The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(O(1), O(1)).

(0) Obligation:

Runtime Complexity TRS:
The TRS R consists of the following 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)

Rewrite Strategy: INNERMOST

(1) CpxTrsToCdtProof (BOTH BOUNDS(ID, ID) transformation)

Converted CpxTRS to CDT

(2) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0)) → mark(U102(isLNat(z0)))
active(U102(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(U12(isLNat(z1), z0, z1))
active(U111(tt)) → mark(tt)
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U121(tt)) → mark(tt)
active(U131(tt, z0)) → mark(U132(isLNat(z0)))
active(U132(tt)) → mark(tt)
active(U141(tt, z0)) → mark(U142(isLNat(z0)))
active(U142(tt)) → mark(tt)
active(U151(tt, z0)) → mark(U152(isLNat(z0)))
active(U152(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(U172(isLNat(z1), z0, z1))
active(U172(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(U182(isLNat(z0), z0))
active(U182(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(isNatural(z1), z0, z1, z2))
active(U202(tt, z0, z1, z2)) → mark(U203(isLNat(z2), z0, z1, z2))
active(U203(tt, z0, z1, z2)) → mark(U204(splitAt(z0, z2), z1))
active(U204(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0, z1)) → mark(U22(isLNat(z1), z0))
active(U211(tt, z0)) → mark(U212(isLNat(z0), z0))
active(U212(tt, z0)) → mark(z0)
active(U22(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(U222(isLNat(z1), z0, z1))
active(U222(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0, z1)) → mark(U32(isLNat(z1), z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0)) → mark(U42(isLNat(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isLNat(z0)))
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(z0, z1)) → mark(U11(isNatural(z0), z0, z1))
active(fst(pair(z0, z1))) → mark(U21(isLNat(z0), z0, z1))
active(head(cons(z0, z1))) → mark(U31(isNatural(z0), z0, z1))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(isNatural(z0), z1))
active(isLNat(cons(z0, z1))) → mark(U51(isNatural(z0), z1))
active(isLNat(fst(z0))) → mark(U61(isPLNat(z0)))
active(isLNat(natsFrom(z0))) → mark(U71(isNatural(z0)))
active(isLNat(snd(z0))) → mark(U81(isPLNat(z0)))
active(isLNat(tail(z0))) → mark(U91(isLNat(z0)))
active(isLNat(take(z0, z1))) → mark(U101(isNatural(z0), z1))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNat(z0)))
active(isNatural(s(z0))) → mark(U121(isNatural(z0)))
active(isNatural(sel(z0, z1))) → mark(U131(isNatural(z0), z1))
active(isPLNat(pair(z0, z1))) → mark(U141(isLNat(z0), z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(isNatural(z0), z1))
active(natsFrom(z0)) → mark(U161(isNatural(z0), z0))
active(sel(z0, z1)) → mark(U171(isNatural(z0), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(isLNat(z0), z1))
active(splitAt(0, z0)) → mark(U191(isLNat(z0), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(isNatural(z0), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(isNatural(z0), z1))
active(take(z0, z1)) → mark(U221(isNatural(z0), z0, z1))
mark(U101(z0, z1)) → active(U101(mark(z0), z1))
mark(tt) → active(tt)
mark(U102(z0)) → active(U102(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U111(z0)) → active(U111(mark(z0)))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U121(z0)) → active(U121(mark(z0)))
mark(U131(z0, z1)) → active(U131(mark(z0), z1))
mark(U132(z0)) → active(U132(mark(z0)))
mark(U141(z0, z1)) → active(U141(mark(z0), z1))
mark(U142(z0)) → active(U142(mark(z0)))
mark(U151(z0, z1)) → active(U151(mark(z0), z1))
mark(U152(z0)) → active(U152(mark(z0)))
mark(U161(z0, z1)) → active(U161(mark(z0), z1))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(U171(z0, z1, z2)) → active(U171(mark(z0), z1, z2))
mark(U172(z0, z1, z2)) → active(U172(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U181(z0, z1)) → active(U181(mark(z0), z1))
mark(U182(z0, z1)) → active(U182(mark(z0), z1))
mark(U191(z0, z1)) → active(U191(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U201(z0, z1, z2, z3)) → active(U201(mark(z0), z1, z2, z3))
mark(U202(z0, z1, z2, z3)) → active(U202(mark(z0), z1, z2, z3))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U203(z0, z1, z2, z3)) → active(U203(mark(z0), z1, z2, z3))
mark(U204(z0, z1)) → active(U204(mark(z0), z1))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U212(z0, z1)) → active(U212(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(U222(z0, z1, z2)) → active(U222(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0)) → active(U71(mark(z0)))
mark(U81(z0)) → active(U81(mark(z0)))
mark(U91(z0)) → active(U91(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
mark(0) → active(0)
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
U101(mark(z0), z1) → U101(z0, z1)
U101(z0, mark(z1)) → U101(z0, z1)
U101(active(z0), z1) → U101(z0, z1)
U101(z0, active(z1)) → U101(z0, z1)
U102(mark(z0)) → U102(z0)
U102(active(z0)) → U102(z0)
isLNat(mark(z0)) → isLNat(z0)
isLNat(active(z0)) → isLNat(z0)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U111(mark(z0)) → U111(z0)
U111(active(z0)) → U111(z0)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U121(mark(z0)) → U121(z0)
U121(active(z0)) → U121(z0)
U131(mark(z0), z1) → U131(z0, z1)
U131(z0, mark(z1)) → U131(z0, z1)
U131(active(z0), z1) → U131(z0, z1)
U131(z0, active(z1)) → U131(z0, z1)
U132(mark(z0)) → U132(z0)
U132(active(z0)) → U132(z0)
U141(mark(z0), z1) → U141(z0, z1)
U141(z0, mark(z1)) → U141(z0, z1)
U141(active(z0), z1) → U141(z0, z1)
U141(z0, active(z1)) → U141(z0, z1)
U142(mark(z0)) → U142(z0)
U142(active(z0)) → U142(z0)
U151(mark(z0), z1) → U151(z0, z1)
U151(z0, mark(z1)) → U151(z0, z1)
U151(active(z0), z1) → U151(z0, z1)
U151(z0, active(z1)) → U151(z0, z1)
U152(mark(z0)) → U152(z0)
U152(active(z0)) → U152(z0)
U161(mark(z0), z1) → U161(z0, z1)
U161(z0, mark(z1)) → U161(z0, z1)
U161(active(z0), z1) → U161(z0, z1)
U161(z0, active(z1)) → U161(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U171(mark(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, mark(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, mark(z2)) → U171(z0, z1, z2)
U171(active(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, active(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, active(z2)) → U171(z0, z1, z2)
U172(mark(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, mark(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, mark(z2)) → U172(z0, z1, z2)
U172(active(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, active(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, active(z2)) → U172(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U181(mark(z0), z1) → U181(z0, z1)
U181(z0, mark(z1)) → U181(z0, z1)
U181(active(z0), z1) → U181(z0, z1)
U181(z0, active(z1)) → U181(z0, z1)
U182(mark(z0), z1) → U182(z0, z1)
U182(z0, mark(z1)) → U182(z0, z1)
U182(active(z0), z1) → U182(z0, z1)
U182(z0, active(z1)) → U182(z0, z1)
U191(mark(z0), z1) → U191(z0, z1)
U191(z0, mark(z1)) → U191(z0, z1)
U191(active(z0), z1) → U191(z0, z1)
U191(z0, active(z1)) → U191(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
U201(mark(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, mark(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, mark(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, mark(z3)) → U201(z0, z1, z2, z3)
U201(active(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, active(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, active(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, active(z3)) → U201(z0, z1, z2, z3)
U202(mark(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, mark(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, mark(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, mark(z3)) → U202(z0, z1, z2, z3)
U202(active(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, active(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, active(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, active(z3)) → U202(z0, z1, z2, z3)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U203(mark(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, mark(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, mark(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, mark(z3)) → U203(z0, z1, z2, z3)
U203(active(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, active(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, active(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, active(z3)) → U203(z0, z1, z2, z3)
U204(mark(z0), z1) → U204(z0, z1)
U204(z0, mark(z1)) → U204(z0, z1)
U204(active(z0), z1) → U204(z0, z1)
U204(z0, active(z1)) → U204(z0, z1)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U211(mark(z0), z1) → U211(z0, z1)
U211(z0, mark(z1)) → U211(z0, z1)
U211(active(z0), z1) → U211(z0, z1)
U211(z0, active(z1)) → U211(z0, z1)
U212(mark(z0), z1) → U212(z0, z1)
U212(z0, mark(z1)) → U212(z0, z1)
U212(active(z0), z1) → U212(z0, z1)
U212(z0, active(z1)) → U212(z0, z1)
U221(mark(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, mark(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, mark(z2)) → U221(z0, z1, z2)
U221(active(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, active(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, active(z2)) → U221(z0, z1, z2)
U222(mark(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, mark(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, mark(z2)) → U222(z0, z1, z2)
U222(active(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, active(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, active(z2)) → U222(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(z0)
U71(mark(z0)) → U71(z0)
U71(active(z0)) → U71(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
U91(mark(z0)) → U91(z0)
U91(active(z0)) → U91(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)

Tuples:

ACTIVE(U101(tt, z0)) → c(MARK(U102(isLNat(z0))), U102'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U102(tt)) → c1(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c2(MARK(U12(isLNat(z1), z0, z1)), U12'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U111(tt)) → c3(MARK(tt))
ACTIVE(U12(tt, z0, z1)) → c4(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U121(tt)) → c5(MARK(tt))
ACTIVE(U131(tt, z0)) → c6(MARK(U132(isLNat(z0))), U132'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U132(tt)) → c7(MARK(tt))
ACTIVE(U141(tt, z0)) → c8(MARK(U142(isLNat(z0))), U142'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U142(tt)) → c9(MARK(tt))
ACTIVE(U151(tt, z0)) → c10(MARK(U152(isLNat(z0))), U152'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U152(tt)) → c11(MARK(tt))
ACTIVE(U161(tt, z0)) → c12(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c13(MARK(U172(isLNat(z1), z0, z1)), U172'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U172(tt, z0, z1)) → c14(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c15(MARK(U182(isLNat(z0), z0)), U182'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U182(tt, z0)) → c16(MARK(z0))
ACTIVE(U191(tt, z0)) → c17(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c18(MARK(U202(isNatural(z1), z0, z1, z2)), U202'(isNatural(z1), z0, z1, z2), ISNATURAL(z1))
ACTIVE(U202(tt, z0, z1, z2)) → c19(MARK(U203(isLNat(z2), z0, z1, z2)), U203'(isLNat(z2), z0, z1, z2), ISLNAT(z2))
ACTIVE(U203(tt, z0, z1, z2)) → c20(MARK(U204(splitAt(z0, z2), z1)), U204'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U204(pair(z0, z1), z2)) → c21(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0, z1)) → c22(MARK(U22(isLNat(z1), z0)), U22'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U211(tt, z0)) → c23(MARK(U212(isLNat(z0), z0)), U212'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U212(tt, z0)) → c24(MARK(z0))
ACTIVE(U22(tt, z0)) → c25(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c26(MARK(U222(isLNat(z1), z0, z1)), U222'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U222(tt, z0, z1)) → c27(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0, z1)) → c28(MARK(U32(isLNat(z1), z0)), U32'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U32(tt, z0)) → c29(MARK(z0))
ACTIVE(U41(tt, z0)) → c30(MARK(U42(isLNat(z0))), U42'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U42(tt)) → c31(MARK(tt))
ACTIVE(U51(tt, z0)) → c32(MARK(U52(isLNat(z0))), U52'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U52(tt)) → c33(MARK(tt))
ACTIVE(U61(tt)) → c34(MARK(tt))
ACTIVE(U71(tt)) → c35(MARK(tt))
ACTIVE(U81(tt)) → c36(MARK(tt))
ACTIVE(U91(tt)) → c37(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c38(MARK(U11(isNatural(z0), z0, z1)), U11'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(fst(pair(z0, z1))) → c39(MARK(U21(isLNat(z0), z0, z1)), U21'(isLNat(z0), z0, z1), ISLNAT(z0))
ACTIVE(head(cons(z0, z1))) → c40(MARK(U31(isNatural(z0), z0, z1)), U31'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(isLNat(nil)) → c41(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c42(MARK(U41(isNatural(z0), z1)), U41'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(cons(z0, z1))) → c43(MARK(U51(isNatural(z0), z1)), U51'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(fst(z0))) → c44(MARK(U61(isPLNat(z0))), U61'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(natsFrom(z0))) → c45(MARK(U71(isNatural(z0))), U71'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isLNat(snd(z0))) → c46(MARK(U81(isPLNat(z0))), U81'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(tail(z0))) → c47(MARK(U91(isLNat(z0))), U91'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isLNat(take(z0, z1))) → c48(MARK(U101(isNatural(z0), z1)), U101'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isNatural(0)) → c49(MARK(tt))
ACTIVE(isNatural(head(z0))) → c50(MARK(U111(isLNat(z0))), U111'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isNatural(s(z0))) → c51(MARK(U121(isNatural(z0))), U121'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isNatural(sel(z0, z1))) → c52(MARK(U131(isNatural(z0), z1)), U131'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isPLNat(pair(z0, z1))) → c53(MARK(U141(isLNat(z0), z1)), U141'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(isPLNat(splitAt(z0, z1))) → c54(MARK(U151(isNatural(z0), z1)), U151'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(natsFrom(z0)) → c55(MARK(U161(isNatural(z0), z0)), U161'(isNatural(z0), z0), ISNATURAL(z0))
ACTIVE(sel(z0, z1)) → c56(MARK(U171(isNatural(z0), z0, z1)), U171'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(snd(pair(z0, z1))) → c57(MARK(U181(isLNat(z0), z1)), U181'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(splitAt(0, z0)) → c58(MARK(U191(isLNat(z0), z0)), U191'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c59(MARK(U201(isNatural(z0), z0, z1, z2)), U201'(isNatural(z0), z0, z1, z2), ISNATURAL(z0))
ACTIVE(tail(cons(z0, z1))) → c60(MARK(U211(isNatural(z0), z1)), U211'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(take(z0, z1)) → c61(MARK(U221(isNatural(z0), z0, z1)), U221'(isNatural(z0), z0, z1), ISNATURAL(z0))
MARK(U101(z0, z1)) → c62(ACTIVE(U101(mark(z0), z1)), U101'(mark(z0), z1), MARK(z0))
MARK(tt) → c63(ACTIVE(tt))
MARK(U102(z0)) → c64(ACTIVE(U102(mark(z0))), U102'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c65(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c66(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c67(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U111(z0)) → c68(ACTIVE(U111(mark(z0))), U111'(mark(z0)), MARK(z0))
MARK(snd(z0)) → c69(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c70(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U121(z0)) → c71(ACTIVE(U121(mark(z0))), U121'(mark(z0)), MARK(z0))
MARK(U131(z0, z1)) → c72(ACTIVE(U131(mark(z0), z1)), U131'(mark(z0), z1), MARK(z0))
MARK(U132(z0)) → c73(ACTIVE(U132(mark(z0))), U132'(mark(z0)), MARK(z0))
MARK(U141(z0, z1)) → c74(ACTIVE(U141(mark(z0), z1)), U141'(mark(z0), z1), MARK(z0))
MARK(U142(z0)) → c75(ACTIVE(U142(mark(z0))), U142'(mark(z0)), MARK(z0))
MARK(U151(z0, z1)) → c76(ACTIVE(U151(mark(z0), z1)), U151'(mark(z0), z1), MARK(z0))
MARK(U152(z0)) → c77(ACTIVE(U152(mark(z0))), U152'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c78(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c79(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c80(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c81(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c82(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(U172(z0, z1, z2)) → c83(ACTIVE(U172(mark(z0), z1, z2)), U172'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c84(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c85(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c86(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U182(z0, z1)) → c87(ACTIVE(U182(mark(z0), z1)), U182'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c88(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c89(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c90(ACTIVE(nil))
MARK(U201(z0, z1, z2, z3)) → c91(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1, z2, z3)) → c92(ACTIVE(U202(mark(z0), z1, z2, z3)), U202'(mark(z0), z1, z2, z3), MARK(z0))
MARK(isNatural(z0)) → c93(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U203(z0, z1, z2, z3)) → c94(ACTIVE(U203(mark(z0), z1, z2, z3)), U203'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U204(z0, z1)) → c95(ACTIVE(U204(mark(z0), z1)), U204'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) → c96(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c97(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c98(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U212(z0, z1)) → c99(ACTIVE(U212(mark(z0), z1)), U212'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c100(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(U222(z0, z1, z2)) → c101(ACTIVE(U222(mark(z0), z1, z2)), U222'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c102(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c103(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1)) → c104(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1)) → c105(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c106(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0, z1)) → c107(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c108(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c109(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0)) → c110(ACTIVE(U71(mark(z0))), U71'(mark(z0)), MARK(z0))
MARK(U81(z0)) → c111(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(U91(z0)) → c112(ACTIVE(U91(mark(z0))), U91'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c113(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(tail(z0)) → c114(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c115(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c116(ACTIVE(0))
MARK(sel(z0, z1)) → c117(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1) → c118(U101'(z0, z1))
U101'(z0, mark(z1)) → c119(U101'(z0, z1))
U101'(active(z0), z1) → c120(U101'(z0, z1))
U101'(z0, active(z1)) → c121(U101'(z0, z1))
U102'(mark(z0)) → c122(U102'(z0))
U102'(active(z0)) → c123(U102'(z0))
ISLNAT(mark(z0)) → c124(ISLNAT(z0))
ISLNAT(active(z0)) → c125(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c126(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c127(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c128(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c129(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c130(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c131(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c132(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c133(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c134(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c135(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c136(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c137(U12'(z0, z1, z2))
U111'(mark(z0)) → c138(U111'(z0))
U111'(active(z0)) → c139(U111'(z0))
SND(mark(z0)) → c140(SND(z0))
SND(active(z0)) → c141(SND(z0))
SPLITAT(mark(z0), z1) → c142(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c143(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c144(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c145(SPLITAT(z0, z1))
U121'(mark(z0)) → c146(U121'(z0))
U121'(active(z0)) → c147(U121'(z0))
U131'(mark(z0), z1) → c148(U131'(z0, z1))
U131'(z0, mark(z1)) → c149(U131'(z0, z1))
U131'(active(z0), z1) → c150(U131'(z0, z1))
U131'(z0, active(z1)) → c151(U131'(z0, z1))
U132'(mark(z0)) → c152(U132'(z0))
U132'(active(z0)) → c153(U132'(z0))
U141'(mark(z0), z1) → c154(U141'(z0, z1))
U141'(z0, mark(z1)) → c155(U141'(z0, z1))
U141'(active(z0), z1) → c156(U141'(z0, z1))
U141'(z0, active(z1)) → c157(U141'(z0, z1))
U142'(mark(z0)) → c158(U142'(z0))
U142'(active(z0)) → c159(U142'(z0))
U151'(mark(z0), z1) → c160(U151'(z0, z1))
U151'(z0, mark(z1)) → c161(U151'(z0, z1))
U151'(active(z0), z1) → c162(U151'(z0, z1))
U151'(z0, active(z1)) → c163(U151'(z0, z1))
U152'(mark(z0)) → c164(U152'(z0))
U152'(active(z0)) → c165(U152'(z0))
U161'(mark(z0), z1) → c166(U161'(z0, z1))
U161'(z0, mark(z1)) → c167(U161'(z0, z1))
U161'(active(z0), z1) → c168(U161'(z0, z1))
U161'(z0, active(z1)) → c169(U161'(z0, z1))
CONS(mark(z0), z1) → c170(CONS(z0, z1))
CONS(z0, mark(z1)) → c171(CONS(z0, z1))
CONS(active(z0), z1) → c172(CONS(z0, z1))
CONS(z0, active(z1)) → c173(CONS(z0, z1))
NATSFROM(mark(z0)) → c174(NATSFROM(z0))
NATSFROM(active(z0)) → c175(NATSFROM(z0))
S(mark(z0)) → c176(S(z0))
S(active(z0)) → c177(S(z0))
U171'(mark(z0), z1, z2) → c178(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c179(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c180(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c181(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c182(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c183(U171'(z0, z1, z2))
U172'(mark(z0), z1, z2) → c184(U172'(z0, z1, z2))
U172'(z0, mark(z1), z2) → c185(U172'(z0, z1, z2))
U172'(z0, z1, mark(z2)) → c186(U172'(z0, z1, z2))
U172'(active(z0), z1, z2) → c187(U172'(z0, z1, z2))
U172'(z0, active(z1), z2) → c188(U172'(z0, z1, z2))
U172'(z0, z1, active(z2)) → c189(U172'(z0, z1, z2))
HEAD(mark(z0)) → c190(HEAD(z0))
HEAD(active(z0)) → c191(HEAD(z0))
AFTERNTH(mark(z0), z1) → c192(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c193(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c194(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c195(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c196(U181'(z0, z1))
U181'(z0, mark(z1)) → c197(U181'(z0, z1))
U181'(active(z0), z1) → c198(U181'(z0, z1))
U181'(z0, active(z1)) → c199(U181'(z0, z1))
U182'(mark(z0), z1) → c200(U182'(z0, z1))
U182'(z0, mark(z1)) → c201(U182'(z0, z1))
U182'(active(z0), z1) → c202(U182'(z0, z1))
U182'(z0, active(z1)) → c203(U182'(z0, z1))
U191'(mark(z0), z1) → c204(U191'(z0, z1))
U191'(z0, mark(z1)) → c205(U191'(z0, z1))
U191'(active(z0), z1) → c206(U191'(z0, z1))
U191'(z0, active(z1)) → c207(U191'(z0, z1))
PAIR(mark(z0), z1) → c208(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c209(PAIR(z0, z1))
PAIR(active(z0), z1) → c210(PAIR(z0, z1))
PAIR(z0, active(z1)) → c211(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c212(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c213(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c214(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c215(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c216(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c217(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c218(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c219(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1, z2, z3) → c220(U202'(z0, z1, z2, z3))
U202'(z0, mark(z1), z2, z3) → c221(U202'(z0, z1, z2, z3))
U202'(z0, z1, mark(z2), z3) → c222(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, mark(z3)) → c223(U202'(z0, z1, z2, z3))
U202'(active(z0), z1, z2, z3) → c224(U202'(z0, z1, z2, z3))
U202'(z0, active(z1), z2, z3) → c225(U202'(z0, z1, z2, z3))
U202'(z0, z1, active(z2), z3) → c226(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, active(z3)) → c227(U202'(z0, z1, z2, z3))
ISNATURAL(mark(z0)) → c228(ISNATURAL(z0))
ISNATURAL(active(z0)) → c229(ISNATURAL(z0))
U203'(mark(z0), z1, z2, z3) → c230(U203'(z0, z1, z2, z3))
U203'(z0, mark(z1), z2, z3) → c231(U203'(z0, z1, z2, z3))
U203'(z0, z1, mark(z2), z3) → c232(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, mark(z3)) → c233(U203'(z0, z1, z2, z3))
U203'(active(z0), z1, z2, z3) → c234(U203'(z0, z1, z2, z3))
U203'(z0, active(z1), z2, z3) → c235(U203'(z0, z1, z2, z3))
U203'(z0, z1, active(z2), z3) → c236(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, active(z3)) → c237(U203'(z0, z1, z2, z3))
U204'(mark(z0), z1) → c238(U204'(z0, z1))
U204'(z0, mark(z1)) → c239(U204'(z0, z1))
U204'(active(z0), z1) → c240(U204'(z0, z1))
U204'(z0, active(z1)) → c241(U204'(z0, z1))
U21'(mark(z0), z1, z2) → c242(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c243(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c244(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c245(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c246(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c247(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c248(U22'(z0, z1))
U22'(z0, mark(z1)) → c249(U22'(z0, z1))
U22'(active(z0), z1) → c250(U22'(z0, z1))
U22'(z0, active(z1)) → c251(U22'(z0, z1))
U211'(mark(z0), z1) → c252(U211'(z0, z1))
U211'(z0, mark(z1)) → c253(U211'(z0, z1))
U211'(active(z0), z1) → c254(U211'(z0, z1))
U211'(z0, active(z1)) → c255(U211'(z0, z1))
U212'(mark(z0), z1) → c256(U212'(z0, z1))
U212'(z0, mark(z1)) → c257(U212'(z0, z1))
U212'(active(z0), z1) → c258(U212'(z0, z1))
U212'(z0, active(z1)) → c259(U212'(z0, z1))
U221'(mark(z0), z1, z2) → c260(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c261(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c262(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c263(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c264(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c265(U221'(z0, z1, z2))
U222'(mark(z0), z1, z2) → c266(U222'(z0, z1, z2))
U222'(z0, mark(z1), z2) → c267(U222'(z0, z1, z2))
U222'(z0, z1, mark(z2)) → c268(U222'(z0, z1, z2))
U222'(active(z0), z1, z2) → c269(U222'(z0, z1, z2))
U222'(z0, active(z1), z2) → c270(U222'(z0, z1, z2))
U222'(z0, z1, active(z2)) → c271(U222'(z0, z1, z2))
FST(mark(z0)) → c272(FST(z0))
FST(active(z0)) → c273(FST(z0))
U31'(mark(z0), z1, z2) → c274(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c275(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c276(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c277(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c278(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c279(U31'(z0, z1, z2))
U32'(mark(z0), z1) → c280(U32'(z0, z1))
U32'(z0, mark(z1)) → c281(U32'(z0, z1))
U32'(active(z0), z1) → c282(U32'(z0, z1))
U32'(z0, active(z1)) → c283(U32'(z0, z1))
U41'(mark(z0), z1) → c284(U41'(z0, z1))
U41'(z0, mark(z1)) → c285(U41'(z0, z1))
U41'(active(z0), z1) → c286(U41'(z0, z1))
U41'(z0, active(z1)) → c287(U41'(z0, z1))
U42'(mark(z0)) → c288(U42'(z0))
U42'(active(z0)) → c289(U42'(z0))
U51'(mark(z0), z1) → c290(U51'(z0, z1))
U51'(z0, mark(z1)) → c291(U51'(z0, z1))
U51'(active(z0), z1) → c292(U51'(z0, z1))
U51'(z0, active(z1)) → c293(U51'(z0, z1))
U52'(mark(z0)) → c294(U52'(z0))
U52'(active(z0)) → c295(U52'(z0))
U61'(mark(z0)) → c296(U61'(z0))
U61'(active(z0)) → c297(U61'(z0))
U71'(mark(z0)) → c298(U71'(z0))
U71'(active(z0)) → c299(U71'(z0))
U81'(mark(z0)) → c300(U81'(z0))
U81'(active(z0)) → c301(U81'(z0))
U91'(mark(z0)) → c302(U91'(z0))
U91'(active(z0)) → c303(U91'(z0))
ISPLNAT(mark(z0)) → c304(ISPLNAT(z0))
ISPLNAT(active(z0)) → c305(ISPLNAT(z0))
TAIL(mark(z0)) → c306(TAIL(z0))
TAIL(active(z0)) → c307(TAIL(z0))
TAKE(mark(z0), z1) → c308(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c309(TAKE(z0, z1))
TAKE(active(z0), z1) → c310(TAKE(z0, z1))
TAKE(z0, active(z1)) → c311(TAKE(z0, z1))
SEL(mark(z0), z1) → c312(SEL(z0, z1))
SEL(z0, mark(z1)) → c313(SEL(z0, z1))
SEL(active(z0), z1) → c314(SEL(z0, z1))
SEL(z0, active(z1)) → c315(SEL(z0, z1))

S tuples:

ACTIVE(U101(tt, z0)) → c(MARK(U102(isLNat(z0))), U102'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U102(tt)) → c1(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c2(MARK(U12(isLNat(z1), z0, z1)), U12'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U111(tt)) → c3(MARK(tt))
ACTIVE(U12(tt, z0, z1)) → c4(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U121(tt)) → c5(MARK(tt))
ACTIVE(U131(tt, z0)) → c6(MARK(U132(isLNat(z0))), U132'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U132(tt)) → c7(MARK(tt))
ACTIVE(U141(tt, z0)) → c8(MARK(U142(isLNat(z0))), U142'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U142(tt)) → c9(MARK(tt))
ACTIVE(U151(tt, z0)) → c10(MARK(U152(isLNat(z0))), U152'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U152(tt)) → c11(MARK(tt))
ACTIVE(U161(tt, z0)) → c12(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c13(MARK(U172(isLNat(z1), z0, z1)), U172'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U172(tt, z0, z1)) → c14(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c15(MARK(U182(isLNat(z0), z0)), U182'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U182(tt, z0)) → c16(MARK(z0))
ACTIVE(U191(tt, z0)) → c17(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c18(MARK(U202(isNatural(z1), z0, z1, z2)), U202'(isNatural(z1), z0, z1, z2), ISNATURAL(z1))
ACTIVE(U202(tt, z0, z1, z2)) → c19(MARK(U203(isLNat(z2), z0, z1, z2)), U203'(isLNat(z2), z0, z1, z2), ISLNAT(z2))
ACTIVE(U203(tt, z0, z1, z2)) → c20(MARK(U204(splitAt(z0, z2), z1)), U204'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U204(pair(z0, z1), z2)) → c21(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0, z1)) → c22(MARK(U22(isLNat(z1), z0)), U22'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U211(tt, z0)) → c23(MARK(U212(isLNat(z0), z0)), U212'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U212(tt, z0)) → c24(MARK(z0))
ACTIVE(U22(tt, z0)) → c25(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c26(MARK(U222(isLNat(z1), z0, z1)), U222'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U222(tt, z0, z1)) → c27(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0, z1)) → c28(MARK(U32(isLNat(z1), z0)), U32'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U32(tt, z0)) → c29(MARK(z0))
ACTIVE(U41(tt, z0)) → c30(MARK(U42(isLNat(z0))), U42'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U42(tt)) → c31(MARK(tt))
ACTIVE(U51(tt, z0)) → c32(MARK(U52(isLNat(z0))), U52'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U52(tt)) → c33(MARK(tt))
ACTIVE(U61(tt)) → c34(MARK(tt))
ACTIVE(U71(tt)) → c35(MARK(tt))
ACTIVE(U81(tt)) → c36(MARK(tt))
ACTIVE(U91(tt)) → c37(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c38(MARK(U11(isNatural(z0), z0, z1)), U11'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(fst(pair(z0, z1))) → c39(MARK(U21(isLNat(z0), z0, z1)), U21'(isLNat(z0), z0, z1), ISLNAT(z0))
ACTIVE(head(cons(z0, z1))) → c40(MARK(U31(isNatural(z0), z0, z1)), U31'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(isLNat(nil)) → c41(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c42(MARK(U41(isNatural(z0), z1)), U41'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(cons(z0, z1))) → c43(MARK(U51(isNatural(z0), z1)), U51'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(fst(z0))) → c44(MARK(U61(isPLNat(z0))), U61'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(natsFrom(z0))) → c45(MARK(U71(isNatural(z0))), U71'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isLNat(snd(z0))) → c46(MARK(U81(isPLNat(z0))), U81'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(tail(z0))) → c47(MARK(U91(isLNat(z0))), U91'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isLNat(take(z0, z1))) → c48(MARK(U101(isNatural(z0), z1)), U101'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isNatural(0)) → c49(MARK(tt))
ACTIVE(isNatural(head(z0))) → c50(MARK(U111(isLNat(z0))), U111'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isNatural(s(z0))) → c51(MARK(U121(isNatural(z0))), U121'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isNatural(sel(z0, z1))) → c52(MARK(U131(isNatural(z0), z1)), U131'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isPLNat(pair(z0, z1))) → c53(MARK(U141(isLNat(z0), z1)), U141'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(isPLNat(splitAt(z0, z1))) → c54(MARK(U151(isNatural(z0), z1)), U151'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(natsFrom(z0)) → c55(MARK(U161(isNatural(z0), z0)), U161'(isNatural(z0), z0), ISNATURAL(z0))
ACTIVE(sel(z0, z1)) → c56(MARK(U171(isNatural(z0), z0, z1)), U171'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(snd(pair(z0, z1))) → c57(MARK(U181(isLNat(z0), z1)), U181'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(splitAt(0, z0)) → c58(MARK(U191(isLNat(z0), z0)), U191'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c59(MARK(U201(isNatural(z0), z0, z1, z2)), U201'(isNatural(z0), z0, z1, z2), ISNATURAL(z0))
ACTIVE(tail(cons(z0, z1))) → c60(MARK(U211(isNatural(z0), z1)), U211'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(take(z0, z1)) → c61(MARK(U221(isNatural(z0), z0, z1)), U221'(isNatural(z0), z0, z1), ISNATURAL(z0))
MARK(U101(z0, z1)) → c62(ACTIVE(U101(mark(z0), z1)), U101'(mark(z0), z1), MARK(z0))
MARK(tt) → c63(ACTIVE(tt))
MARK(U102(z0)) → c64(ACTIVE(U102(mark(z0))), U102'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c65(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c66(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c67(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U111(z0)) → c68(ACTIVE(U111(mark(z0))), U111'(mark(z0)), MARK(z0))
MARK(snd(z0)) → c69(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c70(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U121(z0)) → c71(ACTIVE(U121(mark(z0))), U121'(mark(z0)), MARK(z0))
MARK(U131(z0, z1)) → c72(ACTIVE(U131(mark(z0), z1)), U131'(mark(z0), z1), MARK(z0))
MARK(U132(z0)) → c73(ACTIVE(U132(mark(z0))), U132'(mark(z0)), MARK(z0))
MARK(U141(z0, z1)) → c74(ACTIVE(U141(mark(z0), z1)), U141'(mark(z0), z1), MARK(z0))
MARK(U142(z0)) → c75(ACTIVE(U142(mark(z0))), U142'(mark(z0)), MARK(z0))
MARK(U151(z0, z1)) → c76(ACTIVE(U151(mark(z0), z1)), U151'(mark(z0), z1), MARK(z0))
MARK(U152(z0)) → c77(ACTIVE(U152(mark(z0))), U152'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c78(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c79(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c80(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c81(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c82(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(U172(z0, z1, z2)) → c83(ACTIVE(U172(mark(z0), z1, z2)), U172'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c84(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c85(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c86(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U182(z0, z1)) → c87(ACTIVE(U182(mark(z0), z1)), U182'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c88(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c89(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c90(ACTIVE(nil))
MARK(U201(z0, z1, z2, z3)) → c91(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1, z2, z3)) → c92(ACTIVE(U202(mark(z0), z1, z2, z3)), U202'(mark(z0), z1, z2, z3), MARK(z0))
MARK(isNatural(z0)) → c93(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U203(z0, z1, z2, z3)) → c94(ACTIVE(U203(mark(z0), z1, z2, z3)), U203'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U204(z0, z1)) → c95(ACTIVE(U204(mark(z0), z1)), U204'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) → c96(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c97(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c98(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U212(z0, z1)) → c99(ACTIVE(U212(mark(z0), z1)), U212'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c100(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(U222(z0, z1, z2)) → c101(ACTIVE(U222(mark(z0), z1, z2)), U222'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c102(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c103(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1)) → c104(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1)) → c105(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c106(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0, z1)) → c107(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c108(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c109(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0)) → c110(ACTIVE(U71(mark(z0))), U71'(mark(z0)), MARK(z0))
MARK(U81(z0)) → c111(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(U91(z0)) → c112(ACTIVE(U91(mark(z0))), U91'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c113(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(tail(z0)) → c114(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c115(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c116(ACTIVE(0))
MARK(sel(z0, z1)) → c117(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1) → c118(U101'(z0, z1))
U101'(z0, mark(z1)) → c119(U101'(z0, z1))
U101'(active(z0), z1) → c120(U101'(z0, z1))
U101'(z0, active(z1)) → c121(U101'(z0, z1))
U102'(mark(z0)) → c122(U102'(z0))
U102'(active(z0)) → c123(U102'(z0))
ISLNAT(mark(z0)) → c124(ISLNAT(z0))
ISLNAT(active(z0)) → c125(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c126(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c127(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c128(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c129(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c130(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c131(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c132(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c133(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c134(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c135(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c136(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c137(U12'(z0, z1, z2))
U111'(mark(z0)) → c138(U111'(z0))
U111'(active(z0)) → c139(U111'(z0))
SND(mark(z0)) → c140(SND(z0))
SND(active(z0)) → c141(SND(z0))
SPLITAT(mark(z0), z1) → c142(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c143(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c144(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c145(SPLITAT(z0, z1))
U121'(mark(z0)) → c146(U121'(z0))
U121'(active(z0)) → c147(U121'(z0))
U131'(mark(z0), z1) → c148(U131'(z0, z1))
U131'(z0, mark(z1)) → c149(U131'(z0, z1))
U131'(active(z0), z1) → c150(U131'(z0, z1))
U131'(z0, active(z1)) → c151(U131'(z0, z1))
U132'(mark(z0)) → c152(U132'(z0))
U132'(active(z0)) → c153(U132'(z0))
U141'(mark(z0), z1) → c154(U141'(z0, z1))
U141'(z0, mark(z1)) → c155(U141'(z0, z1))
U141'(active(z0), z1) → c156(U141'(z0, z1))
U141'(z0, active(z1)) → c157(U141'(z0, z1))
U142'(mark(z0)) → c158(U142'(z0))
U142'(active(z0)) → c159(U142'(z0))
U151'(mark(z0), z1) → c160(U151'(z0, z1))
U151'(z0, mark(z1)) → c161(U151'(z0, z1))
U151'(active(z0), z1) → c162(U151'(z0, z1))
U151'(z0, active(z1)) → c163(U151'(z0, z1))
U152'(mark(z0)) → c164(U152'(z0))
U152'(active(z0)) → c165(U152'(z0))
U161'(mark(z0), z1) → c166(U161'(z0, z1))
U161'(z0, mark(z1)) → c167(U161'(z0, z1))
U161'(active(z0), z1) → c168(U161'(z0, z1))
U161'(z0, active(z1)) → c169(U161'(z0, z1))
CONS(mark(z0), z1) → c170(CONS(z0, z1))
CONS(z0, mark(z1)) → c171(CONS(z0, z1))
CONS(active(z0), z1) → c172(CONS(z0, z1))
CONS(z0, active(z1)) → c173(CONS(z0, z1))
NATSFROM(mark(z0)) → c174(NATSFROM(z0))
NATSFROM(active(z0)) → c175(NATSFROM(z0))
S(mark(z0)) → c176(S(z0))
S(active(z0)) → c177(S(z0))
U171'(mark(z0), z1, z2) → c178(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c179(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c180(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c181(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c182(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c183(U171'(z0, z1, z2))
U172'(mark(z0), z1, z2) → c184(U172'(z0, z1, z2))
U172'(z0, mark(z1), z2) → c185(U172'(z0, z1, z2))
U172'(z0, z1, mark(z2)) → c186(U172'(z0, z1, z2))
U172'(active(z0), z1, z2) → c187(U172'(z0, z1, z2))
U172'(z0, active(z1), z2) → c188(U172'(z0, z1, z2))
U172'(z0, z1, active(z2)) → c189(U172'(z0, z1, z2))
HEAD(mark(z0)) → c190(HEAD(z0))
HEAD(active(z0)) → c191(HEAD(z0))
AFTERNTH(mark(z0), z1) → c192(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c193(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c194(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c195(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c196(U181'(z0, z1))
U181'(z0, mark(z1)) → c197(U181'(z0, z1))
U181'(active(z0), z1) → c198(U181'(z0, z1))
U181'(z0, active(z1)) → c199(U181'(z0, z1))
U182'(mark(z0), z1) → c200(U182'(z0, z1))
U182'(z0, mark(z1)) → c201(U182'(z0, z1))
U182'(active(z0), z1) → c202(U182'(z0, z1))
U182'(z0, active(z1)) → c203(U182'(z0, z1))
U191'(mark(z0), z1) → c204(U191'(z0, z1))
U191'(z0, mark(z1)) → c205(U191'(z0, z1))
U191'(active(z0), z1) → c206(U191'(z0, z1))
U191'(z0, active(z1)) → c207(U191'(z0, z1))
PAIR(mark(z0), z1) → c208(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c209(PAIR(z0, z1))
PAIR(active(z0), z1) → c210(PAIR(z0, z1))
PAIR(z0, active(z1)) → c211(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c212(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c213(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c214(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c215(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c216(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c217(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c218(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c219(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1, z2, z3) → c220(U202'(z0, z1, z2, z3))
U202'(z0, mark(z1), z2, z3) → c221(U202'(z0, z1, z2, z3))
U202'(z0, z1, mark(z2), z3) → c222(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, mark(z3)) → c223(U202'(z0, z1, z2, z3))
U202'(active(z0), z1, z2, z3) → c224(U202'(z0, z1, z2, z3))
U202'(z0, active(z1), z2, z3) → c225(U202'(z0, z1, z2, z3))
U202'(z0, z1, active(z2), z3) → c226(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, active(z3)) → c227(U202'(z0, z1, z2, z3))
ISNATURAL(mark(z0)) → c228(ISNATURAL(z0))
ISNATURAL(active(z0)) → c229(ISNATURAL(z0))
U203'(mark(z0), z1, z2, z3) → c230(U203'(z0, z1, z2, z3))
U203'(z0, mark(z1), z2, z3) → c231(U203'(z0, z1, z2, z3))
U203'(z0, z1, mark(z2), z3) → c232(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, mark(z3)) → c233(U203'(z0, z1, z2, z3))
U203'(active(z0), z1, z2, z3) → c234(U203'(z0, z1, z2, z3))
U203'(z0, active(z1), z2, z3) → c235(U203'(z0, z1, z2, z3))
U203'(z0, z1, active(z2), z3) → c236(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, active(z3)) → c237(U203'(z0, z1, z2, z3))
U204'(mark(z0), z1) → c238(U204'(z0, z1))
U204'(z0, mark(z1)) → c239(U204'(z0, z1))
U204'(active(z0), z1) → c240(U204'(z0, z1))
U204'(z0, active(z1)) → c241(U204'(z0, z1))
U21'(mark(z0), z1, z2) → c242(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c243(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c244(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c245(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c246(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c247(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c248(U22'(z0, z1))
U22'(z0, mark(z1)) → c249(U22'(z0, z1))
U22'(active(z0), z1) → c250(U22'(z0, z1))
U22'(z0, active(z1)) → c251(U22'(z0, z1))
U211'(mark(z0), z1) → c252(U211'(z0, z1))
U211'(z0, mark(z1)) → c253(U211'(z0, z1))
U211'(active(z0), z1) → c254(U211'(z0, z1))
U211'(z0, active(z1)) → c255(U211'(z0, z1))
U212'(mark(z0), z1) → c256(U212'(z0, z1))
U212'(z0, mark(z1)) → c257(U212'(z0, z1))
U212'(active(z0), z1) → c258(U212'(z0, z1))
U212'(z0, active(z1)) → c259(U212'(z0, z1))
U221'(mark(z0), z1, z2) → c260(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c261(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c262(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c263(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c264(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c265(U221'(z0, z1, z2))
U222'(mark(z0), z1, z2) → c266(U222'(z0, z1, z2))
U222'(z0, mark(z1), z2) → c267(U222'(z0, z1, z2))
U222'(z0, z1, mark(z2)) → c268(U222'(z0, z1, z2))
U222'(active(z0), z1, z2) → c269(U222'(z0, z1, z2))
U222'(z0, active(z1), z2) → c270(U222'(z0, z1, z2))
U222'(z0, z1, active(z2)) → c271(U222'(z0, z1, z2))
FST(mark(z0)) → c272(FST(z0))
FST(active(z0)) → c273(FST(z0))
U31'(mark(z0), z1, z2) → c274(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c275(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c276(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c277(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c278(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c279(U31'(z0, z1, z2))
U32'(mark(z0), z1) → c280(U32'(z0, z1))
U32'(z0, mark(z1)) → c281(U32'(z0, z1))
U32'(active(z0), z1) → c282(U32'(z0, z1))
U32'(z0, active(z1)) → c283(U32'(z0, z1))
U41'(mark(z0), z1) → c284(U41'(z0, z1))
U41'(z0, mark(z1)) → c285(U41'(z0, z1))
U41'(active(z0), z1) → c286(U41'(z0, z1))
U41'(z0, active(z1)) → c287(U41'(z0, z1))
U42'(mark(z0)) → c288(U42'(z0))
U42'(active(z0)) → c289(U42'(z0))
U51'(mark(z0), z1) → c290(U51'(z0, z1))
U51'(z0, mark(z1)) → c291(U51'(z0, z1))
U51'(active(z0), z1) → c292(U51'(z0, z1))
U51'(z0, active(z1)) → c293(U51'(z0, z1))
U52'(mark(z0)) → c294(U52'(z0))
U52'(active(z0)) → c295(U52'(z0))
U61'(mark(z0)) → c296(U61'(z0))
U61'(active(z0)) → c297(U61'(z0))
U71'(mark(z0)) → c298(U71'(z0))
U71'(active(z0)) → c299(U71'(z0))
U81'(mark(z0)) → c300(U81'(z0))
U81'(active(z0)) → c301(U81'(z0))
U91'(mark(z0)) → c302(U91'(z0))
U91'(active(z0)) → c303(U91'(z0))
ISPLNAT(mark(z0)) → c304(ISPLNAT(z0))
ISPLNAT(active(z0)) → c305(ISPLNAT(z0))
TAIL(mark(z0)) → c306(TAIL(z0))
TAIL(active(z0)) → c307(TAIL(z0))
TAKE(mark(z0), z1) → c308(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c309(TAKE(z0, z1))
TAKE(active(z0), z1) → c310(TAKE(z0, z1))
TAKE(z0, active(z1)) → c311(TAKE(z0, z1))
SEL(mark(z0), z1) → c312(SEL(z0, z1))
SEL(z0, mark(z1)) → c313(SEL(z0, z1))
SEL(active(z0), z1) → c314(SEL(z0, z1))
SEL(z0, active(z1)) → c315(SEL(z0, z1))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

ACTIVE, MARK, U101', U102', ISLNAT, U11', U12', U111', SND, SPLITAT, U121', U131', U132', U141', U142', U151', U152', U161', CONS, NATSFROM, S, U171', U172', HEAD, AFTERNTH, U181', U182', U191', PAIR, U201', U202', ISNATURAL, U203', U204', U21', U22', U211', U212', U221', U222', FST, U31', U32', U41', U42', U51', U52', U61', U71', U81', U91', ISPLNAT, TAIL, TAKE, SEL

Compound Symbols:

c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28, c29, c30, c31, c32, c33, c34, c35, c36, c37, c38, c39, c40, c41, c42, c43, c44, c45, c46, c47, c48, c49, c50, c51, c52, c53, c54, c55, c56, c57, c58, c59, c60, c61, c62, c63, c64, c65, c66, c67, c68, c69, c70, c71, c72, c73, c74, c75, c76, c77, c78, c79, c80, c81, c82, c83, c84, c85, c86, c87, c88, c89, c90, c91, c92, c93, c94, c95, c96, c97, c98, c99, c100, c101, c102, c103, c104, c105, c106, c107, c108, c109, c110, c111, c112, c113, c114, c115, c116, c117, c118, c119, c120, c121, c122, c123, c124, c125, c126, c127, c128, c129, c130, c131, c132, c133, c134, c135, c136, c137, c138, c139, c140, c141, c142, c143, c144, c145, c146, c147, c148, c149, c150, c151, c152, c153, c154, c155, c156, c157, c158, c159, c160, c161, c162, c163, c164, c165, c166, c167, c168, c169, c170, c171, c172, c173, c174, c175, c176, c177, c178, c179, c180, c181, c182, c183, c184, c185, c186, c187, c188, c189, c190, c191, c192, c193, c194, c195, c196, c197, c198, c199, c200, c201, c202, c203, c204, c205, c206, c207, c208, c209, c210, c211, c212, c213, c214, c215, c216, c217, c218, c219, c220, c221, c222, c223, c224, c225, c226, c227, c228, c229, c230, c231, c232, c233, c234, c235, c236, c237, c238, c239, c240, c241, c242, c243, c244, c245, c246, c247, c248, c249, c250, c251, c252, c253, c254, c255, c256, c257, c258, c259, c260, c261, c262, c263, c264, c265, c266, c267, c268, c269, c270, c271, c272, c273, c274, c275, c276, c277, c278, c279, c280, c281, c282, c283, c284, c285, c286, c287, c288, c289, c290, c291, c292, c293, c294, c295, c296, c297, c298, c299, c300, c301, c302, c303, c304, c305, c306, c307, c308, c309, c310, c311, c312, c313, c314, c315

(3) CdtUnreachableProof (EQUIVALENT transformation)

The following tuples could be removed as they are not reachable from basic start terms:

ACTIVE(U101(tt, z0)) → c(MARK(U102(isLNat(z0))), U102'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U102(tt)) → c1(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c2(MARK(U12(isLNat(z1), z0, z1)), U12'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U111(tt)) → c3(MARK(tt))
ACTIVE(U12(tt, z0, z1)) → c4(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U121(tt)) → c5(MARK(tt))
ACTIVE(U131(tt, z0)) → c6(MARK(U132(isLNat(z0))), U132'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U132(tt)) → c7(MARK(tt))
ACTIVE(U141(tt, z0)) → c8(MARK(U142(isLNat(z0))), U142'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U142(tt)) → c9(MARK(tt))
ACTIVE(U151(tt, z0)) → c10(MARK(U152(isLNat(z0))), U152'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U152(tt)) → c11(MARK(tt))
ACTIVE(U161(tt, z0)) → c12(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c13(MARK(U172(isLNat(z1), z0, z1)), U172'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U172(tt, z0, z1)) → c14(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c15(MARK(U182(isLNat(z0), z0)), U182'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U182(tt, z0)) → c16(MARK(z0))
ACTIVE(U191(tt, z0)) → c17(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c18(MARK(U202(isNatural(z1), z0, z1, z2)), U202'(isNatural(z1), z0, z1, z2), ISNATURAL(z1))
ACTIVE(U202(tt, z0, z1, z2)) → c19(MARK(U203(isLNat(z2), z0, z1, z2)), U203'(isLNat(z2), z0, z1, z2), ISLNAT(z2))
ACTIVE(U203(tt, z0, z1, z2)) → c20(MARK(U204(splitAt(z0, z2), z1)), U204'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U204(pair(z0, z1), z2)) → c21(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0, z1)) → c22(MARK(U22(isLNat(z1), z0)), U22'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U211(tt, z0)) → c23(MARK(U212(isLNat(z0), z0)), U212'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(U212(tt, z0)) → c24(MARK(z0))
ACTIVE(U22(tt, z0)) → c25(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c26(MARK(U222(isLNat(z1), z0, z1)), U222'(isLNat(z1), z0, z1), ISLNAT(z1))
ACTIVE(U222(tt, z0, z1)) → c27(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0, z1)) → c28(MARK(U32(isLNat(z1), z0)), U32'(isLNat(z1), z0), ISLNAT(z1))
ACTIVE(U32(tt, z0)) → c29(MARK(z0))
ACTIVE(U41(tt, z0)) → c30(MARK(U42(isLNat(z0))), U42'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U42(tt)) → c31(MARK(tt))
ACTIVE(U51(tt, z0)) → c32(MARK(U52(isLNat(z0))), U52'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U52(tt)) → c33(MARK(tt))
ACTIVE(U61(tt)) → c34(MARK(tt))
ACTIVE(U71(tt)) → c35(MARK(tt))
ACTIVE(U81(tt)) → c36(MARK(tt))
ACTIVE(U91(tt)) → c37(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c38(MARK(U11(isNatural(z0), z0, z1)), U11'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(fst(pair(z0, z1))) → c39(MARK(U21(isLNat(z0), z0, z1)), U21'(isLNat(z0), z0, z1), ISLNAT(z0))
ACTIVE(head(cons(z0, z1))) → c40(MARK(U31(isNatural(z0), z0, z1)), U31'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(isLNat(nil)) → c41(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c42(MARK(U41(isNatural(z0), z1)), U41'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(cons(z0, z1))) → c43(MARK(U51(isNatural(z0), z1)), U51'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isLNat(fst(z0))) → c44(MARK(U61(isPLNat(z0))), U61'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(natsFrom(z0))) → c45(MARK(U71(isNatural(z0))), U71'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isLNat(snd(z0))) → c46(MARK(U81(isPLNat(z0))), U81'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(isLNat(tail(z0))) → c47(MARK(U91(isLNat(z0))), U91'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isLNat(take(z0, z1))) → c48(MARK(U101(isNatural(z0), z1)), U101'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isNatural(0)) → c49(MARK(tt))
ACTIVE(isNatural(head(z0))) → c50(MARK(U111(isLNat(z0))), U111'(isLNat(z0)), ISLNAT(z0))
ACTIVE(isNatural(s(z0))) → c51(MARK(U121(isNatural(z0))), U121'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(isNatural(sel(z0, z1))) → c52(MARK(U131(isNatural(z0), z1)), U131'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(isPLNat(pair(z0, z1))) → c53(MARK(U141(isLNat(z0), z1)), U141'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(isPLNat(splitAt(z0, z1))) → c54(MARK(U151(isNatural(z0), z1)), U151'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(natsFrom(z0)) → c55(MARK(U161(isNatural(z0), z0)), U161'(isNatural(z0), z0), ISNATURAL(z0))
ACTIVE(sel(z0, z1)) → c56(MARK(U171(isNatural(z0), z0, z1)), U171'(isNatural(z0), z0, z1), ISNATURAL(z0))
ACTIVE(snd(pair(z0, z1))) → c57(MARK(U181(isLNat(z0), z1)), U181'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(splitAt(0, z0)) → c58(MARK(U191(isLNat(z0), z0)), U191'(isLNat(z0), z0), ISLNAT(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c59(MARK(U201(isNatural(z0), z0, z1, z2)), U201'(isNatural(z0), z0, z1, z2), ISNATURAL(z0))
ACTIVE(tail(cons(z0, z1))) → c60(MARK(U211(isNatural(z0), z1)), U211'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(take(z0, z1)) → c61(MARK(U221(isNatural(z0), z0, z1)), U221'(isNatural(z0), z0, z1), ISNATURAL(z0))
MARK(U101(z0, z1)) → c62(ACTIVE(U101(mark(z0), z1)), U101'(mark(z0), z1), MARK(z0))
MARK(U102(z0)) → c64(ACTIVE(U102(mark(z0))), U102'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c65(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c66(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(U12(z0, z1, z2)) → c67(ACTIVE(U12(mark(z0), z1, z2)), U12'(mark(z0), z1, z2), MARK(z0))
MARK(U111(z0)) → c68(ACTIVE(U111(mark(z0))), U111'(mark(z0)), MARK(z0))
MARK(snd(z0)) → c69(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c70(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U121(z0)) → c71(ACTIVE(U121(mark(z0))), U121'(mark(z0)), MARK(z0))
MARK(U131(z0, z1)) → c72(ACTIVE(U131(mark(z0), z1)), U131'(mark(z0), z1), MARK(z0))
MARK(U132(z0)) → c73(ACTIVE(U132(mark(z0))), U132'(mark(z0)), MARK(z0))
MARK(U141(z0, z1)) → c74(ACTIVE(U141(mark(z0), z1)), U141'(mark(z0), z1), MARK(z0))
MARK(U142(z0)) → c75(ACTIVE(U142(mark(z0))), U142'(mark(z0)), MARK(z0))
MARK(U151(z0, z1)) → c76(ACTIVE(U151(mark(z0), z1)), U151'(mark(z0), z1), MARK(z0))
MARK(U152(z0)) → c77(ACTIVE(U152(mark(z0))), U152'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c78(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c79(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c80(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c81(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c82(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(U172(z0, z1, z2)) → c83(ACTIVE(U172(mark(z0), z1, z2)), U172'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c84(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c85(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c86(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U182(z0, z1)) → c87(ACTIVE(U182(mark(z0), z1)), U182'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c88(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c89(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U201(z0, z1, z2, z3)) → c91(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1, z2, z3)) → c92(ACTIVE(U202(mark(z0), z1, z2, z3)), U202'(mark(z0), z1, z2, z3), MARK(z0))
MARK(isNatural(z0)) → c93(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U203(z0, z1, z2, z3)) → c94(ACTIVE(U203(mark(z0), z1, z2, z3)), U203'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U204(z0, z1)) → c95(ACTIVE(U204(mark(z0), z1)), U204'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1, z2)) → c96(ACTIVE(U21(mark(z0), z1, z2)), U21'(mark(z0), z1, z2), MARK(z0))
MARK(U22(z0, z1)) → c97(ACTIVE(U22(mark(z0), z1)), U22'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c98(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U212(z0, z1)) → c99(ACTIVE(U212(mark(z0), z1)), U212'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c100(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(U222(z0, z1, z2)) → c101(ACTIVE(U222(mark(z0), z1, z2)), U222'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c102(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1, z2)) → c103(ACTIVE(U31(mark(z0), z1, z2)), U31'(mark(z0), z1, z2), MARK(z0))
MARK(U32(z0, z1)) → c104(ACTIVE(U32(mark(z0), z1)), U32'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1)) → c105(ACTIVE(U41(mark(z0), z1)), U41'(mark(z0), z1), MARK(z0))
MARK(U42(z0)) → c106(ACTIVE(U42(mark(z0))), U42'(mark(z0)), MARK(z0))
MARK(U51(z0, z1)) → c107(ACTIVE(U51(mark(z0), z1)), U51'(mark(z0), z1), MARK(z0))
MARK(U52(z0)) → c108(ACTIVE(U52(mark(z0))), U52'(mark(z0)), MARK(z0))
MARK(U61(z0)) → c109(ACTIVE(U61(mark(z0))), U61'(mark(z0)), MARK(z0))
MARK(U71(z0)) → c110(ACTIVE(U71(mark(z0))), U71'(mark(z0)), MARK(z0))
MARK(U81(z0)) → c111(ACTIVE(U81(mark(z0))), U81'(mark(z0)), MARK(z0))
MARK(U91(z0)) → c112(ACTIVE(U91(mark(z0))), U91'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c113(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(tail(z0)) → c114(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c115(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(sel(z0, z1)) → c117(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1) → c118(U101'(z0, z1))
U101'(z0, mark(z1)) → c119(U101'(z0, z1))
U101'(active(z0), z1) → c120(U101'(z0, z1))
U101'(z0, active(z1)) → c121(U101'(z0, z1))
U102'(mark(z0)) → c122(U102'(z0))
U102'(active(z0)) → c123(U102'(z0))
ISLNAT(mark(z0)) → c124(ISLNAT(z0))
ISLNAT(active(z0)) → c125(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c126(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c127(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c128(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c129(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c130(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c131(U11'(z0, z1, z2))
U12'(mark(z0), z1, z2) → c132(U12'(z0, z1, z2))
U12'(z0, mark(z1), z2) → c133(U12'(z0, z1, z2))
U12'(z0, z1, mark(z2)) → c134(U12'(z0, z1, z2))
U12'(active(z0), z1, z2) → c135(U12'(z0, z1, z2))
U12'(z0, active(z1), z2) → c136(U12'(z0, z1, z2))
U12'(z0, z1, active(z2)) → c137(U12'(z0, z1, z2))
U111'(mark(z0)) → c138(U111'(z0))
U111'(active(z0)) → c139(U111'(z0))
SND(mark(z0)) → c140(SND(z0))
SND(active(z0)) → c141(SND(z0))
SPLITAT(mark(z0), z1) → c142(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c143(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c144(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c145(SPLITAT(z0, z1))
U121'(mark(z0)) → c146(U121'(z0))
U121'(active(z0)) → c147(U121'(z0))
U131'(mark(z0), z1) → c148(U131'(z0, z1))
U131'(z0, mark(z1)) → c149(U131'(z0, z1))
U131'(active(z0), z1) → c150(U131'(z0, z1))
U131'(z0, active(z1)) → c151(U131'(z0, z1))
U132'(mark(z0)) → c152(U132'(z0))
U132'(active(z0)) → c153(U132'(z0))
U141'(mark(z0), z1) → c154(U141'(z0, z1))
U141'(z0, mark(z1)) → c155(U141'(z0, z1))
U141'(active(z0), z1) → c156(U141'(z0, z1))
U141'(z0, active(z1)) → c157(U141'(z0, z1))
U142'(mark(z0)) → c158(U142'(z0))
U142'(active(z0)) → c159(U142'(z0))
U151'(mark(z0), z1) → c160(U151'(z0, z1))
U151'(z0, mark(z1)) → c161(U151'(z0, z1))
U151'(active(z0), z1) → c162(U151'(z0, z1))
U151'(z0, active(z1)) → c163(U151'(z0, z1))
U152'(mark(z0)) → c164(U152'(z0))
U152'(active(z0)) → c165(U152'(z0))
U161'(mark(z0), z1) → c166(U161'(z0, z1))
U161'(z0, mark(z1)) → c167(U161'(z0, z1))
U161'(active(z0), z1) → c168(U161'(z0, z1))
U161'(z0, active(z1)) → c169(U161'(z0, z1))
CONS(mark(z0), z1) → c170(CONS(z0, z1))
CONS(z0, mark(z1)) → c171(CONS(z0, z1))
CONS(active(z0), z1) → c172(CONS(z0, z1))
CONS(z0, active(z1)) → c173(CONS(z0, z1))
NATSFROM(mark(z0)) → c174(NATSFROM(z0))
NATSFROM(active(z0)) → c175(NATSFROM(z0))
S(mark(z0)) → c176(S(z0))
S(active(z0)) → c177(S(z0))
U171'(mark(z0), z1, z2) → c178(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c179(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c180(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c181(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c182(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c183(U171'(z0, z1, z2))
U172'(mark(z0), z1, z2) → c184(U172'(z0, z1, z2))
U172'(z0, mark(z1), z2) → c185(U172'(z0, z1, z2))
U172'(z0, z1, mark(z2)) → c186(U172'(z0, z1, z2))
U172'(active(z0), z1, z2) → c187(U172'(z0, z1, z2))
U172'(z0, active(z1), z2) → c188(U172'(z0, z1, z2))
U172'(z0, z1, active(z2)) → c189(U172'(z0, z1, z2))
HEAD(mark(z0)) → c190(HEAD(z0))
HEAD(active(z0)) → c191(HEAD(z0))
AFTERNTH(mark(z0), z1) → c192(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c193(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c194(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c195(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c196(U181'(z0, z1))
U181'(z0, mark(z1)) → c197(U181'(z0, z1))
U181'(active(z0), z1) → c198(U181'(z0, z1))
U181'(z0, active(z1)) → c199(U181'(z0, z1))
U182'(mark(z0), z1) → c200(U182'(z0, z1))
U182'(z0, mark(z1)) → c201(U182'(z0, z1))
U182'(active(z0), z1) → c202(U182'(z0, z1))
U182'(z0, active(z1)) → c203(U182'(z0, z1))
U191'(mark(z0), z1) → c204(U191'(z0, z1))
U191'(z0, mark(z1)) → c205(U191'(z0, z1))
U191'(active(z0), z1) → c206(U191'(z0, z1))
U191'(z0, active(z1)) → c207(U191'(z0, z1))
PAIR(mark(z0), z1) → c208(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c209(PAIR(z0, z1))
PAIR(active(z0), z1) → c210(PAIR(z0, z1))
PAIR(z0, active(z1)) → c211(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c212(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c213(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c214(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c215(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c216(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c217(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c218(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c219(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1, z2, z3) → c220(U202'(z0, z1, z2, z3))
U202'(z0, mark(z1), z2, z3) → c221(U202'(z0, z1, z2, z3))
U202'(z0, z1, mark(z2), z3) → c222(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, mark(z3)) → c223(U202'(z0, z1, z2, z3))
U202'(active(z0), z1, z2, z3) → c224(U202'(z0, z1, z2, z3))
U202'(z0, active(z1), z2, z3) → c225(U202'(z0, z1, z2, z3))
U202'(z0, z1, active(z2), z3) → c226(U202'(z0, z1, z2, z3))
U202'(z0, z1, z2, active(z3)) → c227(U202'(z0, z1, z2, z3))
ISNATURAL(mark(z0)) → c228(ISNATURAL(z0))
ISNATURAL(active(z0)) → c229(ISNATURAL(z0))
U203'(mark(z0), z1, z2, z3) → c230(U203'(z0, z1, z2, z3))
U203'(z0, mark(z1), z2, z3) → c231(U203'(z0, z1, z2, z3))
U203'(z0, z1, mark(z2), z3) → c232(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, mark(z3)) → c233(U203'(z0, z1, z2, z3))
U203'(active(z0), z1, z2, z3) → c234(U203'(z0, z1, z2, z3))
U203'(z0, active(z1), z2, z3) → c235(U203'(z0, z1, z2, z3))
U203'(z0, z1, active(z2), z3) → c236(U203'(z0, z1, z2, z3))
U203'(z0, z1, z2, active(z3)) → c237(U203'(z0, z1, z2, z3))
U204'(mark(z0), z1) → c238(U204'(z0, z1))
U204'(z0, mark(z1)) → c239(U204'(z0, z1))
U204'(active(z0), z1) → c240(U204'(z0, z1))
U204'(z0, active(z1)) → c241(U204'(z0, z1))
U21'(mark(z0), z1, z2) → c242(U21'(z0, z1, z2))
U21'(z0, mark(z1), z2) → c243(U21'(z0, z1, z2))
U21'(z0, z1, mark(z2)) → c244(U21'(z0, z1, z2))
U21'(active(z0), z1, z2) → c245(U21'(z0, z1, z2))
U21'(z0, active(z1), z2) → c246(U21'(z0, z1, z2))
U21'(z0, z1, active(z2)) → c247(U21'(z0, z1, z2))
U22'(mark(z0), z1) → c248(U22'(z0, z1))
U22'(z0, mark(z1)) → c249(U22'(z0, z1))
U22'(active(z0), z1) → c250(U22'(z0, z1))
U22'(z0, active(z1)) → c251(U22'(z0, z1))
U211'(mark(z0), z1) → c252(U211'(z0, z1))
U211'(z0, mark(z1)) → c253(U211'(z0, z1))
U211'(active(z0), z1) → c254(U211'(z0, z1))
U211'(z0, active(z1)) → c255(U211'(z0, z1))
U212'(mark(z0), z1) → c256(U212'(z0, z1))
U212'(z0, mark(z1)) → c257(U212'(z0, z1))
U212'(active(z0), z1) → c258(U212'(z0, z1))
U212'(z0, active(z1)) → c259(U212'(z0, z1))
U221'(mark(z0), z1, z2) → c260(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c261(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c262(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c263(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c264(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c265(U221'(z0, z1, z2))
U222'(mark(z0), z1, z2) → c266(U222'(z0, z1, z2))
U222'(z0, mark(z1), z2) → c267(U222'(z0, z1, z2))
U222'(z0, z1, mark(z2)) → c268(U222'(z0, z1, z2))
U222'(active(z0), z1, z2) → c269(U222'(z0, z1, z2))
U222'(z0, active(z1), z2) → c270(U222'(z0, z1, z2))
U222'(z0, z1, active(z2)) → c271(U222'(z0, z1, z2))
FST(mark(z0)) → c272(FST(z0))
FST(active(z0)) → c273(FST(z0))
U31'(mark(z0), z1, z2) → c274(U31'(z0, z1, z2))
U31'(z0, mark(z1), z2) → c275(U31'(z0, z1, z2))
U31'(z0, z1, mark(z2)) → c276(U31'(z0, z1, z2))
U31'(active(z0), z1, z2) → c277(U31'(z0, z1, z2))
U31'(z0, active(z1), z2) → c278(U31'(z0, z1, z2))
U31'(z0, z1, active(z2)) → c279(U31'(z0, z1, z2))
U32'(mark(z0), z1) → c280(U32'(z0, z1))
U32'(z0, mark(z1)) → c281(U32'(z0, z1))
U32'(active(z0), z1) → c282(U32'(z0, z1))
U32'(z0, active(z1)) → c283(U32'(z0, z1))
U41'(mark(z0), z1) → c284(U41'(z0, z1))
U41'(z0, mark(z1)) → c285(U41'(z0, z1))
U41'(active(z0), z1) → c286(U41'(z0, z1))
U41'(z0, active(z1)) → c287(U41'(z0, z1))
U42'(mark(z0)) → c288(U42'(z0))
U42'(active(z0)) → c289(U42'(z0))
U51'(mark(z0), z1) → c290(U51'(z0, z1))
U51'(z0, mark(z1)) → c291(U51'(z0, z1))
U51'(active(z0), z1) → c292(U51'(z0, z1))
U51'(z0, active(z1)) → c293(U51'(z0, z1))
U52'(mark(z0)) → c294(U52'(z0))
U52'(active(z0)) → c295(U52'(z0))
U61'(mark(z0)) → c296(U61'(z0))
U61'(active(z0)) → c297(U61'(z0))
U71'(mark(z0)) → c298(U71'(z0))
U71'(active(z0)) → c299(U71'(z0))
U81'(mark(z0)) → c300(U81'(z0))
U81'(active(z0)) → c301(U81'(z0))
U91'(mark(z0)) → c302(U91'(z0))
U91'(active(z0)) → c303(U91'(z0))
ISPLNAT(mark(z0)) → c304(ISPLNAT(z0))
ISPLNAT(active(z0)) → c305(ISPLNAT(z0))
TAIL(mark(z0)) → c306(TAIL(z0))
TAIL(active(z0)) → c307(TAIL(z0))
TAKE(mark(z0), z1) → c308(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c309(TAKE(z0, z1))
TAKE(active(z0), z1) → c310(TAKE(z0, z1))
TAKE(z0, active(z1)) → c311(TAKE(z0, z1))
SEL(mark(z0), z1) → c312(SEL(z0, z1))
SEL(z0, mark(z1)) → c313(SEL(z0, z1))
SEL(active(z0), z1) → c314(SEL(z0, z1))
SEL(z0, active(z1)) → c315(SEL(z0, z1))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0)) → mark(U102(isLNat(z0)))
active(U102(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(U12(isLNat(z1), z0, z1))
active(U111(tt)) → mark(tt)
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U121(tt)) → mark(tt)
active(U131(tt, z0)) → mark(U132(isLNat(z0)))
active(U132(tt)) → mark(tt)
active(U141(tt, z0)) → mark(U142(isLNat(z0)))
active(U142(tt)) → mark(tt)
active(U151(tt, z0)) → mark(U152(isLNat(z0)))
active(U152(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(U172(isLNat(z1), z0, z1))
active(U172(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(U182(isLNat(z0), z0))
active(U182(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(isNatural(z1), z0, z1, z2))
active(U202(tt, z0, z1, z2)) → mark(U203(isLNat(z2), z0, z1, z2))
active(U203(tt, z0, z1, z2)) → mark(U204(splitAt(z0, z2), z1))
active(U204(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0, z1)) → mark(U22(isLNat(z1), z0))
active(U211(tt, z0)) → mark(U212(isLNat(z0), z0))
active(U212(tt, z0)) → mark(z0)
active(U22(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(U222(isLNat(z1), z0, z1))
active(U222(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0, z1)) → mark(U32(isLNat(z1), z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0)) → mark(U42(isLNat(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isLNat(z0)))
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(z0, z1)) → mark(U11(isNatural(z0), z0, z1))
active(fst(pair(z0, z1))) → mark(U21(isLNat(z0), z0, z1))
active(head(cons(z0, z1))) → mark(U31(isNatural(z0), z0, z1))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(isNatural(z0), z1))
active(isLNat(cons(z0, z1))) → mark(U51(isNatural(z0), z1))
active(isLNat(fst(z0))) → mark(U61(isPLNat(z0)))
active(isLNat(natsFrom(z0))) → mark(U71(isNatural(z0)))
active(isLNat(snd(z0))) → mark(U81(isPLNat(z0)))
active(isLNat(tail(z0))) → mark(U91(isLNat(z0)))
active(isLNat(take(z0, z1))) → mark(U101(isNatural(z0), z1))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNat(z0)))
active(isNatural(s(z0))) → mark(U121(isNatural(z0)))
active(isNatural(sel(z0, z1))) → mark(U131(isNatural(z0), z1))
active(isPLNat(pair(z0, z1))) → mark(U141(isLNat(z0), z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(isNatural(z0), z1))
active(natsFrom(z0)) → mark(U161(isNatural(z0), z0))
active(sel(z0, z1)) → mark(U171(isNatural(z0), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(isLNat(z0), z1))
active(splitAt(0, z0)) → mark(U191(isLNat(z0), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(isNatural(z0), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(isNatural(z0), z1))
active(take(z0, z1)) → mark(U221(isNatural(z0), z0, z1))
mark(U101(z0, z1)) → active(U101(mark(z0), z1))
mark(tt) → active(tt)
mark(U102(z0)) → active(U102(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U111(z0)) → active(U111(mark(z0)))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U121(z0)) → active(U121(mark(z0)))
mark(U131(z0, z1)) → active(U131(mark(z0), z1))
mark(U132(z0)) → active(U132(mark(z0)))
mark(U141(z0, z1)) → active(U141(mark(z0), z1))
mark(U142(z0)) → active(U142(mark(z0)))
mark(U151(z0, z1)) → active(U151(mark(z0), z1))
mark(U152(z0)) → active(U152(mark(z0)))
mark(U161(z0, z1)) → active(U161(mark(z0), z1))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(U171(z0, z1, z2)) → active(U171(mark(z0), z1, z2))
mark(U172(z0, z1, z2)) → active(U172(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U181(z0, z1)) → active(U181(mark(z0), z1))
mark(U182(z0, z1)) → active(U182(mark(z0), z1))
mark(U191(z0, z1)) → active(U191(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U201(z0, z1, z2, z3)) → active(U201(mark(z0), z1, z2, z3))
mark(U202(z0, z1, z2, z3)) → active(U202(mark(z0), z1, z2, z3))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U203(z0, z1, z2, z3)) → active(U203(mark(z0), z1, z2, z3))
mark(U204(z0, z1)) → active(U204(mark(z0), z1))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U212(z0, z1)) → active(U212(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(U222(z0, z1, z2)) → active(U222(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0)) → active(U71(mark(z0)))
mark(U81(z0)) → active(U81(mark(z0)))
mark(U91(z0)) → active(U91(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
mark(0) → active(0)
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
U101(mark(z0), z1) → U101(z0, z1)
U101(z0, mark(z1)) → U101(z0, z1)
U101(active(z0), z1) → U101(z0, z1)
U101(z0, active(z1)) → U101(z0, z1)
U102(mark(z0)) → U102(z0)
U102(active(z0)) → U102(z0)
isLNat(mark(z0)) → isLNat(z0)
isLNat(active(z0)) → isLNat(z0)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U111(mark(z0)) → U111(z0)
U111(active(z0)) → U111(z0)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U121(mark(z0)) → U121(z0)
U121(active(z0)) → U121(z0)
U131(mark(z0), z1) → U131(z0, z1)
U131(z0, mark(z1)) → U131(z0, z1)
U131(active(z0), z1) → U131(z0, z1)
U131(z0, active(z1)) → U131(z0, z1)
U132(mark(z0)) → U132(z0)
U132(active(z0)) → U132(z0)
U141(mark(z0), z1) → U141(z0, z1)
U141(z0, mark(z1)) → U141(z0, z1)
U141(active(z0), z1) → U141(z0, z1)
U141(z0, active(z1)) → U141(z0, z1)
U142(mark(z0)) → U142(z0)
U142(active(z0)) → U142(z0)
U151(mark(z0), z1) → U151(z0, z1)
U151(z0, mark(z1)) → U151(z0, z1)
U151(active(z0), z1) → U151(z0, z1)
U151(z0, active(z1)) → U151(z0, z1)
U152(mark(z0)) → U152(z0)
U152(active(z0)) → U152(z0)
U161(mark(z0), z1) → U161(z0, z1)
U161(z0, mark(z1)) → U161(z0, z1)
U161(active(z0), z1) → U161(z0, z1)
U161(z0, active(z1)) → U161(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U171(mark(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, mark(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, mark(z2)) → U171(z0, z1, z2)
U171(active(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, active(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, active(z2)) → U171(z0, z1, z2)
U172(mark(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, mark(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, mark(z2)) → U172(z0, z1, z2)
U172(active(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, active(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, active(z2)) → U172(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U181(mark(z0), z1) → U181(z0, z1)
U181(z0, mark(z1)) → U181(z0, z1)
U181(active(z0), z1) → U181(z0, z1)
U181(z0, active(z1)) → U181(z0, z1)
U182(mark(z0), z1) → U182(z0, z1)
U182(z0, mark(z1)) → U182(z0, z1)
U182(active(z0), z1) → U182(z0, z1)
U182(z0, active(z1)) → U182(z0, z1)
U191(mark(z0), z1) → U191(z0, z1)
U191(z0, mark(z1)) → U191(z0, z1)
U191(active(z0), z1) → U191(z0, z1)
U191(z0, active(z1)) → U191(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
U201(mark(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, mark(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, mark(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, mark(z3)) → U201(z0, z1, z2, z3)
U201(active(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, active(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, active(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, active(z3)) → U201(z0, z1, z2, z3)
U202(mark(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, mark(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, mark(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, mark(z3)) → U202(z0, z1, z2, z3)
U202(active(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, active(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, active(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, active(z3)) → U202(z0, z1, z2, z3)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U203(mark(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, mark(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, mark(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, mark(z3)) → U203(z0, z1, z2, z3)
U203(active(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, active(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, active(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, active(z3)) → U203(z0, z1, z2, z3)
U204(mark(z0), z1) → U204(z0, z1)
U204(z0, mark(z1)) → U204(z0, z1)
U204(active(z0), z1) → U204(z0, z1)
U204(z0, active(z1)) → U204(z0, z1)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U211(mark(z0), z1) → U211(z0, z1)
U211(z0, mark(z1)) → U211(z0, z1)
U211(active(z0), z1) → U211(z0, z1)
U211(z0, active(z1)) → U211(z0, z1)
U212(mark(z0), z1) → U212(z0, z1)
U212(z0, mark(z1)) → U212(z0, z1)
U212(active(z0), z1) → U212(z0, z1)
U212(z0, active(z1)) → U212(z0, z1)
U221(mark(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, mark(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, mark(z2)) → U221(z0, z1, z2)
U221(active(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, active(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, active(z2)) → U221(z0, z1, z2)
U222(mark(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, mark(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, mark(z2)) → U222(z0, z1, z2)
U222(active(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, active(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, active(z2)) → U222(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(z0)
U71(mark(z0)) → U71(z0)
U71(active(z0)) → U71(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
U91(mark(z0)) → U91(z0)
U91(active(z0)) → U91(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)

Tuples:

MARK(tt) → c63(ACTIVE(tt))
MARK(nil) → c90(ACTIVE(nil))
MARK(0) → c116(ACTIVE(0))

S tuples:

MARK(tt) → c63(ACTIVE(tt))
MARK(nil) → c90(ACTIVE(nil))
MARK(0) → c116(ACTIVE(0))

K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:

MARK

Compound Symbols:

c63, c90, c116

(5) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID) transformation)

Removed 3 trailing nodes:

MARK(0) → c116(ACTIVE(0))
MARK(nil) → c90(ACTIVE(nil))
MARK(tt) → c63(ACTIVE(tt))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0)) → mark(U102(isLNat(z0)))
active(U102(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(U12(isLNat(z1), z0, z1))
active(U111(tt)) → mark(tt)
active(U12(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U121(tt)) → mark(tt)
active(U131(tt, z0)) → mark(U132(isLNat(z0)))
active(U132(tt)) → mark(tt)
active(U141(tt, z0)) → mark(U142(isLNat(z0)))
active(U142(tt)) → mark(tt)
active(U151(tt, z0)) → mark(U152(isLNat(z0)))
active(U152(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(U172(isLNat(z1), z0, z1))
active(U172(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(U182(isLNat(z0), z0))
active(U182(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(isNatural(z1), z0, z1, z2))
active(U202(tt, z0, z1, z2)) → mark(U203(isLNat(z2), z0, z1, z2))
active(U203(tt, z0, z1, z2)) → mark(U204(splitAt(z0, z2), z1))
active(U204(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0, z1)) → mark(U22(isLNat(z1), z0))
active(U211(tt, z0)) → mark(U212(isLNat(z0), z0))
active(U212(tt, z0)) → mark(z0)
active(U22(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(U222(isLNat(z1), z0, z1))
active(U222(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0, z1)) → mark(U32(isLNat(z1), z0))
active(U32(tt, z0)) → mark(z0)
active(U41(tt, z0)) → mark(U42(isLNat(z0)))
active(U42(tt)) → mark(tt)
active(U51(tt, z0)) → mark(U52(isLNat(z0)))
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(z0, z1)) → mark(U11(isNatural(z0), z0, z1))
active(fst(pair(z0, z1))) → mark(U21(isLNat(z0), z0, z1))
active(head(cons(z0, z1))) → mark(U31(isNatural(z0), z0, z1))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(isNatural(z0), z1))
active(isLNat(cons(z0, z1))) → mark(U51(isNatural(z0), z1))
active(isLNat(fst(z0))) → mark(U61(isPLNat(z0)))
active(isLNat(natsFrom(z0))) → mark(U71(isNatural(z0)))
active(isLNat(snd(z0))) → mark(U81(isPLNat(z0)))
active(isLNat(tail(z0))) → mark(U91(isLNat(z0)))
active(isLNat(take(z0, z1))) → mark(U101(isNatural(z0), z1))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNat(z0)))
active(isNatural(s(z0))) → mark(U121(isNatural(z0)))
active(isNatural(sel(z0, z1))) → mark(U131(isNatural(z0), z1))
active(isPLNat(pair(z0, z1))) → mark(U141(isLNat(z0), z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(isNatural(z0), z1))
active(natsFrom(z0)) → mark(U161(isNatural(z0), z0))
active(sel(z0, z1)) → mark(U171(isNatural(z0), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(isLNat(z0), z1))
active(splitAt(0, z0)) → mark(U191(isLNat(z0), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(isNatural(z0), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(isNatural(z0), z1))
active(take(z0, z1)) → mark(U221(isNatural(z0), z0, z1))
mark(U101(z0, z1)) → active(U101(mark(z0), z1))
mark(tt) → active(tt)
mark(U102(z0)) → active(U102(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(U12(z0, z1, z2)) → active(U12(mark(z0), z1, z2))
mark(U111(z0)) → active(U111(mark(z0)))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U121(z0)) → active(U121(mark(z0)))
mark(U131(z0, z1)) → active(U131(mark(z0), z1))
mark(U132(z0)) → active(U132(mark(z0)))
mark(U141(z0, z1)) → active(U141(mark(z0), z1))
mark(U142(z0)) → active(U142(mark(z0)))
mark(U151(z0, z1)) → active(U151(mark(z0), z1))
mark(U152(z0)) → active(U152(mark(z0)))
mark(U161(z0, z1)) → active(U161(mark(z0), z1))
mark(cons(z0, z1)) → active(cons(mark(z0), z1))
mark(natsFrom(z0)) → active(natsFrom(mark(z0)))
mark(s(z0)) → active(s(mark(z0)))
mark(U171(z0, z1, z2)) → active(U171(mark(z0), z1, z2))
mark(U172(z0, z1, z2)) → active(U172(mark(z0), z1, z2))
mark(head(z0)) → active(head(mark(z0)))
mark(afterNth(z0, z1)) → active(afterNth(mark(z0), mark(z1)))
mark(U181(z0, z1)) → active(U181(mark(z0), z1))
mark(U182(z0, z1)) → active(U182(mark(z0), z1))
mark(U191(z0, z1)) → active(U191(mark(z0), z1))
mark(pair(z0, z1)) → active(pair(mark(z0), mark(z1)))
mark(nil) → active(nil)
mark(U201(z0, z1, z2, z3)) → active(U201(mark(z0), z1, z2, z3))
mark(U202(z0, z1, z2, z3)) → active(U202(mark(z0), z1, z2, z3))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U203(z0, z1, z2, z3)) → active(U203(mark(z0), z1, z2, z3))
mark(U204(z0, z1)) → active(U204(mark(z0), z1))
mark(U21(z0, z1, z2)) → active(U21(mark(z0), z1, z2))
mark(U22(z0, z1)) → active(U22(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U212(z0, z1)) → active(U212(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(U222(z0, z1, z2)) → active(U222(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1, z2)) → active(U31(mark(z0), z1, z2))
mark(U32(z0, z1)) → active(U32(mark(z0), z1))
mark(U41(z0, z1)) → active(U41(mark(z0), z1))
mark(U42(z0)) → active(U42(mark(z0)))
mark(U51(z0, z1)) → active(U51(mark(z0), z1))
mark(U52(z0)) → active(U52(mark(z0)))
mark(U61(z0)) → active(U61(mark(z0)))
mark(U71(z0)) → active(U71(mark(z0)))
mark(U81(z0)) → active(U81(mark(z0)))
mark(U91(z0)) → active(U91(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(tail(z0)) → active(tail(mark(z0)))
mark(take(z0, z1)) → active(take(mark(z0), mark(z1)))
mark(0) → active(0)
mark(sel(z0, z1)) → active(sel(mark(z0), mark(z1)))
U101(mark(z0), z1) → U101(z0, z1)
U101(z0, mark(z1)) → U101(z0, z1)
U101(active(z0), z1) → U101(z0, z1)
U101(z0, active(z1)) → U101(z0, z1)
U102(mark(z0)) → U102(z0)
U102(active(z0)) → U102(z0)
isLNat(mark(z0)) → isLNat(z0)
isLNat(active(z0)) → isLNat(z0)
U11(mark(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, mark(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, mark(z2)) → U11(z0, z1, z2)
U11(active(z0), z1, z2) → U11(z0, z1, z2)
U11(z0, active(z1), z2) → U11(z0, z1, z2)
U11(z0, z1, active(z2)) → U11(z0, z1, z2)
U12(mark(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, mark(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, mark(z2)) → U12(z0, z1, z2)
U12(active(z0), z1, z2) → U12(z0, z1, z2)
U12(z0, active(z1), z2) → U12(z0, z1, z2)
U12(z0, z1, active(z2)) → U12(z0, z1, z2)
U111(mark(z0)) → U111(z0)
U111(active(z0)) → U111(z0)
snd(mark(z0)) → snd(z0)
snd(active(z0)) → snd(z0)
splitAt(mark(z0), z1) → splitAt(z0, z1)
splitAt(z0, mark(z1)) → splitAt(z0, z1)
splitAt(active(z0), z1) → splitAt(z0, z1)
splitAt(z0, active(z1)) → splitAt(z0, z1)
U121(mark(z0)) → U121(z0)
U121(active(z0)) → U121(z0)
U131(mark(z0), z1) → U131(z0, z1)
U131(z0, mark(z1)) → U131(z0, z1)
U131(active(z0), z1) → U131(z0, z1)
U131(z0, active(z1)) → U131(z0, z1)
U132(mark(z0)) → U132(z0)
U132(active(z0)) → U132(z0)
U141(mark(z0), z1) → U141(z0, z1)
U141(z0, mark(z1)) → U141(z0, z1)
U141(active(z0), z1) → U141(z0, z1)
U141(z0, active(z1)) → U141(z0, z1)
U142(mark(z0)) → U142(z0)
U142(active(z0)) → U142(z0)
U151(mark(z0), z1) → U151(z0, z1)
U151(z0, mark(z1)) → U151(z0, z1)
U151(active(z0), z1) → U151(z0, z1)
U151(z0, active(z1)) → U151(z0, z1)
U152(mark(z0)) → U152(z0)
U152(active(z0)) → U152(z0)
U161(mark(z0), z1) → U161(z0, z1)
U161(z0, mark(z1)) → U161(z0, z1)
U161(active(z0), z1) → U161(z0, z1)
U161(z0, active(z1)) → U161(z0, z1)
cons(mark(z0), z1) → cons(z0, z1)
cons(z0, mark(z1)) → cons(z0, z1)
cons(active(z0), z1) → cons(z0, z1)
cons(z0, active(z1)) → cons(z0, z1)
natsFrom(mark(z0)) → natsFrom(z0)
natsFrom(active(z0)) → natsFrom(z0)
s(mark(z0)) → s(z0)
s(active(z0)) → s(z0)
U171(mark(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, mark(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, mark(z2)) → U171(z0, z1, z2)
U171(active(z0), z1, z2) → U171(z0, z1, z2)
U171(z0, active(z1), z2) → U171(z0, z1, z2)
U171(z0, z1, active(z2)) → U171(z0, z1, z2)
U172(mark(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, mark(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, mark(z2)) → U172(z0, z1, z2)
U172(active(z0), z1, z2) → U172(z0, z1, z2)
U172(z0, active(z1), z2) → U172(z0, z1, z2)
U172(z0, z1, active(z2)) → U172(z0, z1, z2)
head(mark(z0)) → head(z0)
head(active(z0)) → head(z0)
afterNth(mark(z0), z1) → afterNth(z0, z1)
afterNth(z0, mark(z1)) → afterNth(z0, z1)
afterNth(active(z0), z1) → afterNth(z0, z1)
afterNth(z0, active(z1)) → afterNth(z0, z1)
U181(mark(z0), z1) → U181(z0, z1)
U181(z0, mark(z1)) → U181(z0, z1)
U181(active(z0), z1) → U181(z0, z1)
U181(z0, active(z1)) → U181(z0, z1)
U182(mark(z0), z1) → U182(z0, z1)
U182(z0, mark(z1)) → U182(z0, z1)
U182(active(z0), z1) → U182(z0, z1)
U182(z0, active(z1)) → U182(z0, z1)
U191(mark(z0), z1) → U191(z0, z1)
U191(z0, mark(z1)) → U191(z0, z1)
U191(active(z0), z1) → U191(z0, z1)
U191(z0, active(z1)) → U191(z0, z1)
pair(mark(z0), z1) → pair(z0, z1)
pair(z0, mark(z1)) → pair(z0, z1)
pair(active(z0), z1) → pair(z0, z1)
pair(z0, active(z1)) → pair(z0, z1)
U201(mark(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, mark(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, mark(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, mark(z3)) → U201(z0, z1, z2, z3)
U201(active(z0), z1, z2, z3) → U201(z0, z1, z2, z3)
U201(z0, active(z1), z2, z3) → U201(z0, z1, z2, z3)
U201(z0, z1, active(z2), z3) → U201(z0, z1, z2, z3)
U201(z0, z1, z2, active(z3)) → U201(z0, z1, z2, z3)
U202(mark(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, mark(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, mark(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, mark(z3)) → U202(z0, z1, z2, z3)
U202(active(z0), z1, z2, z3) → U202(z0, z1, z2, z3)
U202(z0, active(z1), z2, z3) → U202(z0, z1, z2, z3)
U202(z0, z1, active(z2), z3) → U202(z0, z1, z2, z3)
U202(z0, z1, z2, active(z3)) → U202(z0, z1, z2, z3)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U203(mark(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, mark(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, mark(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, mark(z3)) → U203(z0, z1, z2, z3)
U203(active(z0), z1, z2, z3) → U203(z0, z1, z2, z3)
U203(z0, active(z1), z2, z3) → U203(z0, z1, z2, z3)
U203(z0, z1, active(z2), z3) → U203(z0, z1, z2, z3)
U203(z0, z1, z2, active(z3)) → U203(z0, z1, z2, z3)
U204(mark(z0), z1) → U204(z0, z1)
U204(z0, mark(z1)) → U204(z0, z1)
U204(active(z0), z1) → U204(z0, z1)
U204(z0, active(z1)) → U204(z0, z1)
U21(mark(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, mark(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, mark(z2)) → U21(z0, z1, z2)
U21(active(z0), z1, z2) → U21(z0, z1, z2)
U21(z0, active(z1), z2) → U21(z0, z1, z2)
U21(z0, z1, active(z2)) → U21(z0, z1, z2)
U22(mark(z0), z1) → U22(z0, z1)
U22(z0, mark(z1)) → U22(z0, z1)
U22(active(z0), z1) → U22(z0, z1)
U22(z0, active(z1)) → U22(z0, z1)
U211(mark(z0), z1) → U211(z0, z1)
U211(z0, mark(z1)) → U211(z0, z1)
U211(active(z0), z1) → U211(z0, z1)
U211(z0, active(z1)) → U211(z0, z1)
U212(mark(z0), z1) → U212(z0, z1)
U212(z0, mark(z1)) → U212(z0, z1)
U212(active(z0), z1) → U212(z0, z1)
U212(z0, active(z1)) → U212(z0, z1)
U221(mark(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, mark(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, mark(z2)) → U221(z0, z1, z2)
U221(active(z0), z1, z2) → U221(z0, z1, z2)
U221(z0, active(z1), z2) → U221(z0, z1, z2)
U221(z0, z1, active(z2)) → U221(z0, z1, z2)
U222(mark(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, mark(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, mark(z2)) → U222(z0, z1, z2)
U222(active(z0), z1, z2) → U222(z0, z1, z2)
U222(z0, active(z1), z2) → U222(z0, z1, z2)
U222(z0, z1, active(z2)) → U222(z0, z1, z2)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, mark(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, mark(z2)) → U31(z0, z1, z2)
U31(active(z0), z1, z2) → U31(z0, z1, z2)
U31(z0, active(z1), z2) → U31(z0, z1, z2)
U31(z0, z1, active(z2)) → U31(z0, z1, z2)
U32(mark(z0), z1) → U32(z0, z1)
U32(z0, mark(z1)) → U32(z0, z1)
U32(active(z0), z1) → U32(z0, z1)
U32(z0, active(z1)) → U32(z0, z1)
U41(mark(z0), z1) → U41(z0, z1)
U41(z0, mark(z1)) → U41(z0, z1)
U41(active(z0), z1) → U41(z0, z1)
U41(z0, active(z1)) → U41(z0, z1)
U42(mark(z0)) → U42(z0)
U42(active(z0)) → U42(z0)
U51(mark(z0), z1) → U51(z0, z1)
U51(z0, mark(z1)) → U51(z0, z1)
U51(active(z0), z1) → U51(z0, z1)
U51(z0, active(z1)) → U51(z0, z1)
U52(mark(z0)) → U52(z0)
U52(active(z0)) → U52(z0)
U61(mark(z0)) → U61(z0)
U61(active(z0)) → U61(z0)
U71(mark(z0)) → U71(z0)
U71(active(z0)) → U71(z0)
U81(mark(z0)) → U81(z0)
U81(active(z0)) → U81(z0)
U91(mark(z0)) → U91(z0)
U91(active(z0)) → U91(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
tail(mark(z0)) → tail(z0)
tail(active(z0)) → tail(z0)
take(mark(z0), z1) → take(z0, z1)
take(z0, mark(z1)) → take(z0, z1)
take(active(z0), z1) → take(z0, z1)
take(z0, active(z1)) → take(z0, z1)
sel(mark(z0), z1) → sel(z0, z1)
sel(z0, mark(z1)) → sel(z0, z1)
sel(active(z0), z1) → sel(z0, z1)
sel(z0, active(z1)) → sel(z0, z1)

Tuples:none
S tuples:none
K tuples:none
Defined Rule Symbols:

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

Defined Pair Symbols:none

Compound Symbols:none

(7) SIsEmptyProof (EQUIVALENT transformation)

The set S is empty

(8) BOUNDS(O(1), O(1))