) → U204(X1, X2)U204(X1, mark(X2)) → U204(X1, X2)
U204(active(X1), X2) → U204(X1, X2)U204(X1, active(X2)) → U204(X1, X2)
U21(mark(X1), X2, X3) → U21(X1, X2, X3)U21(X1, mark(X2), X3) → U21(X1, X2, X3)
U21(X1, X2, mark(X3)) → U21(X1, X2, X3)U21(active(X1), X2, X3) → U21(X1, X2, X3)
U21(X1, active(X2), X3) → U21(X1, X2, X3)U21(X1, X2, active(X3)) → U21(X1, X2, X3)
U22(mark(X1), X2) → U22(X1, X2)U22(X1, mark(X2)) → U22(X1, X2)
U22(active(X1), X2) → U22(X1, X2)U22(X1, active(X2)) → U22(X1, X2)
U211(mark(X1), X2) → U211(X1, X2)U211(X1, mark(X2)) → U211(X1, X2)
U211(active(X1), X2) → U211(X1, X2)U211(X1, active(X2)) → U211(X1, X2)
U212(mark(X1), X2) → U212(X1, X2)U212(X1, mark(X2)) → U212(X1, X2)
U212(active(X1), X2) → U212(X1, X2)U212(X1, active(X2)) → U212(X1, X2)
U221(mark(X1), X2, X3) → U221(X1, X2, X3)U221(X1, mark(X2), X3) → U221(X1, X2, X3)
U221(X1, X2, mark(X3)) → U221(X1, X2, X3)U221(active(X1), X2, X3) → U221(X1, X2, X3)
U221(X1, active(X2), X3) → U221(X1, X2, X3)U221(X1, X2, active(X3)) → U221(X1, X2, X3)
U222(mark(X1), X2, X3) → U222(X1, X2, X3)U222(X1, mark(X2), X3) → U222(X1, X2, X3)
U222(X1, X2, mark(X3)) → U222(X1, X2, X3)U222(active(X1), X2, X3) → U222(X1, X2, X3)
U222(X1, active(X2), X3) → U222(X1, X2, X3)U222(X1, X2, active(X3)) → U222(X1, X2, X3)
fst(mark(X)) → fst(X)fst(active(X)) → fst(X)
U31(mark(X1), X2, X3) → U31(X1, X2, X3)U31(X1, mark(X2), X3) → U31(X1, X2, X3)
U31(X1, X2, mark(X3)) → U31(X1, X2, X3)U31(active(X1), X2, X3) → U31(X1, X2, X3)
U31(X1, active(X2), X3) → U31(X1, X2, X3)U31(X1, X2, active(X3)) → U31(X1, X2, X3)
U32(mark(X1), X2) → U32(X1, X2)U32(X1, mark(X2)) → U32(X1, X2)
U32(active(X1), X2) → U32(X1, X2)U32(X1, active(X2)) → U32(X1, X2)
U41(mark(X1), X2) → U41(X1, X2)U41(X1, mark(X2)) → U41(X1, X2)
U41(active(X1), X2) → U41(X1, X2)U41(X1, active(X2)) → U41(X1, X2)
U42(mark(X)) → U42(X)U42(active(X)) → U42(X)
U51(mark(X1), X2) → U51(X1, X2)U51(X1, mark(X2)) → U51(X1, X2)
U51(active(X1), X2) → U51(X1, X2)U51(X1, active(X2)) → U51(X1, X2)
U52(mark(X)) → U52(X)U52(active(X)) → U52(X)
U61(mark(X)) → U61(X)U61(active(X)) → U61(X)
U71(mark(X)) → U71(X)U71(active(X)) → U71(X)
U81(mark(X)) → U81(X)U81(active(X)) → U81(X)
U91(mark(X)) → U91(X)U91(active(X)) → U91(X)
isPLNat(mark(X)) → isPLNat(X)isPLNat(active(X)) → isPLNat(X)
tail(mark(X)) → tail(X)tail(active(X)) → tail(X)
take(mark(X1), X2) → take(X1, X2)take(X1, mark(X2)) → take(X1, X2)
take(active(X1), X2) → take(X1, X2)take(X1, active(X2)) → take(X1, X2)
sel(mark(X1), X2) → sel(X1, X2)sel(X1, mark(X2)) → sel(X1, X2)
sel(active(X1), X2) → sel(X1, X2)sel(X1, active(X2)) → sel(X1, X2)

Original Signature

Termination of terms over the following signature is verified: natsFrom, U161, U204, U203, fst, U111, U61, U211, U212, head, U21, U22, U151, mark, isPLNat, U152, tail, U71, U191, 0, U121, U221, isLNat, U222, active, U31, U32, U181, U182, pair, isNatural, U132, U131, U42, U41, U91, cons, snd, U171, U172, splitAt, U201, U142, U202, U141, s, U51, tt, take, U81, U52, U11, U12, afterNth, U102, sel, U101, nil