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