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, V1, V2)) → mark(U102(isNatural(V1), V2))
active(U102(tt, V2)) → mark(U103(isLNat(V2)))
active(U103(tt)) → mark(tt)
active(U11(tt, N, XS)) → mark(snd(splitAt(N, XS)))
active(U111(tt, V1)) → mark(U112(isLNat(V1)))
active(U112(tt)) → mark(tt)
active(U121(tt, V1)) → mark(U122(isNatural(V1)))
active(U122(tt)) → mark(tt)
active(U131(tt, V1, V2)) → mark(U132(isNatural(V1), V2))
active(U132(tt, V2)) → mark(U133(isLNat(V2)))
active(U133(tt)) → mark(tt)
active(U141(tt, V1, V2)) → mark(U142(isLNat(V1), V2))
active(U142(tt, V2)) → mark(U143(isLNat(V2)))
active(U143(tt)) → mark(tt)
active(U151(tt, V1, V2)) → mark(U152(isNatural(V1), V2))
active(U152(tt, V2)) → mark(U153(isLNat(V2)))
active(U153(tt)) → mark(tt)
active(U161(tt, N)) → mark(cons(N, natsFrom(s(N))))
active(U171(tt, N, XS)) → mark(head(afterNth(N, XS)))
active(U181(tt, Y)) → mark(Y)
active(U191(tt, XS)) → mark(pair(nil, XS))
active(U201(tt, N, X, XS)) → mark(U202(splitAt(N, XS), X))
active(U202(pair(YS, ZS), X)) → mark(pair(cons(X, YS), ZS))
active(U21(tt, X)) → mark(X)
active(U211(tt, XS)) → mark(XS)
active(U221(tt, N, XS)) → mark(fst(splitAt(N, XS)))
active(U31(tt, N)) → mark(N)
active(U41(tt, V1, V2)) → mark(U42(isNatural(V1), V2))
active(U42(tt, V2)) → mark(U43(isLNat(V2)))
active(U43(tt)) → mark(tt)
active(U51(tt, V1, V2)) → mark(U52(isNatural(V1), V2))
active(U52(tt, V2)) → mark(U53(isLNat(V2)))
active(U53(tt)) → mark(tt)
active(U61(tt, V1)) → mark(U62(isPLNat(V1)))
active(U62(tt)) → mark(tt)
active(U71(tt, V1)) → mark(U72(isNatural(V1)))
active(U72(tt)) → mark(tt)
active(U81(tt, V1)) → mark(U82(isPLNat(V1)))
active(U82(tt)) → mark(tt)
active(U91(tt, V1)) → mark(U92(isLNat(V1)))
active(U92(tt)) → mark(tt)
active(afterNth(N, XS)) → mark(U11(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
active(and(tt, X)) → mark(X)
active(fst(pair(X, Y))) → mark(U21(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), X))
active(head(cons(N, XS))) → mark(U31(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(V1, V2))) → mark(U41(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
active(isLNat(cons(V1, V2))) → mark(U51(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
active(isLNat(fst(V1))) → mark(U61(isPLNatKind(V1), V1))
active(isLNat(natsFrom(V1))) → mark(U71(isNaturalKind(V1), V1))
active(isLNat(snd(V1))) → mark(U81(isPLNatKind(V1), V1))
active(isLNat(tail(V1))) → mark(U91(isLNatKind(V1), V1))
active(isLNat(take(V1, V2))) → mark(U101(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
active(isLNatKind(nil)) → mark(tt)
active(isLNatKind(afterNth(V1, V2))) → mark(and(isNaturalKind(V1), isLNatKind(V2)))
active(isLNatKind(cons(V1, V2))) → mark(and(isNaturalKind(V1), isLNatKind(V2)))
active(isLNatKind(fst(V1))) → mark(isPLNatKind(V1))
active(isLNatKind(natsFrom(V1))) → mark(isNaturalKind(V1))
active(isLNatKind(snd(V1))) → mark(isPLNatKind(V1))
active(isLNatKind(tail(V1))) → mark(isLNatKind(V1))
active(isLNatKind(take(V1, V2))) → mark(and(isNaturalKind(V1), isLNatKind(V2)))
active(isNatural(0)) → mark(tt)
active(isNatural(head(V1))) → mark(U111(isLNatKind(V1), V1))
active(isNatural(s(V1))) → mark(U121(isNaturalKind(V1), V1))
active(isNatural(sel(V1, V2))) → mark(U131(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
active(isNaturalKind(0)) → mark(tt)
active(isNaturalKind(head(V1))) → mark(isLNatKind(V1))
active(isNaturalKind(s(V1))) → mark(isNaturalKind(V1))
active(isNaturalKind(sel(V1, V2))) → mark(and(isNaturalKind(V1), isLNatKind(V2)))
active(isPLNat(pair(V1, V2))) → mark(U141(and(isLNatKind(V1), isLNatKind(V2)), V1, V2))
active(isPLNat(splitAt(V1, V2))) → mark(U151(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
active(isPLNatKind(pair(V1, V2))) → mark(and(isLNatKind(V1), isLNatKind(V2)))
active(isPLNatKind(splitAt(V1, V2))) → mark(and(isNaturalKind(V1), isLNatKind(V2)))
active(natsFrom(N)) → mark(U161(and(isNatural(N), isNaturalKind(N)), N))
active(sel(N, XS)) → mark(U171(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
active(snd(pair(X, Y))) → mark(U181(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), Y))
active(splitAt(0, XS)) → mark(U191(and(isLNat(XS), isLNatKind(XS)), XS))
active(splitAt(s(N), cons(X, XS))) → mark(U201(and(and(isNatural(N), isNaturalKind(N)), and(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS)))), N, X, XS))
active(tail(cons(N, XS))) → mark(U211(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), XS))
active(take(N, XS)) → mark(U221(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
mark(U101(X1, X2, X3)) → active(U101(mark(X1), X2, X3))
mark(tt) → active(tt)
mark(U102(X1, X2)) → active(U102(mark(X1), X2))
mark(isNatural(X)) → active(isNatural(X))
mark(U103(X)) → active(U103(mark(X)))
mark(isLNat(X)) → active(isLNat(X))
mark(U11(X1, X2, X3)) → active(U11(mark(X1), X2, X3))
mark(snd(X)) → active(snd(mark(X)))
mark(splitAt(X1, X2)) → active(splitAt(mark(X1), mark(X2)))
mark(U111(X1, X2)) → active(U111(mark(X1), X2))
mark(U112(X)) → active(U112(mark(X)))
mark(U121(X1, X2)) → active(U121(mark(X1), X2))
mark(U122(X)) → active(U122(mark(X)))
mark(U131(X1, X2, X3)) → active(U131(mark(X1), X2, X3))
mark(U132(X1, X2)) → active(U132(mark(X1), X2))
mark(U133(X)) → active(U133(mark(X)))
mark(U141(X1, X2, X3)) → active(U141(mark(X1), X2, X3))
mark(U142(X1, X2)) → active(U142(mark(X1), X2))
mark(U143(X)) → active(U143(mark(X)))
mark(U151(X1, X2, X3)) → active(U151(mark(X1), X2, X3))
mark(U152(X1, X2)) → active(U152(mark(X1), X2))
mark(U153(X)) → active(U153(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(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(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)) → active(U202(mark(X1), X2))
mark(U21(X1, X2)) → active(U21(mark(X1), X2))
mark(U211(X1, X2)) → active(U211(mark(X1), X2))
mark(U221(X1, X2, X3)) → active(U221(mark(X1), X2, X3))
mark(fst(X)) → active(fst(mark(X)))
mark(U31(X1, X2)) → active(U31(mark(X1), X2))
mark(U41(X1, X2, X3)) → active(U41(mark(X1), X2, X3))
mark(U42(X1, X2)) → active(U42(mark(X1), X2))
mark(U43(X)) → active(U43(mark(X)))
mark(U51(X1, X2, X3)) → active(U51(mark(X1), X2, X3))
mark(U52(X1, X2)) → active(U52(mark(X1), X2))
mark(U53(X)) → active(U53(mark(X)))
mark(U61(X1, X2)) → active(U61(mark(X1), X2))
mark(U62(X)) → active(U62(mark(X)))
mark(isPLNat(X)) → active(isPLNat(X))
mark(U71(X1, X2)) → active(U71(mark(X1), X2))
mark(U72(X)) → active(U72(mark(X)))
mark(U81(X1, X2)) → active(U81(mark(X1), X2))
mark(U82(X)) → active(U82(mark(X)))
mark(U91(X1, X2)) → active(U91(mark(X1), X2))
mark(U92(X)) → active(U92(mark(X)))
mark(and(X1, X2)) → active(and(mark(X1), X2))
mark(isNaturalKind(X)) → active(isNaturalKind(X))
mark(isLNatKind(X)) → active(isLNatKind(X))
mark(isPLNatKind(X)) → active(isPLNatKind(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, X3) → U101(X1, X2, X3)
U101(X1, mark(X2), X3) → U101(X1, X2, X3)
U101(X1, X2, mark(X3)) → U101(X1, X2, X3)
U101(active(X1), X2, X3) → U101(X1, X2, X3)
U101(X1, active(X2), X3) → U101(X1, X2, X3)
U101(X1, X2, active(X3)) → U101(X1, X2, X3)
U102(mark(X1), X2) → U102(X1, X2)
U102(X1, mark(X2)) → U102(X1, X2)
U102(active(X1), X2) → U102(X1, X2)
U102(X1, active(X2)) → U102(X1, X2)
isNatural(mark(X)) → isNatural(X)
isNatural(active(X)) → isNatural(X)
U103(mark(X)) → U103(X)
U103(active(X)) → U103(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)
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)
U111(mark(X1), X2) → U111(X1, X2)
U111(X1, mark(X2)) → U111(X1, X2)
U111(active(X1), X2) → U111(X1, X2)
U111(X1, active(X2)) → U111(X1, X2)
U112(mark(X)) → U112(X)
U112(active(X)) → U112(X)
U121(mark(X1), X2) → U121(X1, X2)
U121(X1, mark(X2)) → U121(X1, X2)
U121(active(X1), X2) → U121(X1, X2)
U121(X1, active(X2)) → U121(X1, X2)
U122(mark(X)) → U122(X)
U122(active(X)) → U122(X)
U131(mark(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, mark(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, mark(X3)) → U131(X1, X2, X3)
U131(active(X1), X2, X3) → U131(X1, X2, X3)
U131(X1, active(X2), X3) → U131(X1, X2, X3)
U131(X1, X2, active(X3)) → U131(X1, X2, X3)
U132(mark(X1), X2) → U132(X1, X2)
U132(X1, mark(X2)) → U132(X1, X2)
U132(active(X1), X2) → U132(X1, X2)
U132(X1, active(X2)) → U132(X1, X2)
U133(mark(X)) → U133(X)
U133(active(X)) → U133(X)
U141(mark(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, mark(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, mark(X3)) → U141(X1, X2, X3)
U141(active(X1), X2, X3) → U141(X1, X2, X3)
U141(X1, active(X2), X3) → U141(X1, X2, X3)
U141(X1, X2, active(X3)) → U141(X1, X2, X3)
U142(mark(X1), X2) → U142(X1, X2)
U142(X1, mark(X2)) → U142(X1, X2)
U142(active(X1), X2) → U142(X1, X2)
U142(X1, active(X2)) → U142(X1, X2)
U143(mark(X)) → U143(X)
U143(active(X)) → U143(X)
U151(mark(X1), X2, X3) → U151(X1, X2, X3)
U151(X1, mark(X2), X3) → U151(X1, X2, X3)
U151(X1, X2, mark(X3)) → U151(X1, X2, X3)
U151(active(X1), X2, X3) → U151(X1, X2, X3)
U151(X1, active(X2), X3) → U151(X1, X2, X3)
U151(X1, X2, active(X3)) → U151(X1, X2, X3)
U152(mark(X1), X2) → U152(X1, X2)
U152(X1, mark(X2)) → U152(X1, X2)
U152(active(X1), X2) → U152(X1, X2)
U152(X1, active(X2)) → U152(X1, X2)
U153(mark(X)) → U153(X)
U153(active(X)) → U153(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)
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)
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) → U202(X1, X2)
U202(X1, mark(X2)) → U202(X1, X2)
U202(active(X1), X2) → U202(X1, X2)
U202(X1, active(X2)) → U202(X1, X2)
U21(mark(X1), X2) → U21(X1, X2)
U21(X1, mark(X2)) → U21(X1, X2)
U21(active(X1), X2) → U21(X1, X2)
U21(X1, active(X2)) → U21(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)
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)
fst(mark(X)) → fst(X)
fst(active(X)) → fst(X)
U31(mark(X1), X2) → U31(X1, X2)
U31(X1, mark(X2)) → U31(X1, X2)
U31(active(X1), X2) → U31(X1, X2)
U31(X1, active(X2)) → U31(X1, X2)
U41(mark(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, mark(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, mark(X3)) → U41(X1, X2, X3)
U41(active(X1), X2, X3) → U41(X1, X2, X3)
U41(X1, active(X2), X3) → U41(X1, X2, X3)
U41(X1, X2, active(X3)) → U41(X1, X2, X3)
U42(mark(X1), X2) → U42(X1, X2)
U42(X1, mark(X2)) → U42(X1, X2)
U42(active(X1), X2) → U42(X1, X2)
U42(X1, active(X2)) → U42(X1, X2)
U43(mark(X)) → U43(X)
U43(active(X)) → U43(X)
U51(mark(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, mark(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, mark(X3)) → U51(X1, X2, X3)
U51(active(X1), X2, X3) → U51(X1, X2, X3)
U51(X1, active(X2), X3) → U51(X1, X2, X3)
U51(X1, X2, active(X3)) → U51(X1, X2, X3)
U52(mark(X1), X2) → U52(X1, X2)
U52(X1, mark(X2)) → U52(X1, X2)
U52(active(X1), X2) → U52(X1, X2)
U52(X1, active(X2)) → U52(X1, X2)
U53(mark(X)) → U53(X)
U53(active(X)) → U53(X)
U61(mark(X1), X2) → U61(X1, X2)
U61(X1, mark(X2)) → U61(X1, X2)
U61(active(X1), X2) → U61(X1, X2)
U61(X1, active(X2)) → U61(X1, X2)
U62(mark(X)) → U62(X)
U62(active(X)) → U62(X)
isPLNat(mark(X)) → isPLNat(X)
isPLNat(active(X)) → isPLNat(X)
U71(mark(X1), X2) → U71(X1, X2)
U71(X1, mark(X2)) → U71(X1, X2)
U71(active(X1), X2) → U71(X1, X2)
U71(X1, active(X2)) → U71(X1, X2)
U72(mark(X)) → U72(X)
U72(active(X)) → U72(X)
U81(mark(X1), X2) → U81(X1, X2)
U81(X1, mark(X2)) → U81(X1, X2)
U81(active(X1), X2) → U81(X1, X2)
U81(X1, active(X2)) → U81(X1, X2)
U82(mark(X)) → U82(X)
U82(active(X)) → U82(X)
U91(mark(X1), X2) → U91(X1, X2)
U91(X1, mark(X2)) → U91(X1, X2)
U91(active(X1), X2) → U91(X1, X2)
U91(X1, active(X2)) → U91(X1, X2)
U92(mark(X)) → U92(X)
U92(active(X)) → U92(X)
and(mark(X1), X2) → and(X1, X2)
and(X1, mark(X2)) → and(X1, X2)
and(active(X1), X2) → and(X1, X2)
and(X1, active(X2)) → and(X1, X2)
isNaturalKind(mark(X)) → isNaturalKind(X)
isNaturalKind(active(X)) → isNaturalKind(X)
isLNatKind(mark(X)) → isLNatKind(X)
isLNatKind(active(X)) → isLNatKind(X)
isPLNatKind(mark(X)) → isPLNatKind(X)
isPLNatKind(active(X)) → isPLNatKind(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, z1)) → mark(U102(isNatural(z0), z1))
active(U102(tt, z0)) → mark(U103(isLNat(z0)))
active(U103(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U111(tt, z0)) → mark(U112(isLNat(z0)))
active(U112(tt)) → mark(tt)
active(U121(tt, z0)) → mark(U122(isNatural(z0)))
active(U122(tt)) → mark(tt)
active(U131(tt, z0, z1)) → mark(U132(isNatural(z0), z1))
active(U132(tt, z0)) → mark(U133(isLNat(z0)))
active(U133(tt)) → mark(tt)
active(U141(tt, z0, z1)) → mark(U142(isLNat(z0), z1))
active(U142(tt, z0)) → mark(U143(isLNat(z0)))
active(U143(tt)) → mark(tt)
active(U151(tt, z0, z1)) → mark(U152(isNatural(z0), z1))
active(U152(tt, z0)) → mark(U153(isLNat(z0)))
active(U153(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(splitAt(z0, z2), z1))
active(U202(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0)) → mark(z0)
active(U211(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(isNatural(z0), z1))
active(U42(tt, z0)) → mark(U43(isLNat(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNatural(z0), z1))
active(U52(tt, z0)) → mark(U53(isLNat(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isPLNat(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatural(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt, z0)) → mark(U82(isPLNat(z0)))
active(U82(tt)) → mark(tt)
active(U91(tt, z0)) → mark(U92(isLNat(z0)))
active(U92(tt)) → mark(tt)
active(afterNth(z0, z1)) → mark(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(and(tt, z0)) → mark(z0)
active(fst(pair(z0, z1))) → mark(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(head(cons(z0, z1))) → mark(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(cons(z0, z1))) → mark(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(fst(z0))) → mark(U61(isPLNatKind(z0), z0))
active(isLNat(natsFrom(z0))) → mark(U71(isNaturalKind(z0), z0))
active(isLNat(snd(z0))) → mark(U81(isPLNatKind(z0), z0))
active(isLNat(tail(z0))) → mark(U91(isLNatKind(z0), z0))
active(isLNat(take(z0, z1))) → mark(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNatKind(nil)) → mark(tt)
active(isLNatKind(afterNth(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(cons(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(fst(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(natsFrom(z0))) → mark(isNaturalKind(z0))
active(isLNatKind(snd(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(tail(z0))) → mark(isLNatKind(z0))
active(isLNatKind(take(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNatKind(z0), z0))
active(isNatural(s(z0))) → mark(U121(isNaturalKind(z0), z0))
active(isNatural(sel(z0, z1))) → mark(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isNaturalKind(0)) → mark(tt)
active(isNaturalKind(head(z0))) → mark(isLNatKind(z0))
active(isNaturalKind(s(z0))) → mark(isNaturalKind(z0))
active(isNaturalKind(sel(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isPLNat(pair(z0, z1))) → mark(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNatKind(pair(z0, z1))) → mark(and(isLNatKind(z0), isLNatKind(z1)))
active(isPLNatKind(splitAt(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(natsFrom(z0)) → mark(U161(and(isNatural(z0), isNaturalKind(z0)), z0))
active(sel(z0, z1)) → mark(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(splitAt(0, z0)) → mark(U191(and(isLNat(z0), isLNatKind(z0)), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(take(z0, z1)) → mark(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1)) → active(U102(mark(z0), z1))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U103(z0)) → active(U103(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U111(z0, z1)) → active(U111(mark(z0), z1))
mark(U112(z0)) → active(U112(mark(z0)))
mark(U121(z0, z1)) → active(U121(mark(z0), z1))
mark(U122(z0)) → active(U122(mark(z0)))
mark(U131(z0, z1, z2)) → active(U131(mark(z0), z1, z2))
mark(U132(z0, z1)) → active(U132(mark(z0), z1))
mark(U133(z0)) → active(U133(mark(z0)))
mark(U141(z0, z1, z2)) → active(U141(mark(z0), z1, z2))
mark(U142(z0, z1)) → active(U142(mark(z0), z1))
mark(U143(z0)) → active(U143(mark(z0)))
mark(U151(z0, z1, z2)) → active(U151(mark(z0), z1, z2))
mark(U152(z0, z1)) → active(U152(mark(z0), z1))
mark(U153(z0)) → active(U153(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(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(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)) → active(U202(mark(z0), z1))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(U81(z0, z1)) → active(U81(mark(z0), z1))
mark(U82(z0)) → active(U82(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isNaturalKind(z0)) → active(isNaturalKind(z0))
mark(isLNatKind(z0)) → active(isLNatKind(z0))
mark(isPLNatKind(z0)) → active(isPLNatKind(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, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1) → U102(z0, z1)
U102(z0, mark(z1)) → U102(z0, z1)
U102(active(z0), z1) → U102(z0, z1)
U102(z0, active(z1)) → U102(z0, z1)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U103(mark(z0)) → U103(z0)
U103(active(z0)) → U103(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)
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)
U111(mark(z0), z1) → U111(z0, z1)
U111(z0, mark(z1)) → U111(z0, z1)
U111(active(z0), z1) → U111(z0, z1)
U111(z0, active(z1)) → U111(z0, z1)
U112(mark(z0)) → U112(z0)
U112(active(z0)) → U112(z0)
U121(mark(z0), z1) → U121(z0, z1)
U121(z0, mark(z1)) → U121(z0, z1)
U121(active(z0), z1) → U121(z0, z1)
U121(z0, active(z1)) → U121(z0, z1)
U122(mark(z0)) → U122(z0)
U122(active(z0)) → U122(z0)
U131(mark(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, mark(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, mark(z2)) → U131(z0, z1, z2)
U131(active(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, active(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, active(z2)) → U131(z0, z1, z2)
U132(mark(z0), z1) → U132(z0, z1)
U132(z0, mark(z1)) → U132(z0, z1)
U132(active(z0), z1) → U132(z0, z1)
U132(z0, active(z1)) → U132(z0, z1)
U133(mark(z0)) → U133(z0)
U133(active(z0)) → U133(z0)
U141(mark(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, mark(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, mark(z2)) → U141(z0, z1, z2)
U141(active(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, active(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, active(z2)) → U141(z0, z1, z2)
U142(mark(z0), z1) → U142(z0, z1)
U142(z0, mark(z1)) → U142(z0, z1)
U142(active(z0), z1) → U142(z0, z1)
U142(z0, active(z1)) → U142(z0, z1)
U143(mark(z0)) → U143(z0)
U143(active(z0)) → U143(z0)
U151(mark(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, mark(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, mark(z2)) → U151(z0, z1, z2)
U151(active(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, active(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, active(z2)) → U151(z0, z1, z2)
U152(mark(z0), z1) → U152(z0, z1)
U152(z0, mark(z1)) → U152(z0, z1)
U152(active(z0), z1) → U152(z0, z1)
U152(z0, active(z1)) → U152(z0, z1)
U153(mark(z0)) → U153(z0)
U153(active(z0)) → U153(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)
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)
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) → U202(z0, z1)
U202(z0, mark(z1)) → U202(z0, z1)
U202(active(z0), z1) → U202(z0, z1)
U202(z0, active(z1)) → U202(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(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)
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)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
U81(mark(z0), z1) → U81(z0, z1)
U81(z0, mark(z1)) → U81(z0, z1)
U81(active(z0), z1) → U81(z0, z1)
U81(z0, active(z1)) → U81(z0, z1)
U82(mark(z0)) → U82(z0)
U82(active(z0)) → U82(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isNaturalKind(mark(z0)) → isNaturalKind(z0)
isNaturalKind(active(z0)) → isNaturalKind(z0)
isLNatKind(mark(z0)) → isLNatKind(z0)
isLNatKind(active(z0)) → isLNatKind(z0)
isPLNatKind(mark(z0)) → isPLNatKind(z0)
isPLNatKind(active(z0)) → isPLNatKind(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, z1)) → c(MARK(U102(isNatural(z0), z1)), U102'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U102(tt, z0)) → c1(MARK(U103(isLNat(z0))), U103'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U103(tt)) → c2(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c3(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U111(tt, z0)) → c4(MARK(U112(isLNat(z0))), U112'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U112(tt)) → c5(MARK(tt))
ACTIVE(U121(tt, z0)) → c6(MARK(U122(isNatural(z0))), U122'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U122(tt)) → c7(MARK(tt))
ACTIVE(U131(tt, z0, z1)) → c8(MARK(U132(isNatural(z0), z1)), U132'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U132(tt, z0)) → c9(MARK(U133(isLNat(z0))), U133'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U133(tt)) → c10(MARK(tt))
ACTIVE(U141(tt, z0, z1)) → c11(MARK(U142(isLNat(z0), z1)), U142'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(U142(tt, z0)) → c12(MARK(U143(isLNat(z0))), U143'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U143(tt)) → c13(MARK(tt))
ACTIVE(U151(tt, z0, z1)) → c14(MARK(U152(isNatural(z0), z1)), U152'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U152(tt, z0)) → c15(MARK(U153(isLNat(z0))), U153'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U153(tt)) → c16(MARK(tt))
ACTIVE(U161(tt, z0)) → c17(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c18(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c19(MARK(z0))
ACTIVE(U191(tt, z0)) → c20(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c21(MARK(U202(splitAt(z0, z2), z1)), U202'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U202(pair(z0, z1), z2)) → c22(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0)) → c23(MARK(z0))
ACTIVE(U211(tt, z0)) → c24(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c25(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0)) → c26(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c27(MARK(U42(isNatural(z0), z1)), U42'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U42(tt, z0)) → c28(MARK(U43(isLNat(z0))), U43'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U43(tt)) → c29(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c30(MARK(U52(isNatural(z0), z1)), U52'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U52(tt, z0)) → c31(MARK(U53(isLNat(z0))), U53'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U53(tt)) → c32(MARK(tt))
ACTIVE(U61(tt, z0)) → c33(MARK(U62(isPLNat(z0))), U62'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U62(tt)) → c34(MARK(tt))
ACTIVE(U71(tt, z0)) → c35(MARK(U72(isNatural(z0))), U72'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U72(tt)) → c36(MARK(tt))
ACTIVE(U81(tt, z0)) → c37(MARK(U82(isPLNat(z0))), U82'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U82(tt)) → c38(MARK(tt))
ACTIVE(U91(tt, z0)) → c39(MARK(U92(isLNat(z0))), U92'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U92(tt)) → c40(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c41(MARK(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U11'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(and(tt, z0)) → c42(MARK(z0))
ACTIVE(fst(pair(z0, z1))) → c43(MARK(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U21'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(head(cons(z0, z1))) → c44(MARK(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U31'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(isLNat(nil)) → c45(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c46(MARK(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U41'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(cons(z0, z1))) → c47(MARK(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U51'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(fst(z0))) → c48(MARK(U61(isPLNatKind(z0), z0)), U61'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(natsFrom(z0))) → c49(MARK(U71(isNaturalKind(z0), z0)), U71'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isLNat(snd(z0))) → c50(MARK(U81(isPLNatKind(z0), z0)), U81'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(tail(z0))) → c51(MARK(U91(isLNatKind(z0), z0)), U91'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isLNat(take(z0, z1))) → c52(MARK(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U101'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(nil)) → c53(MARK(tt))
ACTIVE(isLNatKind(afterNth(z0, z1))) → c54(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(cons(z0, z1))) → c55(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(fst(z0))) → c56(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(natsFrom(z0))) → c57(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isLNatKind(snd(z0))) → c58(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(tail(z0))) → c59(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isLNatKind(take(z0, z1))) → c60(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNatural(0)) → c61(MARK(tt))
ACTIVE(isNatural(head(z0))) → c62(MARK(U111(isLNatKind(z0), z0)), U111'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isNatural(s(z0))) → c63(MARK(U121(isNaturalKind(z0), z0)), U121'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isNatural(sel(z0, z1))) → c64(MARK(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U131'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNaturalKind(0)) → c65(MARK(tt))
ACTIVE(isNaturalKind(head(z0))) → c66(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isNaturalKind(s(z0))) → c67(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isNaturalKind(sel(z0, z1))) → c68(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(pair(z0, z1))) → c69(MARK(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1)), U141'(and(isLNatKind(z0), isLNatKind(z1)), z0, z1), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(splitAt(z0, z1))) → c70(MARK(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U151'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(pair(z0, z1))) → c71(MARK(and(isLNatKind(z0), isLNatKind(z1))), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(splitAt(z0, z1))) → c72(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(natsFrom(z0)) → c73(MARK(U161(and(isNatural(z0), isNaturalKind(z0)), z0)), U161'(and(isNatural(z0), isNaturalKind(z0)), z0), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0))
ACTIVE(sel(z0, z1)) → c74(MARK(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U171'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(snd(pair(z0, z1))) → c75(MARK(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U181'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(splitAt(0, z0)) → c76(MARK(U191(and(isLNat(z0), isLNatKind(z0)), z0)), U191'(and(isLNat(z0), isLNatKind(z0)), z0), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c77(MARK(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2)), U201'(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2), AND(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2))), AND(isNatural(z1), isNaturalKind(z1)), ISNATURAL(z1), ISNATURALKIND(z1), AND(isLNat(z2), isLNatKind(z2)), ISLNAT(z2), ISLNATKIND(z2))
ACTIVE(tail(cons(z0, z1))) → c78(MARK(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U211'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(take(z0, z1)) → c79(MARK(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U221'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
MARK(U101(z0, z1, z2)) → c80(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c81(ACTIVE(tt))
MARK(U102(z0, z1)) → c82(ACTIVE(U102(mark(z0), z1)), U102'(mark(z0), z1), MARK(z0))
MARK(isNatural(z0)) → c83(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U103(z0)) → c84(ACTIVE(U103(mark(z0))), U103'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c85(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c86(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c87(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c88(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U111(z0, z1)) → c89(ACTIVE(U111(mark(z0), z1)), U111'(mark(z0), z1), MARK(z0))
MARK(U112(z0)) → c90(ACTIVE(U112(mark(z0))), U112'(mark(z0)), MARK(z0))
MARK(U121(z0, z1)) → c91(ACTIVE(U121(mark(z0), z1)), U121'(mark(z0), z1), MARK(z0))
MARK(U122(z0)) → c92(ACTIVE(U122(mark(z0))), U122'(mark(z0)), MARK(z0))
MARK(U131(z0, z1, z2)) → c93(ACTIVE(U131(mark(z0), z1, z2)), U131'(mark(z0), z1, z2), MARK(z0))
MARK(U132(z0, z1)) → c94(ACTIVE(U132(mark(z0), z1)), U132'(mark(z0), z1), MARK(z0))
MARK(U133(z0)) → c95(ACTIVE(U133(mark(z0))), U133'(mark(z0)), MARK(z0))
MARK(U141(z0, z1, z2)) → c96(ACTIVE(U141(mark(z0), z1, z2)), U141'(mark(z0), z1, z2), MARK(z0))
MARK(U142(z0, z1)) → c97(ACTIVE(U142(mark(z0), z1)), U142'(mark(z0), z1), MARK(z0))
MARK(U143(z0)) → c98(ACTIVE(U143(mark(z0))), U143'(mark(z0)), MARK(z0))
MARK(U151(z0, z1, z2)) → c99(ACTIVE(U151(mark(z0), z1, z2)), U151'(mark(z0), z1, z2), MARK(z0))
MARK(U152(z0, z1)) → c100(ACTIVE(U152(mark(z0), z1)), U152'(mark(z0), z1), MARK(z0))
MARK(U153(z0)) → c101(ACTIVE(U153(mark(z0))), U153'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c102(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c103(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c104(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c105(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c106(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c107(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c108(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c109(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c110(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c111(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c112(ACTIVE(nil))
MARK(U201(z0, z1, z2, z3)) → c113(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1)) → c114(ACTIVE(U202(mark(z0), z1)), U202'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1)) → c115(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c116(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c117(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c118(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c119(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c120(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c121(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c122(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c123(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c124(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c125(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c126(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c127(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c128(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(U71(z0, z1)) → c129(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c130(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(U81(z0, z1)) → c131(ACTIVE(U81(mark(z0), z1)), U81'(mark(z0), z1), MARK(z0))
MARK(U82(z0)) → c132(ACTIVE(U82(mark(z0))), U82'(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c133(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c134(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
MARK(and(z0, z1)) → c135(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNaturalKind(z0)) → c136(ACTIVE(isNaturalKind(z0)), ISNATURALKIND(z0))
MARK(isLNatKind(z0)) → c137(ACTIVE(isLNatKind(z0)), ISLNATKIND(z0))
MARK(isPLNatKind(z0)) → c138(ACTIVE(isPLNatKind(z0)), ISPLNATKIND(z0))
MARK(tail(z0)) → c139(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c140(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c141(ACTIVE(0))
MARK(sel(z0, z1)) → c142(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1, z2) → c143(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c144(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c145(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c146(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c147(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c148(U101'(z0, z1, z2))
U102'(mark(z0), z1) → c149(U102'(z0, z1))
U102'(z0, mark(z1)) → c150(U102'(z0, z1))
U102'(active(z0), z1) → c151(U102'(z0, z1))
U102'(z0, active(z1)) → c152(U102'(z0, z1))
ISNATURAL(mark(z0)) → c153(ISNATURAL(z0))
ISNATURAL(active(z0)) → c154(ISNATURAL(z0))
U103'(mark(z0)) → c155(U103'(z0))
U103'(active(z0)) → c156(U103'(z0))
ISLNAT(mark(z0)) → c157(ISLNAT(z0))
ISLNAT(active(z0)) → c158(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c159(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c160(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c161(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c162(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c163(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c164(U11'(z0, z1, z2))
SND(mark(z0)) → c165(SND(z0))
SND(active(z0)) → c166(SND(z0))
SPLITAT(mark(z0), z1) → c167(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c168(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c169(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c170(SPLITAT(z0, z1))
U111'(mark(z0), z1) → c171(U111'(z0, z1))
U111'(z0, mark(z1)) → c172(U111'(z0, z1))
U111'(active(z0), z1) → c173(U111'(z0, z1))
U111'(z0, active(z1)) → c174(U111'(z0, z1))
U112'(mark(z0)) → c175(U112'(z0))
U112'(active(z0)) → c176(U112'(z0))
U121'(mark(z0), z1) → c177(U121'(z0, z1))
U121'(z0, mark(z1)) → c178(U121'(z0, z1))
U121'(active(z0), z1) → c179(U121'(z0, z1))
U121'(z0, active(z1)) → c180(U121'(z0, z1))
U122'(mark(z0)) → c181(U122'(z0))
U122'(active(z0)) → c182(U122'(z0))
U131'(mark(z0), z1, z2) → c183(U131'(z0, z1, z2))
U131'(z0, mark(z1), z2) → c184(U131'(z0, z1, z2))
U131'(z0, z1, mark(z2)) → c185(U131'(z0, z1, z2))
U131'(active(z0), z1, z2) → c186(U131'(z0, z1, z2))
U131'(z0, active(z1), z2) → c187(U131'(z0, z1, z2))
U131'(z0, z1, active(z2)) → c188(U131'(z0, z1, z2))
U132'(mark(z0), z1) → c189(U132'(z0, z1))
U132'(z0, mark(z1)) → c190(U132'(z0, z1))
U132'(active(z0), z1) → c191(U132'(z0, z1))
U132'(z0, active(z1)) → c192(U132'(z0, z1))
U133'(mark(z0)) → c193(U133'(z0))
U133'(active(z0)) → c194(U133'(z0))
U141'(mark(z0), z1, z2) → c195(U141'(z0, z1, z2))
U141'(z0, mark(z1), z2) → c196(U141'(z0, z1, z2))
U141'(z0, z1, mark(z2)) → c197(U141'(z0, z1, z2))
U141'(active(z0), z1, z2) → c198(U141'(z0, z1, z2))
U141'(z0, active(z1), z2) → c199(U141'(z0, z1, z2))
U141'(z0, z1, active(z2)) → c200(U141'(z0, z1, z2))
U142'(mark(z0), z1) → c201(U142'(z0, z1))
U142'(z0, mark(z1)) → c202(U142'(z0, z1))
U142'(active(z0), z1) → c203(U142'(z0, z1))
U142'(z0, active(z1)) → c204(U142'(z0, z1))
U143'(mark(z0)) → c205(U143'(z0))
U143'(active(z0)) → c206(U143'(z0))
U151'(mark(z0), z1, z2) → c207(U151'(z0, z1, z2))
U151'(z0, mark(z1), z2) → c208(U151'(z0, z1, z2))
U151'(z0, z1, mark(z2)) → c209(U151'(z0, z1, z2))
U151'(active(z0), z1, z2) → c210(U151'(z0, z1, z2))
U151'(z0, active(z1), z2) → c211(U151'(z0, z1, z2))
U151'(z0, z1, active(z2)) → c212(U151'(z0, z1, z2))
U152'(mark(z0), z1) → c213(U152'(z0, z1))
U152'(z0, mark(z1)) → c214(U152'(z0, z1))
U152'(active(z0), z1) → c215(U152'(z0, z1))
U152'(z0, active(z1)) → c216(U152'(z0, z1))
U153'(mark(z0)) → c217(U153'(z0))
U153'(active(z0)) → c218(U153'(z0))
U161'(mark(z0), z1) → c219(U161'(z0, z1))
U161'(z0, mark(z1)) → c220(U161'(z0, z1))
U161'(active(z0), z1) → c221(U161'(z0, z1))
U161'(z0, active(z1)) → c222(U161'(z0, z1))
CONS(mark(z0), z1) → c223(CONS(z0, z1))
CONS(z0, mark(z1)) → c224(CONS(z0, z1))
CONS(active(z0), z1) → c225(CONS(z0, z1))
CONS(z0, active(z1)) → c226(CONS(z0, z1))
NATSFROM(mark(z0)) → c227(NATSFROM(z0))
NATSFROM(active(z0)) → c228(NATSFROM(z0))
S(mark(z0)) → c229(S(z0))
S(active(z0)) → c230(S(z0))
U171'(mark(z0), z1, z2) → c231(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c232(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c233(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c234(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c235(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c236(U171'(z0, z1, z2))
HEAD(mark(z0)) → c237(HEAD(z0))
HEAD(active(z0)) → c238(HEAD(z0))
AFTERNTH(mark(z0), z1) → c239(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c240(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c241(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c242(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c243(U181'(z0, z1))
U181'(z0, mark(z1)) → c244(U181'(z0, z1))
U181'(active(z0), z1) → c245(U181'(z0, z1))
U181'(z0, active(z1)) → c246(U181'(z0, z1))
U191'(mark(z0), z1) → c247(U191'(z0, z1))
U191'(z0, mark(z1)) → c248(U191'(z0, z1))
U191'(active(z0), z1) → c249(U191'(z0, z1))
U191'(z0, active(z1)) → c250(U191'(z0, z1))
PAIR(mark(z0), z1) → c251(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c252(PAIR(z0, z1))
PAIR(active(z0), z1) → c253(PAIR(z0, z1))
PAIR(z0, active(z1)) → c254(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c255(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c256(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c257(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c258(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c259(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c260(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c261(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c262(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1) → c263(U202'(z0, z1))
U202'(z0, mark(z1)) → c264(U202'(z0, z1))
U202'(active(z0), z1) → c265(U202'(z0, z1))
U202'(z0, active(z1)) → c266(U202'(z0, z1))
U21'(mark(z0), z1) → c267(U21'(z0, z1))
U21'(z0, mark(z1)) → c268(U21'(z0, z1))
U21'(active(z0), z1) → c269(U21'(z0, z1))
U21'(z0, active(z1)) → c270(U21'(z0, z1))
U211'(mark(z0), z1) → c271(U211'(z0, z1))
U211'(z0, mark(z1)) → c272(U211'(z0, z1))
U211'(active(z0), z1) → c273(U211'(z0, z1))
U211'(z0, active(z1)) → c274(U211'(z0, z1))
U221'(mark(z0), z1, z2) → c275(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c276(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c277(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c278(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c279(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c280(U221'(z0, z1, z2))
FST(mark(z0)) → c281(FST(z0))
FST(active(z0)) → c282(FST(z0))
U31'(mark(z0), z1) → c283(U31'(z0, z1))
U31'(z0, mark(z1)) → c284(U31'(z0, z1))
U31'(active(z0), z1) → c285(U31'(z0, z1))
U31'(z0, active(z1)) → c286(U31'(z0, z1))
U41'(mark(z0), z1, z2) → c287(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c288(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c289(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c290(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c291(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c292(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c293(U42'(z0, z1))
U42'(z0, mark(z1)) → c294(U42'(z0, z1))
U42'(active(z0), z1) → c295(U42'(z0, z1))
U42'(z0, active(z1)) → c296(U42'(z0, z1))
U43'(mark(z0)) → c297(U43'(z0))
U43'(active(z0)) → c298(U43'(z0))
U51'(mark(z0), z1, z2) → c299(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c300(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c301(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c302(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c303(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c304(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c305(U52'(z0, z1))
U52'(z0, mark(z1)) → c306(U52'(z0, z1))
U52'(active(z0), z1) → c307(U52'(z0, z1))
U52'(z0, active(z1)) → c308(U52'(z0, z1))
U53'(mark(z0)) → c309(U53'(z0))
U53'(active(z0)) → c310(U53'(z0))
U61'(mark(z0), z1) → c311(U61'(z0, z1))
U61'(z0, mark(z1)) → c312(U61'(z0, z1))
U61'(active(z0), z1) → c313(U61'(z0, z1))
U61'(z0, active(z1)) → c314(U61'(z0, z1))
U62'(mark(z0)) → c315(U62'(z0))
U62'(active(z0)) → c316(U62'(z0))
ISPLNAT(mark(z0)) → c317(ISPLNAT(z0))
ISPLNAT(active(z0)) → c318(ISPLNAT(z0))
U71'(mark(z0), z1) → c319(U71'(z0, z1))
U71'(z0, mark(z1)) → c320(U71'(z0, z1))
U71'(active(z0), z1) → c321(U71'(z0, z1))
U71'(z0, active(z1)) → c322(U71'(z0, z1))
U72'(mark(z0)) → c323(U72'(z0))
U72'(active(z0)) → c324(U72'(z0))
U81'(mark(z0), z1) → c325(U81'(z0, z1))
U81'(z0, mark(z1)) → c326(U81'(z0, z1))
U81'(active(z0), z1) → c327(U81'(z0, z1))
U81'(z0, active(z1)) → c328(U81'(z0, z1))
U82'(mark(z0)) → c329(U82'(z0))
U82'(active(z0)) → c330(U82'(z0))
U91'(mark(z0), z1) → c331(U91'(z0, z1))
U91'(z0, mark(z1)) → c332(U91'(z0, z1))
U91'(active(z0), z1) → c333(U91'(z0, z1))
U91'(z0, active(z1)) → c334(U91'(z0, z1))
U92'(mark(z0)) → c335(U92'(z0))
U92'(active(z0)) → c336(U92'(z0))
AND(mark(z0), z1) → c337(AND(z0, z1))
AND(z0, mark(z1)) → c338(AND(z0, z1))
AND(active(z0), z1) → c339(AND(z0, z1))
AND(z0, active(z1)) → c340(AND(z0, z1))
ISNATURALKIND(mark(z0)) → c341(ISNATURALKIND(z0))
ISNATURALKIND(active(z0)) → c342(ISNATURALKIND(z0))
ISLNATKIND(mark(z0)) → c343(ISLNATKIND(z0))
ISLNATKIND(active(z0)) → c344(ISLNATKIND(z0))
ISPLNATKIND(mark(z0)) → c345(ISPLNATKIND(z0))
ISPLNATKIND(active(z0)) → c346(ISPLNATKIND(z0))
TAIL(mark(z0)) → c347(TAIL(z0))
TAIL(active(z0)) → c348(TAIL(z0))
TAKE(mark(z0), z1) → c349(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c350(TAKE(z0, z1))
TAKE(active(z0), z1) → c351(TAKE(z0, z1))
TAKE(z0, active(z1)) → c352(TAKE(z0, z1))
SEL(mark(z0), z1) → c353(SEL(z0, z1))
SEL(z0, mark(z1)) → c354(SEL(z0, z1))
SEL(active(z0), z1) → c355(SEL(z0, z1))
SEL(z0, active(z1)) → c356(SEL(z0, z1))

S tuples:

ACTIVE(U101(tt, z0, z1)) → c(MARK(U102(isNatural(z0), z1)), U102'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U102(tt, z0)) → c1(MARK(U103(isLNat(z0))), U103'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U103(tt)) → c2(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c3(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U111(tt, z0)) → c4(MARK(U112(isLNat(z0))), U112'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U112(tt)) → c5(MARK(tt))
ACTIVE(U121(tt, z0)) → c6(MARK(U122(isNatural(z0))), U122'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U122(tt)) → c7(MARK(tt))
ACTIVE(U131(tt, z0, z1)) → c8(MARK(U132(isNatural(z0), z1)), U132'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U132(tt, z0)) → c9(MARK(U133(isLNat(z0))), U133'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U133(tt)) → c10(MARK(tt))
ACTIVE(U141(tt, z0, z1)) → c11(MARK(U142(isLNat(z0), z1)), U142'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(U142(tt, z0)) → c12(MARK(U143(isLNat(z0))), U143'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U143(tt)) → c13(MARK(tt))
ACTIVE(U151(tt, z0, z1)) → c14(MARK(U152(isNatural(z0), z1)), U152'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U152(tt, z0)) → c15(MARK(U153(isLNat(z0))), U153'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U153(tt)) → c16(MARK(tt))
ACTIVE(U161(tt, z0)) → c17(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c18(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c19(MARK(z0))
ACTIVE(U191(tt, z0)) → c20(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c21(MARK(U202(splitAt(z0, z2), z1)), U202'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U202(pair(z0, z1), z2)) → c22(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0)) → c23(MARK(z0))
ACTIVE(U211(tt, z0)) → c24(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c25(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0)) → c26(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c27(MARK(U42(isNatural(z0), z1)), U42'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U42(tt, z0)) → c28(MARK(U43(isLNat(z0))), U43'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U43(tt)) → c29(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c30(MARK(U52(isNatural(z0), z1)), U52'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U52(tt, z0)) → c31(MARK(U53(isLNat(z0))), U53'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U53(tt)) → c32(MARK(tt))
ACTIVE(U61(tt, z0)) → c33(MARK(U62(isPLNat(z0))), U62'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U62(tt)) → c34(MARK(tt))
ACTIVE(U71(tt, z0)) → c35(MARK(U72(isNatural(z0))), U72'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U72(tt)) → c36(MARK(tt))
ACTIVE(U81(tt, z0)) → c37(MARK(U82(isPLNat(z0))), U82'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U82(tt)) → c38(MARK(tt))
ACTIVE(U91(tt, z0)) → c39(MARK(U92(isLNat(z0))), U92'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U92(tt)) → c40(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c41(MARK(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U11'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(and(tt, z0)) → c42(MARK(z0))
ACTIVE(fst(pair(z0, z1))) → c43(MARK(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U21'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(head(cons(z0, z1))) → c44(MARK(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U31'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(isLNat(nil)) → c45(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c46(MARK(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U41'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(cons(z0, z1))) → c47(MARK(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U51'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(fst(z0))) → c48(MARK(U61(isPLNatKind(z0), z0)), U61'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(natsFrom(z0))) → c49(MARK(U71(isNaturalKind(z0), z0)), U71'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isLNat(snd(z0))) → c50(MARK(U81(isPLNatKind(z0), z0)), U81'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(tail(z0))) → c51(MARK(U91(isLNatKind(z0), z0)), U91'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isLNat(take(z0, z1))) → c52(MARK(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U101'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(nil)) → c53(MARK(tt))
ACTIVE(isLNatKind(afterNth(z0, z1))) → c54(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(cons(z0, z1))) → c55(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(fst(z0))) → c56(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(natsFrom(z0))) → c57(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isLNatKind(snd(z0))) → c58(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(tail(z0))) → c59(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isLNatKind(take(z0, z1))) → c60(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNatural(0)) → c61(MARK(tt))
ACTIVE(isNatural(head(z0))) → c62(MARK(U111(isLNatKind(z0), z0)), U111'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isNatural(s(z0))) → c63(MARK(U121(isNaturalKind(z0), z0)), U121'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isNatural(sel(z0, z1))) → c64(MARK(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U131'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNaturalKind(0)) → c65(MARK(tt))
ACTIVE(isNaturalKind(head(z0))) → c66(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isNaturalKind(s(z0))) → c67(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isNaturalKind(sel(z0, z1))) → c68(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(pair(z0, z1))) → c69(MARK(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1)), U141'(and(isLNatKind(z0), isLNatKind(z1)), z0, z1), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(splitAt(z0, z1))) → c70(MARK(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U151'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(pair(z0, z1))) → c71(MARK(and(isLNatKind(z0), isLNatKind(z1))), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(splitAt(z0, z1))) → c72(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(natsFrom(z0)) → c73(MARK(U161(and(isNatural(z0), isNaturalKind(z0)), z0)), U161'(and(isNatural(z0), isNaturalKind(z0)), z0), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0))
ACTIVE(sel(z0, z1)) → c74(MARK(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U171'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(snd(pair(z0, z1))) → c75(MARK(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U181'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(splitAt(0, z0)) → c76(MARK(U191(and(isLNat(z0), isLNatKind(z0)), z0)), U191'(and(isLNat(z0), isLNatKind(z0)), z0), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c77(MARK(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2)), U201'(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2), AND(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2))), AND(isNatural(z1), isNaturalKind(z1)), ISNATURAL(z1), ISNATURALKIND(z1), AND(isLNat(z2), isLNatKind(z2)), ISLNAT(z2), ISLNATKIND(z2))
ACTIVE(tail(cons(z0, z1))) → c78(MARK(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U211'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(take(z0, z1)) → c79(MARK(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U221'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
MARK(U101(z0, z1, z2)) → c80(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(tt) → c81(ACTIVE(tt))
MARK(U102(z0, z1)) → c82(ACTIVE(U102(mark(z0), z1)), U102'(mark(z0), z1), MARK(z0))
MARK(isNatural(z0)) → c83(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U103(z0)) → c84(ACTIVE(U103(mark(z0))), U103'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c85(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c86(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c87(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c88(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U111(z0, z1)) → c89(ACTIVE(U111(mark(z0), z1)), U111'(mark(z0), z1), MARK(z0))
MARK(U112(z0)) → c90(ACTIVE(U112(mark(z0))), U112'(mark(z0)), MARK(z0))
MARK(U121(z0, z1)) → c91(ACTIVE(U121(mark(z0), z1)), U121'(mark(z0), z1), MARK(z0))
MARK(U122(z0)) → c92(ACTIVE(U122(mark(z0))), U122'(mark(z0)), MARK(z0))
MARK(U131(z0, z1, z2)) → c93(ACTIVE(U131(mark(z0), z1, z2)), U131'(mark(z0), z1, z2), MARK(z0))
MARK(U132(z0, z1)) → c94(ACTIVE(U132(mark(z0), z1)), U132'(mark(z0), z1), MARK(z0))
MARK(U133(z0)) → c95(ACTIVE(U133(mark(z0))), U133'(mark(z0)), MARK(z0))
MARK(U141(z0, z1, z2)) → c96(ACTIVE(U141(mark(z0), z1, z2)), U141'(mark(z0), z1, z2), MARK(z0))
MARK(U142(z0, z1)) → c97(ACTIVE(U142(mark(z0), z1)), U142'(mark(z0), z1), MARK(z0))
MARK(U143(z0)) → c98(ACTIVE(U143(mark(z0))), U143'(mark(z0)), MARK(z0))
MARK(U151(z0, z1, z2)) → c99(ACTIVE(U151(mark(z0), z1, z2)), U151'(mark(z0), z1, z2), MARK(z0))
MARK(U152(z0, z1)) → c100(ACTIVE(U152(mark(z0), z1)), U152'(mark(z0), z1), MARK(z0))
MARK(U153(z0)) → c101(ACTIVE(U153(mark(z0))), U153'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c102(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c103(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c104(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c105(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c106(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c107(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c108(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c109(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c110(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c111(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(nil) → c112(ACTIVE(nil))
MARK(U201(z0, z1, z2, z3)) → c113(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1)) → c114(ACTIVE(U202(mark(z0), z1)), U202'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1)) → c115(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c116(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c117(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c118(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c119(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c120(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c121(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c122(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c123(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c124(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c125(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c126(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c127(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c128(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(U71(z0, z1)) → c129(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c130(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(U81(z0, z1)) → c131(ACTIVE(U81(mark(z0), z1)), U81'(mark(z0), z1), MARK(z0))
MARK(U82(z0)) → c132(ACTIVE(U82(mark(z0))), U82'(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c133(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c134(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
MARK(and(z0, z1)) → c135(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNaturalKind(z0)) → c136(ACTIVE(isNaturalKind(z0)), ISNATURALKIND(z0))
MARK(isLNatKind(z0)) → c137(ACTIVE(isLNatKind(z0)), ISLNATKIND(z0))
MARK(isPLNatKind(z0)) → c138(ACTIVE(isPLNatKind(z0)), ISPLNATKIND(z0))
MARK(tail(z0)) → c139(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c140(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(0) → c141(ACTIVE(0))
MARK(sel(z0, z1)) → c142(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1, z2) → c143(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c144(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c145(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c146(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c147(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c148(U101'(z0, z1, z2))
U102'(mark(z0), z1) → c149(U102'(z0, z1))
U102'(z0, mark(z1)) → c150(U102'(z0, z1))
U102'(active(z0), z1) → c151(U102'(z0, z1))
U102'(z0, active(z1)) → c152(U102'(z0, z1))
ISNATURAL(mark(z0)) → c153(ISNATURAL(z0))
ISNATURAL(active(z0)) → c154(ISNATURAL(z0))
U103'(mark(z0)) → c155(U103'(z0))
U103'(active(z0)) → c156(U103'(z0))
ISLNAT(mark(z0)) → c157(ISLNAT(z0))
ISLNAT(active(z0)) → c158(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c159(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c160(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c161(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c162(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c163(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c164(U11'(z0, z1, z2))
SND(mark(z0)) → c165(SND(z0))
SND(active(z0)) → c166(SND(z0))
SPLITAT(mark(z0), z1) → c167(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c168(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c169(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c170(SPLITAT(z0, z1))
U111'(mark(z0), z1) → c171(U111'(z0, z1))
U111'(z0, mark(z1)) → c172(U111'(z0, z1))
U111'(active(z0), z1) → c173(U111'(z0, z1))
U111'(z0, active(z1)) → c174(U111'(z0, z1))
U112'(mark(z0)) → c175(U112'(z0))
U112'(active(z0)) → c176(U112'(z0))
U121'(mark(z0), z1) → c177(U121'(z0, z1))
U121'(z0, mark(z1)) → c178(U121'(z0, z1))
U121'(active(z0), z1) → c179(U121'(z0, z1))
U121'(z0, active(z1)) → c180(U121'(z0, z1))
U122'(mark(z0)) → c181(U122'(z0))
U122'(active(z0)) → c182(U122'(z0))
U131'(mark(z0), z1, z2) → c183(U131'(z0, z1, z2))
U131'(z0, mark(z1), z2) → c184(U131'(z0, z1, z2))
U131'(z0, z1, mark(z2)) → c185(U131'(z0, z1, z2))
U131'(active(z0), z1, z2) → c186(U131'(z0, z1, z2))
U131'(z0, active(z1), z2) → c187(U131'(z0, z1, z2))
U131'(z0, z1, active(z2)) → c188(U131'(z0, z1, z2))
U132'(mark(z0), z1) → c189(U132'(z0, z1))
U132'(z0, mark(z1)) → c190(U132'(z0, z1))
U132'(active(z0), z1) → c191(U132'(z0, z1))
U132'(z0, active(z1)) → c192(U132'(z0, z1))
U133'(mark(z0)) → c193(U133'(z0))
U133'(active(z0)) → c194(U133'(z0))
U141'(mark(z0), z1, z2) → c195(U141'(z0, z1, z2))
U141'(z0, mark(z1), z2) → c196(U141'(z0, z1, z2))
U141'(z0, z1, mark(z2)) → c197(U141'(z0, z1, z2))
U141'(active(z0), z1, z2) → c198(U141'(z0, z1, z2))
U141'(z0, active(z1), z2) → c199(U141'(z0, z1, z2))
U141'(z0, z1, active(z2)) → c200(U141'(z0, z1, z2))
U142'(mark(z0), z1) → c201(U142'(z0, z1))
U142'(z0, mark(z1)) → c202(U142'(z0, z1))
U142'(active(z0), z1) → c203(U142'(z0, z1))
U142'(z0, active(z1)) → c204(U142'(z0, z1))
U143'(mark(z0)) → c205(U143'(z0))
U143'(active(z0)) → c206(U143'(z0))
U151'(mark(z0), z1, z2) → c207(U151'(z0, z1, z2))
U151'(z0, mark(z1), z2) → c208(U151'(z0, z1, z2))
U151'(z0, z1, mark(z2)) → c209(U151'(z0, z1, z2))
U151'(active(z0), z1, z2) → c210(U151'(z0, z1, z2))
U151'(z0, active(z1), z2) → c211(U151'(z0, z1, z2))
U151'(z0, z1, active(z2)) → c212(U151'(z0, z1, z2))
U152'(mark(z0), z1) → c213(U152'(z0, z1))
U152'(z0, mark(z1)) → c214(U152'(z0, z1))
U152'(active(z0), z1) → c215(U152'(z0, z1))
U152'(z0, active(z1)) → c216(U152'(z0, z1))
U153'(mark(z0)) → c217(U153'(z0))
U153'(active(z0)) → c218(U153'(z0))
U161'(mark(z0), z1) → c219(U161'(z0, z1))
U161'(z0, mark(z1)) → c220(U161'(z0, z1))
U161'(active(z0), z1) → c221(U161'(z0, z1))
U161'(z0, active(z1)) → c222(U161'(z0, z1))
CONS(mark(z0), z1) → c223(CONS(z0, z1))
CONS(z0, mark(z1)) → c224(CONS(z0, z1))
CONS(active(z0), z1) → c225(CONS(z0, z1))
CONS(z0, active(z1)) → c226(CONS(z0, z1))
NATSFROM(mark(z0)) → c227(NATSFROM(z0))
NATSFROM(active(z0)) → c228(NATSFROM(z0))
S(mark(z0)) → c229(S(z0))
S(active(z0)) → c230(S(z0))
U171'(mark(z0), z1, z2) → c231(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c232(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c233(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c234(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c235(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c236(U171'(z0, z1, z2))
HEAD(mark(z0)) → c237(HEAD(z0))
HEAD(active(z0)) → c238(HEAD(z0))
AFTERNTH(mark(z0), z1) → c239(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c240(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c241(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c242(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c243(U181'(z0, z1))
U181'(z0, mark(z1)) → c244(U181'(z0, z1))
U181'(active(z0), z1) → c245(U181'(z0, z1))
U181'(z0, active(z1)) → c246(U181'(z0, z1))
U191'(mark(z0), z1) → c247(U191'(z0, z1))
U191'(z0, mark(z1)) → c248(U191'(z0, z1))
U191'(active(z0), z1) → c249(U191'(z0, z1))
U191'(z0, active(z1)) → c250(U191'(z0, z1))
PAIR(mark(z0), z1) → c251(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c252(PAIR(z0, z1))
PAIR(active(z0), z1) → c253(PAIR(z0, z1))
PAIR(z0, active(z1)) → c254(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c255(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c256(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c257(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c258(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c259(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c260(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c261(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c262(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1) → c263(U202'(z0, z1))
U202'(z0, mark(z1)) → c264(U202'(z0, z1))
U202'(active(z0), z1) → c265(U202'(z0, z1))
U202'(z0, active(z1)) → c266(U202'(z0, z1))
U21'(mark(z0), z1) → c267(U21'(z0, z1))
U21'(z0, mark(z1)) → c268(U21'(z0, z1))
U21'(active(z0), z1) → c269(U21'(z0, z1))
U21'(z0, active(z1)) → c270(U21'(z0, z1))
U211'(mark(z0), z1) → c271(U211'(z0, z1))
U211'(z0, mark(z1)) → c272(U211'(z0, z1))
U211'(active(z0), z1) → c273(U211'(z0, z1))
U211'(z0, active(z1)) → c274(U211'(z0, z1))
U221'(mark(z0), z1, z2) → c275(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c276(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c277(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c278(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c279(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c280(U221'(z0, z1, z2))
FST(mark(z0)) → c281(FST(z0))
FST(active(z0)) → c282(FST(z0))
U31'(mark(z0), z1) → c283(U31'(z0, z1))
U31'(z0, mark(z1)) → c284(U31'(z0, z1))
U31'(active(z0), z1) → c285(U31'(z0, z1))
U31'(z0, active(z1)) → c286(U31'(z0, z1))
U41'(mark(z0), z1, z2) → c287(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c288(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c289(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c290(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c291(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c292(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c293(U42'(z0, z1))
U42'(z0, mark(z1)) → c294(U42'(z0, z1))
U42'(active(z0), z1) → c295(U42'(z0, z1))
U42'(z0, active(z1)) → c296(U42'(z0, z1))
U43'(mark(z0)) → c297(U43'(z0))
U43'(active(z0)) → c298(U43'(z0))
U51'(mark(z0), z1, z2) → c299(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c300(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c301(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c302(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c303(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c304(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c305(U52'(z0, z1))
U52'(z0, mark(z1)) → c306(U52'(z0, z1))
U52'(active(z0), z1) → c307(U52'(z0, z1))
U52'(z0, active(z1)) → c308(U52'(z0, z1))
U53'(mark(z0)) → c309(U53'(z0))
U53'(active(z0)) → c310(U53'(z0))
U61'(mark(z0), z1) → c311(U61'(z0, z1))
U61'(z0, mark(z1)) → c312(U61'(z0, z1))
U61'(active(z0), z1) → c313(U61'(z0, z1))
U61'(z0, active(z1)) → c314(U61'(z0, z1))
U62'(mark(z0)) → c315(U62'(z0))
U62'(active(z0)) → c316(U62'(z0))
ISPLNAT(mark(z0)) → c317(ISPLNAT(z0))
ISPLNAT(active(z0)) → c318(ISPLNAT(z0))
U71'(mark(z0), z1) → c319(U71'(z0, z1))
U71'(z0, mark(z1)) → c320(U71'(z0, z1))
U71'(active(z0), z1) → c321(U71'(z0, z1))
U71'(z0, active(z1)) → c322(U71'(z0, z1))
U72'(mark(z0)) → c323(U72'(z0))
U72'(active(z0)) → c324(U72'(z0))
U81'(mark(z0), z1) → c325(U81'(z0, z1))
U81'(z0, mark(z1)) → c326(U81'(z0, z1))
U81'(active(z0), z1) → c327(U81'(z0, z1))
U81'(z0, active(z1)) → c328(U81'(z0, z1))
U82'(mark(z0)) → c329(U82'(z0))
U82'(active(z0)) → c330(U82'(z0))
U91'(mark(z0), z1) → c331(U91'(z0, z1))
U91'(z0, mark(z1)) → c332(U91'(z0, z1))
U91'(active(z0), z1) → c333(U91'(z0, z1))
U91'(z0, active(z1)) → c334(U91'(z0, z1))
U92'(mark(z0)) → c335(U92'(z0))
U92'(active(z0)) → c336(U92'(z0))
AND(mark(z0), z1) → c337(AND(z0, z1))
AND(z0, mark(z1)) → c338(AND(z0, z1))
AND(active(z0), z1) → c339(AND(z0, z1))
AND(z0, active(z1)) → c340(AND(z0, z1))
ISNATURALKIND(mark(z0)) → c341(ISNATURALKIND(z0))
ISNATURALKIND(active(z0)) → c342(ISNATURALKIND(z0))
ISLNATKIND(mark(z0)) → c343(ISLNATKIND(z0))
ISLNATKIND(active(z0)) → c344(ISLNATKIND(z0))
ISPLNATKIND(mark(z0)) → c345(ISPLNATKIND(z0))
ISPLNATKIND(active(z0)) → c346(ISPLNATKIND(z0))
TAIL(mark(z0)) → c347(TAIL(z0))
TAIL(active(z0)) → c348(TAIL(z0))
TAKE(mark(z0), z1) → c349(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c350(TAKE(z0, z1))
TAKE(active(z0), z1) → c351(TAKE(z0, z1))
TAKE(z0, active(z1)) → c352(TAKE(z0, z1))
SEL(mark(z0), z1) → c353(SEL(z0, z1))
SEL(z0, mark(z1)) → c354(SEL(z0, z1))
SEL(active(z0), z1) → c355(SEL(z0, z1))
SEL(z0, active(z1)) → c356(SEL(z0, z1))

K tuples:none
Defined Rule Symbols:

active, mark, U101, U102, isNatural, U103, isLNat, U11, snd, splitAt, U111, U112, U121, U122, U131, U132, U133, U141, U142, U143, U151, U152, U153, U161, cons, natsFrom, s, U171, head, afterNth, U181, U191, pair, U201, U202, U21, U211, U221, fst, U31, U41, U42, U43, U51, U52, U53, U61, U62, isPLNat, U71, U72, U81, U82, U91, U92, and, isNaturalKind, isLNatKind, isPLNatKind, tail, take, sel

Defined Pair Symbols:

ACTIVE, MARK, U101', U102', ISNATURAL, U103', ISLNAT, U11', SND, SPLITAT, U111', U112', U121', U122', U131', U132', U133', U141', U142', U143', U151', U152', U153', U161', CONS, NATSFROM, S, U171', HEAD, AFTERNTH, U181', U191', PAIR, U201', U202', U21', U211', U221', FST, U31', U41', U42', U43', U51', U52', U53', U61', U62', ISPLNAT, U71', U72', U81', U82', U91', U92', AND, ISNATURALKIND, ISLNATKIND, ISPLNATKIND, 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, c316, c317, c318, c319, c320, c321, c322, c323, c324, c325, c326, c327, c328, c329, c330, c331, c332, c333, c334, c335, c336, c337, c338, c339, c340, c341, c342, c343, c344, c345, c346, c347, c348, c349, c350, c351, c352, c353, c354, c355, c356

(3) CdtUnreachableProof (EQUIVALENT transformation)

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

ACTIVE(U101(tt, z0, z1)) → c(MARK(U102(isNatural(z0), z1)), U102'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U102(tt, z0)) → c1(MARK(U103(isLNat(z0))), U103'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U103(tt)) → c2(MARK(tt))
ACTIVE(U11(tt, z0, z1)) → c3(MARK(snd(splitAt(z0, z1))), SND(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U111(tt, z0)) → c4(MARK(U112(isLNat(z0))), U112'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U112(tt)) → c5(MARK(tt))
ACTIVE(U121(tt, z0)) → c6(MARK(U122(isNatural(z0))), U122'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U122(tt)) → c7(MARK(tt))
ACTIVE(U131(tt, z0, z1)) → c8(MARK(U132(isNatural(z0), z1)), U132'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U132(tt, z0)) → c9(MARK(U133(isLNat(z0))), U133'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U133(tt)) → c10(MARK(tt))
ACTIVE(U141(tt, z0, z1)) → c11(MARK(U142(isLNat(z0), z1)), U142'(isLNat(z0), z1), ISLNAT(z0))
ACTIVE(U142(tt, z0)) → c12(MARK(U143(isLNat(z0))), U143'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U143(tt)) → c13(MARK(tt))
ACTIVE(U151(tt, z0, z1)) → c14(MARK(U152(isNatural(z0), z1)), U152'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U152(tt, z0)) → c15(MARK(U153(isLNat(z0))), U153'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U153(tt)) → c16(MARK(tt))
ACTIVE(U161(tt, z0)) → c17(MARK(cons(z0, natsFrom(s(z0)))), CONS(z0, natsFrom(s(z0))), NATSFROM(s(z0)), S(z0))
ACTIVE(U171(tt, z0, z1)) → c18(MARK(head(afterNth(z0, z1))), HEAD(afterNth(z0, z1)), AFTERNTH(z0, z1))
ACTIVE(U181(tt, z0)) → c19(MARK(z0))
ACTIVE(U191(tt, z0)) → c20(MARK(pair(nil, z0)), PAIR(nil, z0))
ACTIVE(U201(tt, z0, z1, z2)) → c21(MARK(U202(splitAt(z0, z2), z1)), U202'(splitAt(z0, z2), z1), SPLITAT(z0, z2))
ACTIVE(U202(pair(z0, z1), z2)) → c22(MARK(pair(cons(z2, z0), z1)), PAIR(cons(z2, z0), z1), CONS(z2, z0))
ACTIVE(U21(tt, z0)) → c23(MARK(z0))
ACTIVE(U211(tt, z0)) → c24(MARK(z0))
ACTIVE(U221(tt, z0, z1)) → c25(MARK(fst(splitAt(z0, z1))), FST(splitAt(z0, z1)), SPLITAT(z0, z1))
ACTIVE(U31(tt, z0)) → c26(MARK(z0))
ACTIVE(U41(tt, z0, z1)) → c27(MARK(U42(isNatural(z0), z1)), U42'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U42(tt, z0)) → c28(MARK(U43(isLNat(z0))), U43'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U43(tt)) → c29(MARK(tt))
ACTIVE(U51(tt, z0, z1)) → c30(MARK(U52(isNatural(z0), z1)), U52'(isNatural(z0), z1), ISNATURAL(z0))
ACTIVE(U52(tt, z0)) → c31(MARK(U53(isLNat(z0))), U53'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U53(tt)) → c32(MARK(tt))
ACTIVE(U61(tt, z0)) → c33(MARK(U62(isPLNat(z0))), U62'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U62(tt)) → c34(MARK(tt))
ACTIVE(U71(tt, z0)) → c35(MARK(U72(isNatural(z0))), U72'(isNatural(z0)), ISNATURAL(z0))
ACTIVE(U72(tt)) → c36(MARK(tt))
ACTIVE(U81(tt, z0)) → c37(MARK(U82(isPLNat(z0))), U82'(isPLNat(z0)), ISPLNAT(z0))
ACTIVE(U82(tt)) → c38(MARK(tt))
ACTIVE(U91(tt, z0)) → c39(MARK(U92(isLNat(z0))), U92'(isLNat(z0)), ISLNAT(z0))
ACTIVE(U92(tt)) → c40(MARK(tt))
ACTIVE(afterNth(z0, z1)) → c41(MARK(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U11'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(and(tt, z0)) → c42(MARK(z0))
ACTIVE(fst(pair(z0, z1))) → c43(MARK(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U21'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(head(cons(z0, z1))) → c44(MARK(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0)), U31'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(isLNat(nil)) → c45(MARK(tt))
ACTIVE(isLNat(afterNth(z0, z1))) → c46(MARK(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U41'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(cons(z0, z1))) → c47(MARK(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U51'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNat(fst(z0))) → c48(MARK(U61(isPLNatKind(z0), z0)), U61'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(natsFrom(z0))) → c49(MARK(U71(isNaturalKind(z0), z0)), U71'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isLNat(snd(z0))) → c50(MARK(U81(isPLNatKind(z0), z0)), U81'(isPLNatKind(z0), z0), ISPLNATKIND(z0))
ACTIVE(isLNat(tail(z0))) → c51(MARK(U91(isLNatKind(z0), z0)), U91'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isLNat(take(z0, z1))) → c52(MARK(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U101'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(nil)) → c53(MARK(tt))
ACTIVE(isLNatKind(afterNth(z0, z1))) → c54(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(cons(z0, z1))) → c55(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isLNatKind(fst(z0))) → c56(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(natsFrom(z0))) → c57(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isLNatKind(snd(z0))) → c58(MARK(isPLNatKind(z0)), ISPLNATKIND(z0))
ACTIVE(isLNatKind(tail(z0))) → c59(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isLNatKind(take(z0, z1))) → c60(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNatural(0)) → c61(MARK(tt))
ACTIVE(isNatural(head(z0))) → c62(MARK(U111(isLNatKind(z0), z0)), U111'(isLNatKind(z0), z0), ISLNATKIND(z0))
ACTIVE(isNatural(s(z0))) → c63(MARK(U121(isNaturalKind(z0), z0)), U121'(isNaturalKind(z0), z0), ISNATURALKIND(z0))
ACTIVE(isNatural(sel(z0, z1))) → c64(MARK(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U131'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isNaturalKind(0)) → c65(MARK(tt))
ACTIVE(isNaturalKind(head(z0))) → c66(MARK(isLNatKind(z0)), ISLNATKIND(z0))
ACTIVE(isNaturalKind(s(z0))) → c67(MARK(isNaturalKind(z0)), ISNATURALKIND(z0))
ACTIVE(isNaturalKind(sel(z0, z1))) → c68(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(pair(z0, z1))) → c69(MARK(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1)), U141'(and(isLNatKind(z0), isLNatKind(z1)), z0, z1), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNat(splitAt(z0, z1))) → c70(MARK(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1)), U151'(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(pair(z0, z1))) → c71(MARK(and(isLNatKind(z0), isLNatKind(z1))), AND(isLNatKind(z0), isLNatKind(z1)), ISLNATKIND(z0), ISLNATKIND(z1))
ACTIVE(isPLNatKind(splitAt(z0, z1))) → c72(MARK(and(isNaturalKind(z0), isLNatKind(z1))), AND(isNaturalKind(z0), isLNatKind(z1)), ISNATURALKIND(z0), ISLNATKIND(z1))
ACTIVE(natsFrom(z0)) → c73(MARK(U161(and(isNatural(z0), isNaturalKind(z0)), z0)), U161'(and(isNatural(z0), isNaturalKind(z0)), z0), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0))
ACTIVE(sel(z0, z1)) → c74(MARK(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U171'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(snd(pair(z0, z1))) → c75(MARK(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U181'(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(splitAt(0, z0)) → c76(MARK(U191(and(isLNat(z0), isLNatKind(z0)), z0)), U191'(and(isLNat(z0), isLNatKind(z0)), z0), AND(isLNat(z0), isLNatKind(z0)), ISLNAT(z0), ISLNATKIND(z0))
ACTIVE(splitAt(s(z0), cons(z1, z2))) → c77(MARK(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2)), U201'(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2), AND(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2))), AND(isNatural(z1), isNaturalKind(z1)), ISNATURAL(z1), ISNATURALKIND(z1), AND(isLNat(z2), isLNatKind(z2)), ISLNAT(z2), ISLNATKIND(z2))
ACTIVE(tail(cons(z0, z1))) → c78(MARK(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1)), U211'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
ACTIVE(take(z0, z1)) → c79(MARK(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1)), U221'(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1), AND(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), AND(isNatural(z0), isNaturalKind(z0)), ISNATURAL(z0), ISNATURALKIND(z0), AND(isLNat(z1), isLNatKind(z1)), ISLNAT(z1), ISLNATKIND(z1))
MARK(U101(z0, z1, z2)) → c80(ACTIVE(U101(mark(z0), z1, z2)), U101'(mark(z0), z1, z2), MARK(z0))
MARK(U102(z0, z1)) → c82(ACTIVE(U102(mark(z0), z1)), U102'(mark(z0), z1), MARK(z0))
MARK(isNatural(z0)) → c83(ACTIVE(isNatural(z0)), ISNATURAL(z0))
MARK(U103(z0)) → c84(ACTIVE(U103(mark(z0))), U103'(mark(z0)), MARK(z0))
MARK(isLNat(z0)) → c85(ACTIVE(isLNat(z0)), ISLNAT(z0))
MARK(U11(z0, z1, z2)) → c86(ACTIVE(U11(mark(z0), z1, z2)), U11'(mark(z0), z1, z2), MARK(z0))
MARK(snd(z0)) → c87(ACTIVE(snd(mark(z0))), SND(mark(z0)), MARK(z0))
MARK(splitAt(z0, z1)) → c88(ACTIVE(splitAt(mark(z0), mark(z1))), SPLITAT(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U111(z0, z1)) → c89(ACTIVE(U111(mark(z0), z1)), U111'(mark(z0), z1), MARK(z0))
MARK(U112(z0)) → c90(ACTIVE(U112(mark(z0))), U112'(mark(z0)), MARK(z0))
MARK(U121(z0, z1)) → c91(ACTIVE(U121(mark(z0), z1)), U121'(mark(z0), z1), MARK(z0))
MARK(U122(z0)) → c92(ACTIVE(U122(mark(z0))), U122'(mark(z0)), MARK(z0))
MARK(U131(z0, z1, z2)) → c93(ACTIVE(U131(mark(z0), z1, z2)), U131'(mark(z0), z1, z2), MARK(z0))
MARK(U132(z0, z1)) → c94(ACTIVE(U132(mark(z0), z1)), U132'(mark(z0), z1), MARK(z0))
MARK(U133(z0)) → c95(ACTIVE(U133(mark(z0))), U133'(mark(z0)), MARK(z0))
MARK(U141(z0, z1, z2)) → c96(ACTIVE(U141(mark(z0), z1, z2)), U141'(mark(z0), z1, z2), MARK(z0))
MARK(U142(z0, z1)) → c97(ACTIVE(U142(mark(z0), z1)), U142'(mark(z0), z1), MARK(z0))
MARK(U143(z0)) → c98(ACTIVE(U143(mark(z0))), U143'(mark(z0)), MARK(z0))
MARK(U151(z0, z1, z2)) → c99(ACTIVE(U151(mark(z0), z1, z2)), U151'(mark(z0), z1, z2), MARK(z0))
MARK(U152(z0, z1)) → c100(ACTIVE(U152(mark(z0), z1)), U152'(mark(z0), z1), MARK(z0))
MARK(U153(z0)) → c101(ACTIVE(U153(mark(z0))), U153'(mark(z0)), MARK(z0))
MARK(U161(z0, z1)) → c102(ACTIVE(U161(mark(z0), z1)), U161'(mark(z0), z1), MARK(z0))
MARK(cons(z0, z1)) → c103(ACTIVE(cons(mark(z0), z1)), CONS(mark(z0), z1), MARK(z0))
MARK(natsFrom(z0)) → c104(ACTIVE(natsFrom(mark(z0))), NATSFROM(mark(z0)), MARK(z0))
MARK(s(z0)) → c105(ACTIVE(s(mark(z0))), S(mark(z0)), MARK(z0))
MARK(U171(z0, z1, z2)) → c106(ACTIVE(U171(mark(z0), z1, z2)), U171'(mark(z0), z1, z2), MARK(z0))
MARK(head(z0)) → c107(ACTIVE(head(mark(z0))), HEAD(mark(z0)), MARK(z0))
MARK(afterNth(z0, z1)) → c108(ACTIVE(afterNth(mark(z0), mark(z1))), AFTERNTH(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U181(z0, z1)) → c109(ACTIVE(U181(mark(z0), z1)), U181'(mark(z0), z1), MARK(z0))
MARK(U191(z0, z1)) → c110(ACTIVE(U191(mark(z0), z1)), U191'(mark(z0), z1), MARK(z0))
MARK(pair(z0, z1)) → c111(ACTIVE(pair(mark(z0), mark(z1))), PAIR(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(U201(z0, z1, z2, z3)) → c113(ACTIVE(U201(mark(z0), z1, z2, z3)), U201'(mark(z0), z1, z2, z3), MARK(z0))
MARK(U202(z0, z1)) → c114(ACTIVE(U202(mark(z0), z1)), U202'(mark(z0), z1), MARK(z0))
MARK(U21(z0, z1)) → c115(ACTIVE(U21(mark(z0), z1)), U21'(mark(z0), z1), MARK(z0))
MARK(U211(z0, z1)) → c116(ACTIVE(U211(mark(z0), z1)), U211'(mark(z0), z1), MARK(z0))
MARK(U221(z0, z1, z2)) → c117(ACTIVE(U221(mark(z0), z1, z2)), U221'(mark(z0), z1, z2), MARK(z0))
MARK(fst(z0)) → c118(ACTIVE(fst(mark(z0))), FST(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) → c119(ACTIVE(U31(mark(z0), z1)), U31'(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) → c120(ACTIVE(U41(mark(z0), z1, z2)), U41'(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1)) → c121(ACTIVE(U42(mark(z0), z1)), U42'(mark(z0), z1), MARK(z0))
MARK(U43(z0)) → c122(ACTIVE(U43(mark(z0))), U43'(mark(z0)), MARK(z0))
MARK(U51(z0, z1, z2)) → c123(ACTIVE(U51(mark(z0), z1, z2)), U51'(mark(z0), z1, z2), MARK(z0))
MARK(U52(z0, z1)) → c124(ACTIVE(U52(mark(z0), z1)), U52'(mark(z0), z1), MARK(z0))
MARK(U53(z0)) → c125(ACTIVE(U53(mark(z0))), U53'(mark(z0)), MARK(z0))
MARK(U61(z0, z1)) → c126(ACTIVE(U61(mark(z0), z1)), U61'(mark(z0), z1), MARK(z0))
MARK(U62(z0)) → c127(ACTIVE(U62(mark(z0))), U62'(mark(z0)), MARK(z0))
MARK(isPLNat(z0)) → c128(ACTIVE(isPLNat(z0)), ISPLNAT(z0))
MARK(U71(z0, z1)) → c129(ACTIVE(U71(mark(z0), z1)), U71'(mark(z0), z1), MARK(z0))
MARK(U72(z0)) → c130(ACTIVE(U72(mark(z0))), U72'(mark(z0)), MARK(z0))
MARK(U81(z0, z1)) → c131(ACTIVE(U81(mark(z0), z1)), U81'(mark(z0), z1), MARK(z0))
MARK(U82(z0)) → c132(ACTIVE(U82(mark(z0))), U82'(mark(z0)), MARK(z0))
MARK(U91(z0, z1)) → c133(ACTIVE(U91(mark(z0), z1)), U91'(mark(z0), z1), MARK(z0))
MARK(U92(z0)) → c134(ACTIVE(U92(mark(z0))), U92'(mark(z0)), MARK(z0))
MARK(and(z0, z1)) → c135(ACTIVE(and(mark(z0), z1)), AND(mark(z0), z1), MARK(z0))
MARK(isNaturalKind(z0)) → c136(ACTIVE(isNaturalKind(z0)), ISNATURALKIND(z0))
MARK(isLNatKind(z0)) → c137(ACTIVE(isLNatKind(z0)), ISLNATKIND(z0))
MARK(isPLNatKind(z0)) → c138(ACTIVE(isPLNatKind(z0)), ISPLNATKIND(z0))
MARK(tail(z0)) → c139(ACTIVE(tail(mark(z0))), TAIL(mark(z0)), MARK(z0))
MARK(take(z0, z1)) → c140(ACTIVE(take(mark(z0), mark(z1))), TAKE(mark(z0), mark(z1)), MARK(z0), MARK(z1))
MARK(sel(z0, z1)) → c142(ACTIVE(sel(mark(z0), mark(z1))), SEL(mark(z0), mark(z1)), MARK(z0), MARK(z1))
U101'(mark(z0), z1, z2) → c143(U101'(z0, z1, z2))
U101'(z0, mark(z1), z2) → c144(U101'(z0, z1, z2))
U101'(z0, z1, mark(z2)) → c145(U101'(z0, z1, z2))
U101'(active(z0), z1, z2) → c146(U101'(z0, z1, z2))
U101'(z0, active(z1), z2) → c147(U101'(z0, z1, z2))
U101'(z0, z1, active(z2)) → c148(U101'(z0, z1, z2))
U102'(mark(z0), z1) → c149(U102'(z0, z1))
U102'(z0, mark(z1)) → c150(U102'(z0, z1))
U102'(active(z0), z1) → c151(U102'(z0, z1))
U102'(z0, active(z1)) → c152(U102'(z0, z1))
ISNATURAL(mark(z0)) → c153(ISNATURAL(z0))
ISNATURAL(active(z0)) → c154(ISNATURAL(z0))
U103'(mark(z0)) → c155(U103'(z0))
U103'(active(z0)) → c156(U103'(z0))
ISLNAT(mark(z0)) → c157(ISLNAT(z0))
ISLNAT(active(z0)) → c158(ISLNAT(z0))
U11'(mark(z0), z1, z2) → c159(U11'(z0, z1, z2))
U11'(z0, mark(z1), z2) → c160(U11'(z0, z1, z2))
U11'(z0, z1, mark(z2)) → c161(U11'(z0, z1, z2))
U11'(active(z0), z1, z2) → c162(U11'(z0, z1, z2))
U11'(z0, active(z1), z2) → c163(U11'(z0, z1, z2))
U11'(z0, z1, active(z2)) → c164(U11'(z0, z1, z2))
SND(mark(z0)) → c165(SND(z0))
SND(active(z0)) → c166(SND(z0))
SPLITAT(mark(z0), z1) → c167(SPLITAT(z0, z1))
SPLITAT(z0, mark(z1)) → c168(SPLITAT(z0, z1))
SPLITAT(active(z0), z1) → c169(SPLITAT(z0, z1))
SPLITAT(z0, active(z1)) → c170(SPLITAT(z0, z1))
U111'(mark(z0), z1) → c171(U111'(z0, z1))
U111'(z0, mark(z1)) → c172(U111'(z0, z1))
U111'(active(z0), z1) → c173(U111'(z0, z1))
U111'(z0, active(z1)) → c174(U111'(z0, z1))
U112'(mark(z0)) → c175(U112'(z0))
U112'(active(z0)) → c176(U112'(z0))
U121'(mark(z0), z1) → c177(U121'(z0, z1))
U121'(z0, mark(z1)) → c178(U121'(z0, z1))
U121'(active(z0), z1) → c179(U121'(z0, z1))
U121'(z0, active(z1)) → c180(U121'(z0, z1))
U122'(mark(z0)) → c181(U122'(z0))
U122'(active(z0)) → c182(U122'(z0))
U131'(mark(z0), z1, z2) → c183(U131'(z0, z1, z2))
U131'(z0, mark(z1), z2) → c184(U131'(z0, z1, z2))
U131'(z0, z1, mark(z2)) → c185(U131'(z0, z1, z2))
U131'(active(z0), z1, z2) → c186(U131'(z0, z1, z2))
U131'(z0, active(z1), z2) → c187(U131'(z0, z1, z2))
U131'(z0, z1, active(z2)) → c188(U131'(z0, z1, z2))
U132'(mark(z0), z1) → c189(U132'(z0, z1))
U132'(z0, mark(z1)) → c190(U132'(z0, z1))
U132'(active(z0), z1) → c191(U132'(z0, z1))
U132'(z0, active(z1)) → c192(U132'(z0, z1))
U133'(mark(z0)) → c193(U133'(z0))
U133'(active(z0)) → c194(U133'(z0))
U141'(mark(z0), z1, z2) → c195(U141'(z0, z1, z2))
U141'(z0, mark(z1), z2) → c196(U141'(z0, z1, z2))
U141'(z0, z1, mark(z2)) → c197(U141'(z0, z1, z2))
U141'(active(z0), z1, z2) → c198(U141'(z0, z1, z2))
U141'(z0, active(z1), z2) → c199(U141'(z0, z1, z2))
U141'(z0, z1, active(z2)) → c200(U141'(z0, z1, z2))
U142'(mark(z0), z1) → c201(U142'(z0, z1))
U142'(z0, mark(z1)) → c202(U142'(z0, z1))
U142'(active(z0), z1) → c203(U142'(z0, z1))
U142'(z0, active(z1)) → c204(U142'(z0, z1))
U143'(mark(z0)) → c205(U143'(z0))
U143'(active(z0)) → c206(U143'(z0))
U151'(mark(z0), z1, z2) → c207(U151'(z0, z1, z2))
U151'(z0, mark(z1), z2) → c208(U151'(z0, z1, z2))
U151'(z0, z1, mark(z2)) → c209(U151'(z0, z1, z2))
U151'(active(z0), z1, z2) → c210(U151'(z0, z1, z2))
U151'(z0, active(z1), z2) → c211(U151'(z0, z1, z2))
U151'(z0, z1, active(z2)) → c212(U151'(z0, z1, z2))
U152'(mark(z0), z1) → c213(U152'(z0, z1))
U152'(z0, mark(z1)) → c214(U152'(z0, z1))
U152'(active(z0), z1) → c215(U152'(z0, z1))
U152'(z0, active(z1)) → c216(U152'(z0, z1))
U153'(mark(z0)) → c217(U153'(z0))
U153'(active(z0)) → c218(U153'(z0))
U161'(mark(z0), z1) → c219(U161'(z0, z1))
U161'(z0, mark(z1)) → c220(U161'(z0, z1))
U161'(active(z0), z1) → c221(U161'(z0, z1))
U161'(z0, active(z1)) → c222(U161'(z0, z1))
CONS(mark(z0), z1) → c223(CONS(z0, z1))
CONS(z0, mark(z1)) → c224(CONS(z0, z1))
CONS(active(z0), z1) → c225(CONS(z0, z1))
CONS(z0, active(z1)) → c226(CONS(z0, z1))
NATSFROM(mark(z0)) → c227(NATSFROM(z0))
NATSFROM(active(z0)) → c228(NATSFROM(z0))
S(mark(z0)) → c229(S(z0))
S(active(z0)) → c230(S(z0))
U171'(mark(z0), z1, z2) → c231(U171'(z0, z1, z2))
U171'(z0, mark(z1), z2) → c232(U171'(z0, z1, z2))
U171'(z0, z1, mark(z2)) → c233(U171'(z0, z1, z2))
U171'(active(z0), z1, z2) → c234(U171'(z0, z1, z2))
U171'(z0, active(z1), z2) → c235(U171'(z0, z1, z2))
U171'(z0, z1, active(z2)) → c236(U171'(z0, z1, z2))
HEAD(mark(z0)) → c237(HEAD(z0))
HEAD(active(z0)) → c238(HEAD(z0))
AFTERNTH(mark(z0), z1) → c239(AFTERNTH(z0, z1))
AFTERNTH(z0, mark(z1)) → c240(AFTERNTH(z0, z1))
AFTERNTH(active(z0), z1) → c241(AFTERNTH(z0, z1))
AFTERNTH(z0, active(z1)) → c242(AFTERNTH(z0, z1))
U181'(mark(z0), z1) → c243(U181'(z0, z1))
U181'(z0, mark(z1)) → c244(U181'(z0, z1))
U181'(active(z0), z1) → c245(U181'(z0, z1))
U181'(z0, active(z1)) → c246(U181'(z0, z1))
U191'(mark(z0), z1) → c247(U191'(z0, z1))
U191'(z0, mark(z1)) → c248(U191'(z0, z1))
U191'(active(z0), z1) → c249(U191'(z0, z1))
U191'(z0, active(z1)) → c250(U191'(z0, z1))
PAIR(mark(z0), z1) → c251(PAIR(z0, z1))
PAIR(z0, mark(z1)) → c252(PAIR(z0, z1))
PAIR(active(z0), z1) → c253(PAIR(z0, z1))
PAIR(z0, active(z1)) → c254(PAIR(z0, z1))
U201'(mark(z0), z1, z2, z3) → c255(U201'(z0, z1, z2, z3))
U201'(z0, mark(z1), z2, z3) → c256(U201'(z0, z1, z2, z3))
U201'(z0, z1, mark(z2), z3) → c257(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, mark(z3)) → c258(U201'(z0, z1, z2, z3))
U201'(active(z0), z1, z2, z3) → c259(U201'(z0, z1, z2, z3))
U201'(z0, active(z1), z2, z3) → c260(U201'(z0, z1, z2, z3))
U201'(z0, z1, active(z2), z3) → c261(U201'(z0, z1, z2, z3))
U201'(z0, z1, z2, active(z3)) → c262(U201'(z0, z1, z2, z3))
U202'(mark(z0), z1) → c263(U202'(z0, z1))
U202'(z0, mark(z1)) → c264(U202'(z0, z1))
U202'(active(z0), z1) → c265(U202'(z0, z1))
U202'(z0, active(z1)) → c266(U202'(z0, z1))
U21'(mark(z0), z1) → c267(U21'(z0, z1))
U21'(z0, mark(z1)) → c268(U21'(z0, z1))
U21'(active(z0), z1) → c269(U21'(z0, z1))
U21'(z0, active(z1)) → c270(U21'(z0, z1))
U211'(mark(z0), z1) → c271(U211'(z0, z1))
U211'(z0, mark(z1)) → c272(U211'(z0, z1))
U211'(active(z0), z1) → c273(U211'(z0, z1))
U211'(z0, active(z1)) → c274(U211'(z0, z1))
U221'(mark(z0), z1, z2) → c275(U221'(z0, z1, z2))
U221'(z0, mark(z1), z2) → c276(U221'(z0, z1, z2))
U221'(z0, z1, mark(z2)) → c277(U221'(z0, z1, z2))
U221'(active(z0), z1, z2) → c278(U221'(z0, z1, z2))
U221'(z0, active(z1), z2) → c279(U221'(z0, z1, z2))
U221'(z0, z1, active(z2)) → c280(U221'(z0, z1, z2))
FST(mark(z0)) → c281(FST(z0))
FST(active(z0)) → c282(FST(z0))
U31'(mark(z0), z1) → c283(U31'(z0, z1))
U31'(z0, mark(z1)) → c284(U31'(z0, z1))
U31'(active(z0), z1) → c285(U31'(z0, z1))
U31'(z0, active(z1)) → c286(U31'(z0, z1))
U41'(mark(z0), z1, z2) → c287(U41'(z0, z1, z2))
U41'(z0, mark(z1), z2) → c288(U41'(z0, z1, z2))
U41'(z0, z1, mark(z2)) → c289(U41'(z0, z1, z2))
U41'(active(z0), z1, z2) → c290(U41'(z0, z1, z2))
U41'(z0, active(z1), z2) → c291(U41'(z0, z1, z2))
U41'(z0, z1, active(z2)) → c292(U41'(z0, z1, z2))
U42'(mark(z0), z1) → c293(U42'(z0, z1))
U42'(z0, mark(z1)) → c294(U42'(z0, z1))
U42'(active(z0), z1) → c295(U42'(z0, z1))
U42'(z0, active(z1)) → c296(U42'(z0, z1))
U43'(mark(z0)) → c297(U43'(z0))
U43'(active(z0)) → c298(U43'(z0))
U51'(mark(z0), z1, z2) → c299(U51'(z0, z1, z2))
U51'(z0, mark(z1), z2) → c300(U51'(z0, z1, z2))
U51'(z0, z1, mark(z2)) → c301(U51'(z0, z1, z2))
U51'(active(z0), z1, z2) → c302(U51'(z0, z1, z2))
U51'(z0, active(z1), z2) → c303(U51'(z0, z1, z2))
U51'(z0, z1, active(z2)) → c304(U51'(z0, z1, z2))
U52'(mark(z0), z1) → c305(U52'(z0, z1))
U52'(z0, mark(z1)) → c306(U52'(z0, z1))
U52'(active(z0), z1) → c307(U52'(z0, z1))
U52'(z0, active(z1)) → c308(U52'(z0, z1))
U53'(mark(z0)) → c309(U53'(z0))
U53'(active(z0)) → c310(U53'(z0))
U61'(mark(z0), z1) → c311(U61'(z0, z1))
U61'(z0, mark(z1)) → c312(U61'(z0, z1))
U61'(active(z0), z1) → c313(U61'(z0, z1))
U61'(z0, active(z1)) → c314(U61'(z0, z1))
U62'(mark(z0)) → c315(U62'(z0))
U62'(active(z0)) → c316(U62'(z0))
ISPLNAT(mark(z0)) → c317(ISPLNAT(z0))
ISPLNAT(active(z0)) → c318(ISPLNAT(z0))
U71'(mark(z0), z1) → c319(U71'(z0, z1))
U71'(z0, mark(z1)) → c320(U71'(z0, z1))
U71'(active(z0), z1) → c321(U71'(z0, z1))
U71'(z0, active(z1)) → c322(U71'(z0, z1))
U72'(mark(z0)) → c323(U72'(z0))
U72'(active(z0)) → c324(U72'(z0))
U81'(mark(z0), z1) → c325(U81'(z0, z1))
U81'(z0, mark(z1)) → c326(U81'(z0, z1))
U81'(active(z0), z1) → c327(U81'(z0, z1))
U81'(z0, active(z1)) → c328(U81'(z0, z1))
U82'(mark(z0)) → c329(U82'(z0))
U82'(active(z0)) → c330(U82'(z0))
U91'(mark(z0), z1) → c331(U91'(z0, z1))
U91'(z0, mark(z1)) → c332(U91'(z0, z1))
U91'(active(z0), z1) → c333(U91'(z0, z1))
U91'(z0, active(z1)) → c334(U91'(z0, z1))
U92'(mark(z0)) → c335(U92'(z0))
U92'(active(z0)) → c336(U92'(z0))
AND(mark(z0), z1) → c337(AND(z0, z1))
AND(z0, mark(z1)) → c338(AND(z0, z1))
AND(active(z0), z1) → c339(AND(z0, z1))
AND(z0, active(z1)) → c340(AND(z0, z1))
ISNATURALKIND(mark(z0)) → c341(ISNATURALKIND(z0))
ISNATURALKIND(active(z0)) → c342(ISNATURALKIND(z0))
ISLNATKIND(mark(z0)) → c343(ISLNATKIND(z0))
ISLNATKIND(active(z0)) → c344(ISLNATKIND(z0))
ISPLNATKIND(mark(z0)) → c345(ISPLNATKIND(z0))
ISPLNATKIND(active(z0)) → c346(ISPLNATKIND(z0))
TAIL(mark(z0)) → c347(TAIL(z0))
TAIL(active(z0)) → c348(TAIL(z0))
TAKE(mark(z0), z1) → c349(TAKE(z0, z1))
TAKE(z0, mark(z1)) → c350(TAKE(z0, z1))
TAKE(active(z0), z1) → c351(TAKE(z0, z1))
TAKE(z0, active(z1)) → c352(TAKE(z0, z1))
SEL(mark(z0), z1) → c353(SEL(z0, z1))
SEL(z0, mark(z1)) → c354(SEL(z0, z1))
SEL(active(z0), z1) → c355(SEL(z0, z1))
SEL(z0, active(z1)) → c356(SEL(z0, z1))

(4) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0, z1)) → mark(U102(isNatural(z0), z1))
active(U102(tt, z0)) → mark(U103(isLNat(z0)))
active(U103(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U111(tt, z0)) → mark(U112(isLNat(z0)))
active(U112(tt)) → mark(tt)
active(U121(tt, z0)) → mark(U122(isNatural(z0)))
active(U122(tt)) → mark(tt)
active(U131(tt, z0, z1)) → mark(U132(isNatural(z0), z1))
active(U132(tt, z0)) → mark(U133(isLNat(z0)))
active(U133(tt)) → mark(tt)
active(U141(tt, z0, z1)) → mark(U142(isLNat(z0), z1))
active(U142(tt, z0)) → mark(U143(isLNat(z0)))
active(U143(tt)) → mark(tt)
active(U151(tt, z0, z1)) → mark(U152(isNatural(z0), z1))
active(U152(tt, z0)) → mark(U153(isLNat(z0)))
active(U153(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(splitAt(z0, z2), z1))
active(U202(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0)) → mark(z0)
active(U211(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(isNatural(z0), z1))
active(U42(tt, z0)) → mark(U43(isLNat(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNatural(z0), z1))
active(U52(tt, z0)) → mark(U53(isLNat(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isPLNat(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatural(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt, z0)) → mark(U82(isPLNat(z0)))
active(U82(tt)) → mark(tt)
active(U91(tt, z0)) → mark(U92(isLNat(z0)))
active(U92(tt)) → mark(tt)
active(afterNth(z0, z1)) → mark(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(and(tt, z0)) → mark(z0)
active(fst(pair(z0, z1))) → mark(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(head(cons(z0, z1))) → mark(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(cons(z0, z1))) → mark(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(fst(z0))) → mark(U61(isPLNatKind(z0), z0))
active(isLNat(natsFrom(z0))) → mark(U71(isNaturalKind(z0), z0))
active(isLNat(snd(z0))) → mark(U81(isPLNatKind(z0), z0))
active(isLNat(tail(z0))) → mark(U91(isLNatKind(z0), z0))
active(isLNat(take(z0, z1))) → mark(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNatKind(nil)) → mark(tt)
active(isLNatKind(afterNth(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(cons(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(fst(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(natsFrom(z0))) → mark(isNaturalKind(z0))
active(isLNatKind(snd(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(tail(z0))) → mark(isLNatKind(z0))
active(isLNatKind(take(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNatKind(z0), z0))
active(isNatural(s(z0))) → mark(U121(isNaturalKind(z0), z0))
active(isNatural(sel(z0, z1))) → mark(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isNaturalKind(0)) → mark(tt)
active(isNaturalKind(head(z0))) → mark(isLNatKind(z0))
active(isNaturalKind(s(z0))) → mark(isNaturalKind(z0))
active(isNaturalKind(sel(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isPLNat(pair(z0, z1))) → mark(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNatKind(pair(z0, z1))) → mark(and(isLNatKind(z0), isLNatKind(z1)))
active(isPLNatKind(splitAt(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(natsFrom(z0)) → mark(U161(and(isNatural(z0), isNaturalKind(z0)), z0))
active(sel(z0, z1)) → mark(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(splitAt(0, z0)) → mark(U191(and(isLNat(z0), isLNatKind(z0)), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(take(z0, z1)) → mark(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1)) → active(U102(mark(z0), z1))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U103(z0)) → active(U103(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U111(z0, z1)) → active(U111(mark(z0), z1))
mark(U112(z0)) → active(U112(mark(z0)))
mark(U121(z0, z1)) → active(U121(mark(z0), z1))
mark(U122(z0)) → active(U122(mark(z0)))
mark(U131(z0, z1, z2)) → active(U131(mark(z0), z1, z2))
mark(U132(z0, z1)) → active(U132(mark(z0), z1))
mark(U133(z0)) → active(U133(mark(z0)))
mark(U141(z0, z1, z2)) → active(U141(mark(z0), z1, z2))
mark(U142(z0, z1)) → active(U142(mark(z0), z1))
mark(U143(z0)) → active(U143(mark(z0)))
mark(U151(z0, z1, z2)) → active(U151(mark(z0), z1, z2))
mark(U152(z0, z1)) → active(U152(mark(z0), z1))
mark(U153(z0)) → active(U153(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(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(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)) → active(U202(mark(z0), z1))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(U81(z0, z1)) → active(U81(mark(z0), z1))
mark(U82(z0)) → active(U82(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isNaturalKind(z0)) → active(isNaturalKind(z0))
mark(isLNatKind(z0)) → active(isLNatKind(z0))
mark(isPLNatKind(z0)) → active(isPLNatKind(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, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1) → U102(z0, z1)
U102(z0, mark(z1)) → U102(z0, z1)
U102(active(z0), z1) → U102(z0, z1)
U102(z0, active(z1)) → U102(z0, z1)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U103(mark(z0)) → U103(z0)
U103(active(z0)) → U103(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)
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)
U111(mark(z0), z1) → U111(z0, z1)
U111(z0, mark(z1)) → U111(z0, z1)
U111(active(z0), z1) → U111(z0, z1)
U111(z0, active(z1)) → U111(z0, z1)
U112(mark(z0)) → U112(z0)
U112(active(z0)) → U112(z0)
U121(mark(z0), z1) → U121(z0, z1)
U121(z0, mark(z1)) → U121(z0, z1)
U121(active(z0), z1) → U121(z0, z1)
U121(z0, active(z1)) → U121(z0, z1)
U122(mark(z0)) → U122(z0)
U122(active(z0)) → U122(z0)
U131(mark(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, mark(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, mark(z2)) → U131(z0, z1, z2)
U131(active(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, active(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, active(z2)) → U131(z0, z1, z2)
U132(mark(z0), z1) → U132(z0, z1)
U132(z0, mark(z1)) → U132(z0, z1)
U132(active(z0), z1) → U132(z0, z1)
U132(z0, active(z1)) → U132(z0, z1)
U133(mark(z0)) → U133(z0)
U133(active(z0)) → U133(z0)
U141(mark(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, mark(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, mark(z2)) → U141(z0, z1, z2)
U141(active(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, active(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, active(z2)) → U141(z0, z1, z2)
U142(mark(z0), z1) → U142(z0, z1)
U142(z0, mark(z1)) → U142(z0, z1)
U142(active(z0), z1) → U142(z0, z1)
U142(z0, active(z1)) → U142(z0, z1)
U143(mark(z0)) → U143(z0)
U143(active(z0)) → U143(z0)
U151(mark(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, mark(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, mark(z2)) → U151(z0, z1, z2)
U151(active(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, active(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, active(z2)) → U151(z0, z1, z2)
U152(mark(z0), z1) → U152(z0, z1)
U152(z0, mark(z1)) → U152(z0, z1)
U152(active(z0), z1) → U152(z0, z1)
U152(z0, active(z1)) → U152(z0, z1)
U153(mark(z0)) → U153(z0)
U153(active(z0)) → U153(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)
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)
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) → U202(z0, z1)
U202(z0, mark(z1)) → U202(z0, z1)
U202(active(z0), z1) → U202(z0, z1)
U202(z0, active(z1)) → U202(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(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)
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)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
U81(mark(z0), z1) → U81(z0, z1)
U81(z0, mark(z1)) → U81(z0, z1)
U81(active(z0), z1) → U81(z0, z1)
U81(z0, active(z1)) → U81(z0, z1)
U82(mark(z0)) → U82(z0)
U82(active(z0)) → U82(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isNaturalKind(mark(z0)) → isNaturalKind(z0)
isNaturalKind(active(z0)) → isNaturalKind(z0)
isLNatKind(mark(z0)) → isLNatKind(z0)
isLNatKind(active(z0)) → isLNatKind(z0)
isPLNatKind(mark(z0)) → isPLNatKind(z0)
isPLNatKind(active(z0)) → isPLNatKind(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) → c81(ACTIVE(tt))
MARK(nil) → c112(ACTIVE(nil))
MARK(0) → c141(ACTIVE(0))

S tuples:

MARK(tt) → c81(ACTIVE(tt))
MARK(nil) → c112(ACTIVE(nil))
MARK(0) → c141(ACTIVE(0))

K tuples:none
Defined Rule Symbols:

active, mark, U101, U102, isNatural, U103, isLNat, U11, snd, splitAt, U111, U112, U121, U122, U131, U132, U133, U141, U142, U143, U151, U152, U153, U161, cons, natsFrom, s, U171, head, afterNth, U181, U191, pair, U201, U202, U21, U211, U221, fst, U31, U41, U42, U43, U51, U52, U53, U61, U62, isPLNat, U71, U72, U81, U82, U91, U92, and, isNaturalKind, isLNatKind, isPLNatKind, tail, take, sel

Defined Pair Symbols:

MARK

Compound Symbols:

c81, c112, c141

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

Removed 3 trailing nodes:

MARK(nil) → c112(ACTIVE(nil))
MARK(tt) → c81(ACTIVE(tt))
MARK(0) → c141(ACTIVE(0))

(6) Obligation:

Complexity Dependency Tuples Problem
Rules:

active(U101(tt, z0, z1)) → mark(U102(isNatural(z0), z1))
active(U102(tt, z0)) → mark(U103(isLNat(z0)))
active(U103(tt)) → mark(tt)
active(U11(tt, z0, z1)) → mark(snd(splitAt(z0, z1)))
active(U111(tt, z0)) → mark(U112(isLNat(z0)))
active(U112(tt)) → mark(tt)
active(U121(tt, z0)) → mark(U122(isNatural(z0)))
active(U122(tt)) → mark(tt)
active(U131(tt, z0, z1)) → mark(U132(isNatural(z0), z1))
active(U132(tt, z0)) → mark(U133(isLNat(z0)))
active(U133(tt)) → mark(tt)
active(U141(tt, z0, z1)) → mark(U142(isLNat(z0), z1))
active(U142(tt, z0)) → mark(U143(isLNat(z0)))
active(U143(tt)) → mark(tt)
active(U151(tt, z0, z1)) → mark(U152(isNatural(z0), z1))
active(U152(tt, z0)) → mark(U153(isLNat(z0)))
active(U153(tt)) → mark(tt)
active(U161(tt, z0)) → mark(cons(z0, natsFrom(s(z0))))
active(U171(tt, z0, z1)) → mark(head(afterNth(z0, z1)))
active(U181(tt, z0)) → mark(z0)
active(U191(tt, z0)) → mark(pair(nil, z0))
active(U201(tt, z0, z1, z2)) → mark(U202(splitAt(z0, z2), z1))
active(U202(pair(z0, z1), z2)) → mark(pair(cons(z2, z0), z1))
active(U21(tt, z0)) → mark(z0)
active(U211(tt, z0)) → mark(z0)
active(U221(tt, z0, z1)) → mark(fst(splitAt(z0, z1)))
active(U31(tt, z0)) → mark(z0)
active(U41(tt, z0, z1)) → mark(U42(isNatural(z0), z1))
active(U42(tt, z0)) → mark(U43(isLNat(z0)))
active(U43(tt)) → mark(tt)
active(U51(tt, z0, z1)) → mark(U52(isNatural(z0), z1))
active(U52(tt, z0)) → mark(U53(isLNat(z0)))
active(U53(tt)) → mark(tt)
active(U61(tt, z0)) → mark(U62(isPLNat(z0)))
active(U62(tt)) → mark(tt)
active(U71(tt, z0)) → mark(U72(isNatural(z0)))
active(U72(tt)) → mark(tt)
active(U81(tt, z0)) → mark(U82(isPLNat(z0)))
active(U82(tt)) → mark(tt)
active(U91(tt, z0)) → mark(U92(isLNat(z0)))
active(U92(tt)) → mark(tt)
active(afterNth(z0, z1)) → mark(U11(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(and(tt, z0)) → mark(z0)
active(fst(pair(z0, z1))) → mark(U21(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(head(cons(z0, z1))) → mark(U31(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0))
active(isLNat(nil)) → mark(tt)
active(isLNat(afterNth(z0, z1))) → mark(U41(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(cons(z0, z1))) → mark(U51(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNat(fst(z0))) → mark(U61(isPLNatKind(z0), z0))
active(isLNat(natsFrom(z0))) → mark(U71(isNaturalKind(z0), z0))
active(isLNat(snd(z0))) → mark(U81(isPLNatKind(z0), z0))
active(isLNat(tail(z0))) → mark(U91(isLNatKind(z0), z0))
active(isLNat(take(z0, z1))) → mark(U101(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isLNatKind(nil)) → mark(tt)
active(isLNatKind(afterNth(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(cons(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isLNatKind(fst(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(natsFrom(z0))) → mark(isNaturalKind(z0))
active(isLNatKind(snd(z0))) → mark(isPLNatKind(z0))
active(isLNatKind(tail(z0))) → mark(isLNatKind(z0))
active(isLNatKind(take(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isNatural(0)) → mark(tt)
active(isNatural(head(z0))) → mark(U111(isLNatKind(z0), z0))
active(isNatural(s(z0))) → mark(U121(isNaturalKind(z0), z0))
active(isNatural(sel(z0, z1))) → mark(U131(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isNaturalKind(0)) → mark(tt)
active(isNaturalKind(head(z0))) → mark(isLNatKind(z0))
active(isNaturalKind(s(z0))) → mark(isNaturalKind(z0))
active(isNaturalKind(sel(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(isPLNat(pair(z0, z1))) → mark(U141(and(isLNatKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNat(splitAt(z0, z1))) → mark(U151(and(isNaturalKind(z0), isLNatKind(z1)), z0, z1))
active(isPLNatKind(pair(z0, z1))) → mark(and(isLNatKind(z0), isLNatKind(z1)))
active(isPLNatKind(splitAt(z0, z1))) → mark(and(isNaturalKind(z0), isLNatKind(z1)))
active(natsFrom(z0)) → mark(U161(and(isNatural(z0), isNaturalKind(z0)), z0))
active(sel(z0, z1)) → mark(U171(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
active(snd(pair(z0, z1))) → mark(U181(and(and(isLNat(z0), isLNatKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(splitAt(0, z0)) → mark(U191(and(isLNat(z0), isLNatKind(z0)), z0))
active(splitAt(s(z0), cons(z1, z2))) → mark(U201(and(and(isNatural(z0), isNaturalKind(z0)), and(and(isNatural(z1), isNaturalKind(z1)), and(isLNat(z2), isLNatKind(z2)))), z0, z1, z2))
active(tail(cons(z0, z1))) → mark(U211(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z1))
active(take(z0, z1)) → mark(U221(and(and(isNatural(z0), isNaturalKind(z0)), and(isLNat(z1), isLNatKind(z1))), z0, z1))
mark(U101(z0, z1, z2)) → active(U101(mark(z0), z1, z2))
mark(tt) → active(tt)
mark(U102(z0, z1)) → active(U102(mark(z0), z1))
mark(isNatural(z0)) → active(isNatural(z0))
mark(U103(z0)) → active(U103(mark(z0)))
mark(isLNat(z0)) → active(isLNat(z0))
mark(U11(z0, z1, z2)) → active(U11(mark(z0), z1, z2))
mark(snd(z0)) → active(snd(mark(z0)))
mark(splitAt(z0, z1)) → active(splitAt(mark(z0), mark(z1)))
mark(U111(z0, z1)) → active(U111(mark(z0), z1))
mark(U112(z0)) → active(U112(mark(z0)))
mark(U121(z0, z1)) → active(U121(mark(z0), z1))
mark(U122(z0)) → active(U122(mark(z0)))
mark(U131(z0, z1, z2)) → active(U131(mark(z0), z1, z2))
mark(U132(z0, z1)) → active(U132(mark(z0), z1))
mark(U133(z0)) → active(U133(mark(z0)))
mark(U141(z0, z1, z2)) → active(U141(mark(z0), z1, z2))
mark(U142(z0, z1)) → active(U142(mark(z0), z1))
mark(U143(z0)) → active(U143(mark(z0)))
mark(U151(z0, z1, z2)) → active(U151(mark(z0), z1, z2))
mark(U152(z0, z1)) → active(U152(mark(z0), z1))
mark(U153(z0)) → active(U153(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(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(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)) → active(U202(mark(z0), z1))
mark(U21(z0, z1)) → active(U21(mark(z0), z1))
mark(U211(z0, z1)) → active(U211(mark(z0), z1))
mark(U221(z0, z1, z2)) → active(U221(mark(z0), z1, z2))
mark(fst(z0)) → active(fst(mark(z0)))
mark(U31(z0, z1)) → active(U31(mark(z0), z1))
mark(U41(z0, z1, z2)) → active(U41(mark(z0), z1, z2))
mark(U42(z0, z1)) → active(U42(mark(z0), z1))
mark(U43(z0)) → active(U43(mark(z0)))
mark(U51(z0, z1, z2)) → active(U51(mark(z0), z1, z2))
mark(U52(z0, z1)) → active(U52(mark(z0), z1))
mark(U53(z0)) → active(U53(mark(z0)))
mark(U61(z0, z1)) → active(U61(mark(z0), z1))
mark(U62(z0)) → active(U62(mark(z0)))
mark(isPLNat(z0)) → active(isPLNat(z0))
mark(U71(z0, z1)) → active(U71(mark(z0), z1))
mark(U72(z0)) → active(U72(mark(z0)))
mark(U81(z0, z1)) → active(U81(mark(z0), z1))
mark(U82(z0)) → active(U82(mark(z0)))
mark(U91(z0, z1)) → active(U91(mark(z0), z1))
mark(U92(z0)) → active(U92(mark(z0)))
mark(and(z0, z1)) → active(and(mark(z0), z1))
mark(isNaturalKind(z0)) → active(isNaturalKind(z0))
mark(isLNatKind(z0)) → active(isLNatKind(z0))
mark(isPLNatKind(z0)) → active(isPLNatKind(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, z2) → U101(z0, z1, z2)
U101(z0, mark(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, mark(z2)) → U101(z0, z1, z2)
U101(active(z0), z1, z2) → U101(z0, z1, z2)
U101(z0, active(z1), z2) → U101(z0, z1, z2)
U101(z0, z1, active(z2)) → U101(z0, z1, z2)
U102(mark(z0), z1) → U102(z0, z1)
U102(z0, mark(z1)) → U102(z0, z1)
U102(active(z0), z1) → U102(z0, z1)
U102(z0, active(z1)) → U102(z0, z1)
isNatural(mark(z0)) → isNatural(z0)
isNatural(active(z0)) → isNatural(z0)
U103(mark(z0)) → U103(z0)
U103(active(z0)) → U103(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)
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)
U111(mark(z0), z1) → U111(z0, z1)
U111(z0, mark(z1)) → U111(z0, z1)
U111(active(z0), z1) → U111(z0, z1)
U111(z0, active(z1)) → U111(z0, z1)
U112(mark(z0)) → U112(z0)
U112(active(z0)) → U112(z0)
U121(mark(z0), z1) → U121(z0, z1)
U121(z0, mark(z1)) → U121(z0, z1)
U121(active(z0), z1) → U121(z0, z1)
U121(z0, active(z1)) → U121(z0, z1)
U122(mark(z0)) → U122(z0)
U122(active(z0)) → U122(z0)
U131(mark(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, mark(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, mark(z2)) → U131(z0, z1, z2)
U131(active(z0), z1, z2) → U131(z0, z1, z2)
U131(z0, active(z1), z2) → U131(z0, z1, z2)
U131(z0, z1, active(z2)) → U131(z0, z1, z2)
U132(mark(z0), z1) → U132(z0, z1)
U132(z0, mark(z1)) → U132(z0, z1)
U132(active(z0), z1) → U132(z0, z1)
U132(z0, active(z1)) → U132(z0, z1)
U133(mark(z0)) → U133(z0)
U133(active(z0)) → U133(z0)
U141(mark(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, mark(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, mark(z2)) → U141(z0, z1, z2)
U141(active(z0), z1, z2) → U141(z0, z1, z2)
U141(z0, active(z1), z2) → U141(z0, z1, z2)
U141(z0, z1, active(z2)) → U141(z0, z1, z2)
U142(mark(z0), z1) → U142(z0, z1)
U142(z0, mark(z1)) → U142(z0, z1)
U142(active(z0), z1) → U142(z0, z1)
U142(z0, active(z1)) → U142(z0, z1)
U143(mark(z0)) → U143(z0)
U143(active(z0)) → U143(z0)
U151(mark(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, mark(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, mark(z2)) → U151(z0, z1, z2)
U151(active(z0), z1, z2) → U151(z0, z1, z2)
U151(z0, active(z1), z2) → U151(z0, z1, z2)
U151(z0, z1, active(z2)) → U151(z0, z1, z2)
U152(mark(z0), z1) → U152(z0, z1)
U152(z0, mark(z1)) → U152(z0, z1)
U152(active(z0), z1) → U152(z0, z1)
U152(z0, active(z1)) → U152(z0, z1)
U153(mark(z0)) → U153(z0)
U153(active(z0)) → U153(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)
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)
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) → U202(z0, z1)
U202(z0, mark(z1)) → U202(z0, z1)
U202(active(z0), z1) → U202(z0, z1)
U202(z0, active(z1)) → U202(z0, z1)
U21(mark(z0), z1) → U21(z0, z1)
U21(z0, mark(z1)) → U21(z0, z1)
U21(active(z0), z1) → U21(z0, z1)
U21(z0, active(z1)) → U21(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)
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)
fst(mark(z0)) → fst(z0)
fst(active(z0)) → fst(z0)
U31(mark(z0), z1) → U31(z0, z1)
U31(z0, mark(z1)) → U31(z0, z1)
U31(active(z0), z1) → U31(z0, z1)
U31(z0, active(z1)) → U31(z0, z1)
U41(mark(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, mark(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, mark(z2)) → U41(z0, z1, z2)
U41(active(z0), z1, z2) → U41(z0, z1, z2)
U41(z0, active(z1), z2) → U41(z0, z1, z2)
U41(z0, z1, active(z2)) → U41(z0, z1, z2)
U42(mark(z0), z1) → U42(z0, z1)
U42(z0, mark(z1)) → U42(z0, z1)
U42(active(z0), z1) → U42(z0, z1)
U42(z0, active(z1)) → U42(z0, z1)
U43(mark(z0)) → U43(z0)
U43(active(z0)) → U43(z0)
U51(mark(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, mark(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, mark(z2)) → U51(z0, z1, z2)
U51(active(z0), z1, z2) → U51(z0, z1, z2)
U51(z0, active(z1), z2) → U51(z0, z1, z2)
U51(z0, z1, active(z2)) → U51(z0, z1, z2)
U52(mark(z0), z1) → U52(z0, z1)
U52(z0, mark(z1)) → U52(z0, z1)
U52(active(z0), z1) → U52(z0, z1)
U52(z0, active(z1)) → U52(z0, z1)
U53(mark(z0)) → U53(z0)
U53(active(z0)) → U53(z0)
U61(mark(z0), z1) → U61(z0, z1)
U61(z0, mark(z1)) → U61(z0, z1)
U61(active(z0), z1) → U61(z0, z1)
U61(z0, active(z1)) → U61(z0, z1)
U62(mark(z0)) → U62(z0)
U62(active(z0)) → U62(z0)
isPLNat(mark(z0)) → isPLNat(z0)
isPLNat(active(z0)) → isPLNat(z0)
U71(mark(z0), z1) → U71(z0, z1)
U71(z0, mark(z1)) → U71(z0, z1)
U71(active(z0), z1) → U71(z0, z1)
U71(z0, active(z1)) → U71(z0, z1)
U72(mark(z0)) → U72(z0)
U72(active(z0)) → U72(z0)
U81(mark(z0), z1) → U81(z0, z1)
U81(z0, mark(z1)) → U81(z0, z1)
U81(active(z0), z1) → U81(z0, z1)
U81(z0, active(z1)) → U81(z0, z1)
U82(mark(z0)) → U82(z0)
U82(active(z0)) → U82(z0)
U91(mark(z0), z1) → U91(z0, z1)
U91(z0, mark(z1)) → U91(z0, z1)
U91(active(z0), z1) → U91(z0, z1)
U91(z0, active(z1)) → U91(z0, z1)
U92(mark(z0)) → U92(z0)
U92(active(z0)) → U92(z0)
and(mark(z0), z1) → and(z0, z1)
and(z0, mark(z1)) → and(z0, z1)
and(active(z0), z1) → and(z0, z1)
and(z0, active(z1)) → and(z0, z1)
isNaturalKind(mark(z0)) → isNaturalKind(z0)
isNaturalKind(active(z0)) → isNaturalKind(z0)
isLNatKind(mark(z0)) → isLNatKind(z0)
isLNatKind(active(z0)) → isLNatKind(z0)
isPLNatKind(mark(z0)) → isPLNatKind(z0)
isPLNatKind(active(z0)) → isPLNatKind(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, isNatural, U103, isLNat, U11, snd, splitAt, U111, U112, U121, U122, U131, U132, U133, U141, U142, U143, U151, U152, U153, U161, cons, natsFrom, s, U171, head, afterNth, U181, U191, pair, U201, U202, U21, U211, U221, fst, U31, U41, U42, U43, U51, U52, U53, U61, U62, isPLNat, U71, U72, U81, U82, U91, U92, and, isNaturalKind, isLNatKind, isPLNatKind, 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))