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)

↳ QTRS

  ↳ DependencyPairsProof

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)

U121¹(active(X1), X2) → U121¹(X1, X2)
ACTIVE(U42(tt, V2)) → U43¹(isLNat(V2))
ACTIVE(isNatural(sel(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
TAIL(active(X)) → TAIL(X)
ACTIVE(U62(tt)) → MARK(tt)
ACTIVE(isPLNatKind(splitAt(V1, V2))) → ISNATURALKIND(V1)
ACTIVE(U71(tt, V1)) → U72¹(isNatural(V1))
ACTIVE(splitAt(s(N), cons(X, XS))) → U201¹(and(and(isNatural(N), isNaturalKind(N)), and(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS)))), N, X, XS)
ACTIVE(U142(tt, V2)) → U143¹(isLNat(V2))
MARK(U201(X1, X2, X3, X4)) → U201¹(mark(X1), X2, X3, X4)
FST(mark(X)) → FST(X)
ACTIVE(sel(N, XS)) → MARK(U171(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
ACTIVE(U201(tt, N, X, XS)) → U202¹(splitAt(N, XS), X)
ACTIVE(isNatural(s(V1))) → MARK(U121(isNaturalKind(V1), V1))
ACTIVE(head(cons(N, XS))) → U31¹(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N)
ACTIVE(isLNat(tail(V1))) → ISLNATKIND(V1)
MARK(snd(X)) → SND(mark(X))
MARK(tail(X)) → TAIL(mark(X))
U31¹(mark(X1), X2) → U31¹(X1, X2)
ACTIVE(isLNat(fst(V1))) → ISPLNATKIND(V1)
ACTIVE(take(N, XS)) → AND(isLNat(XS), isLNatKind(XS))
U81¹(mark(X1), X2) → U81¹(X1, X2)
ACTIVE(head(cons(N, XS))) → MARK(U31(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N))
TAKE(active(X1), X2) → TAKE(X1, X2)
U121¹(X1, mark(X2)) → U121¹(X1, X2)
MARK(U133(X)) → ACTIVE(U133(mark(X)))
MARK(U161(X1, X2)) → MARK(X1)
AFTERNTH(active(X1), X2) → AFTERNTH(X1, X2)
ISNATURAL(mark(X)) → ISNATURAL(X)
MARK(U201(X1, X2, X3, X4)) → ACTIVE(U201(mark(X1), X2, X3, X4))
MARK(natsFrom(X)) → ACTIVE(natsFrom(mark(X)))
ACTIVE(fst(pair(X, Y))) → ISLNATKIND(Y)
MARK(U41(X1, X2, X3)) → ACTIVE(U41(mark(X1), X2, X3))
ACTIVE(U11(tt, N, XS)) → SPLITAT(N, XS)
MARK(afterNth(X1, X2)) → ACTIVE(afterNth(mark(X1), mark(X2)))
U112¹(mark(X)) → U112¹(X)
MARK(U62(X)) → ACTIVE(U62(mark(X)))
ACTIVE(isNaturalKind(sel(V1, V2))) → ISNATURALKIND(V1)
ACTIVE(isLNat(nil)) → MARK(tt)
MARK(U121(X1, X2)) → ACTIVE(U121(mark(X1), X2))
ISLNATKIND(active(X)) → ISLNATKIND(X)
U101¹(active(X1), X2, X3) → U101¹(X1, X2, X3)
U132¹(X1, active(X2)) → U132¹(X1, X2)
ISLNAT(active(X)) → ISLNAT(X)
ACTIVE(U141(tt, V1, V2)) → U142¹(isLNat(V1), V2)
MARK(U143(X)) → ACTIVE(U143(mark(X)))
U102¹(X1, active(X2)) → U102¹(X1, X2)
MARK(U61(X1, X2)) → ACTIVE(U61(mark(X1), X2))
ACTIVE(isPLNat(splitAt(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
MARK(U31(X1, X2)) → U31¹(mark(X1), X2)
MARK(s(X)) → ACTIVE(s(mark(X)))
ACTIVE(isPLNatKind(pair(V1, V2))) → ISLNATKIND(V1)
U21¹(X1, mark(X2)) → U21¹(X1, X2)
U111¹(mark(X1), X2) → U111¹(X1, X2)
ISLNATKIND(mark(X)) → ISLNATKIND(X)
ACTIVE(natsFrom(N)) → ISNATURAL(N)
U72¹(mark(X)) → U72¹(X)
ACTIVE(isPLNatKind(pair(V1, V2))) → ISLNATKIND(V2)
S(mark(X)) → S(X)
MARK(U191(X1, X2)) → ACTIVE(U191(mark(X1), X2))
MARK(sel(X1, X2)) → ACTIVE(sel(mark(X1), mark(X2)))
MARK(U71(X1, X2)) → MARK(X1)
ACTIVE(afterNth(N, XS)) → ISNATURALKIND(N)
MARK(sel(X1, X2)) → SEL(mark(X1), mark(X2))
ACTIVE(isLNat(afterNth(V1, V2))) → ISLNATKIND(V2)
ACTIVE(U101(tt, V1, V2)) → ISNATURAL(V1)
MARK(U152(X1, X2)) → MARK(X1)
ACTIVE(sel(N, XS)) → ISNATURAL(N)
U152¹(mark(X1), X2) → U152¹(X1, X2)
MARK(U112(X)) → MARK(X)
U151¹(mark(X1), X2, X3) → U151¹(X1, X2, X3)
U131¹(X1, mark(X2), X3) → U131¹(X1, X2, X3)
ACTIVE(isNaturalKind(head(V1))) → MARK(isLNatKind(V1))
ISNATURAL(active(X)) → ISNATURAL(X)
MARK(U11(X1, X2, X3)) → U11¹(mark(X1), X2, X3)
ACTIVE(isNatural(head(V1))) → ISLNATKIND(V1)
U181¹(active(X1), X2) → U181¹(X1, X2)
U122¹(active(X)) → U122¹(X)
MARK(U131(X1, X2, X3)) → MARK(X1)
MARK(U62(X)) → U62¹(mark(X))
MARK(U81(X1, X2)) → ACTIVE(U81(mark(X1), X2))
U151¹(X1, X2, active(X3)) → U151¹(X1, X2, X3)
ACTIVE(sel(N, XS)) → AND(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS)))
U61¹(X1, mark(X2)) → U61¹(X1, X2)
ACTIVE(U141(tt, V1, V2)) → ISLNAT(V1)
MARK(U51(X1, X2, X3)) → MARK(X1)
ACTIVE(U211(tt, XS)) → MARK(XS)
U131¹(active(X1), X2, X3) → U131¹(X1, X2, X3)
U53¹(active(X)) → U53¹(X)
ACTIVE(fst(pair(X, Y))) → AND(isLNat(X), isLNatKind(X))
ACTIVE(take(N, XS)) → AND(isNatural(N), isNaturalKind(N))
ACTIVE(isPLNat(pair(V1, V2))) → AND(isLNatKind(V1), isLNatKind(V2))
MARK(U11(X1, X2, X3)) → MARK(X1)
MARK(U41(X1, X2, X3)) → MARK(X1)
MARK(cons(X1, X2)) → CONS(mark(X1), X2)
ACTIVE(tail(cons(N, XS))) → AND(isLNat(XS), isLNatKind(XS))
MARK(splitAt(X1, X2)) → MARK(X2)
U91¹(X1, mark(X2)) → U91¹(X1, X2)
MARK(U181(X1, X2)) → MARK(X1)
ACTIVE(isPLNatKind(splitAt(V1, V2))) → MARK(and(isNaturalKind(V1), isLNatKind(V2)))
MARK(splitAt(X1, X2)) → MARK(X1)
TAIL(mark(X)) → TAIL(X)
MARK(U141(X1, X2, X3)) → ACTIVE(U141(mark(X1), X2, X3))
AND(X1, active(X2)) → AND(X1, X2)
MARK(U122(X)) → MARK(X)
MARK(isPLNat(X)) → ACTIVE(isPLNat(X))
ACTIVE(U31(tt, N)) → MARK(N)
ACTIVE(isPLNat(pair(V1, V2))) → ISLNATKIND(V2)
ACTIVE(U142(tt, V2)) → ISLNAT(V2)
MARK(U143(X)) → MARK(X)
MARK(U51(X1, X2, X3)) → U51¹(mark(X1), X2, X3)
U211¹(active(X1), X2) → U211¹(X1, X2)
MARK(U53(X)) → U53¹(mark(X))
ACTIVE(head(cons(N, XS))) → ISNATURALKIND(N)
CONS(active(X1), X2) → CONS(X1, X2)
ACTIVE(isLNatKind(cons(V1, V2))) → ISNATURALKIND(V1)
MARK(U72(X)) → ACTIVE(U72(mark(X)))
ACTIVE(U143(tt)) → MARK(tt)
ACTIVE(U91(tt, V1)) → ISLNAT(V1)
MARK(afterNth(X1, X2)) → MARK(X1)
U221¹(mark(X1), X2, X3) → U221¹(X1, X2, X3)
MARK(U52(X1, X2)) → MARK(X1)
MARK(U11(X1, X2, X3)) → ACTIVE(U11(mark(X1), X2, X3))
ACTIVE(U131(tt, V1, V2)) → MARK(U132(isNatural(V1), V2))
U11¹(X1, active(X2), X3) → U11¹(X1, X2, X3)
MARK(isNaturalKind(X)) → ACTIVE(isNaturalKind(X))
ACTIVE(U102(tt, V2)) → MARK(U103(isLNat(V2)))
U101¹(X1, mark(X2), X3) → U101¹(X1, X2, X3)
U51¹(active(X1), X2, X3) → U51¹(X1, X2, X3)
ACTIVE(isLNat(afterNth(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
MARK(U42(X1, X2)) → U42¹(mark(X1), X2)
ACTIVE(isLNatKind(take(V1, V2))) → ISLNATKIND(V2)
U132¹(mark(X1), X2) → U132¹(X1, X2)
SEL(X1, mark(X2)) → SEL(X1, X2)
SEL(active(X1), X2) → SEL(X1, X2)
ACTIVE(isLNatKind(cons(V1, V2))) → ISLNATKIND(V2)
ACTIVE(U51(tt, V1, V2)) → MARK(U52(isNatural(V1), V2))
MARK(U141(X1, X2, X3)) → MARK(X1)
ACTIVE(isPLNatKind(splitAt(V1, V2))) → ISLNATKIND(V2)
MARK(U221(X1, X2, X3)) → U221¹(mark(X1), X2, X3)
U11¹(X1, X2, active(X3)) → U11¹(X1, X2, X3)
ACTIVE(isLNatKind(tail(V1))) → MARK(isLNatKind(V1))
ACTIVE(fst(pair(X, Y))) → AND(isLNat(Y), isLNatKind(Y))
AFTERNTH(X1, active(X2)) → AFTERNTH(X1, X2)
MARK(U52(X1, X2)) → ACTIVE(U52(mark(X1), X2))
U51¹(X1, mark(X2), X3) → U51¹(X1, X2, X3)
ACTIVE(U132(tt, V2)) → ISLNAT(V2)
MARK(splitAt(X1, X2)) → SPLITAT(mark(X1), mark(X2))
ACTIVE(U101(tt, V1, V2)) → MARK(U102(isNatural(V1), V2))
ISNATURALKIND(mark(X)) → ISNATURALKIND(X)
ACTIVE(afterNth(N, XS)) → AND(isNatural(N), isNaturalKind(N))
ACTIVE(isNaturalKind(s(V1))) → MARK(isNaturalKind(V1))
U42¹(X1, active(X2)) → U42¹(X1, X2)
ACTIVE(isNaturalKind(s(V1))) → ISNATURALKIND(V1)
ACTIVE(isNatural(sel(V1, V2))) → ISLNATKIND(V2)
ACTIVE(isPLNat(pair(V1, V2))) → MARK(U141(and(isLNatKind(V1), isLNatKind(V2)), V1, V2))
U91¹(active(X1), X2) → U91¹(X1, X2)
U41¹(X1, mark(X2), X3) → U41¹(X1, X2, X3)
U191¹(X1, active(X2)) → U191¹(X1, X2)
ACTIVE(U121(tt, V1)) → MARK(U122(isNatural(V1)))
MARK(U21(X1, X2)) → ACTIVE(U21(mark(X1), X2))
U202¹(X1, mark(X2)) → U202¹(X1, X2)
U132¹(X1, mark(X2)) → U132¹(X1, X2)
ACTIVE(U152(tt, V2)) → U153¹(isLNat(V2))
ACTIVE(U42(tt, V2)) → ISLNAT(V2)
ACTIVE(isLNat(take(V1, V2))) → U101¹(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
ACTIVE(natsFrom(N)) → ISNATURALKIND(N)
ACTIVE(isNatural(sel(V1, V2))) → U131¹(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
ACTIVE(splitAt(s(N), cons(X, XS))) → AND(isLNat(XS), isLNatKind(XS))
MARK(U112(X)) → ACTIVE(U112(mark(X)))
AFTERNTH(X1, mark(X2)) → AFTERNTH(X1, X2)
ACTIVE(isLNat(cons(V1, V2))) → MARK(U51(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
ACTIVE(U152(tt, V2)) → ISLNAT(V2)
ACTIVE(tail(cons(N, XS))) → ISNATURALKIND(N)
U51¹(X1, X2, active(X3)) → U51¹(X1, X2, X3)
ACTIVE(snd(pair(X, Y))) → ISLNATKIND(X)
ACTIVE(isLNat(afterNth(V1, V2))) → U41¹(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
ACTIVE(isLNat(natsFrom(V1))) → U71¹(isNaturalKind(V1), V1)
MARK(U191(X1, X2)) → U191¹(mark(X1), X2)
ACTIVE(natsFrom(N)) → U161¹(and(isNatural(N), isNaturalKind(N)), N)
U161¹(active(X1), X2) → U161¹(X1, X2)
ACTIVE(fst(pair(X, Y))) → ISLNATKIND(X)
ACTIVE(isLNatKind(natsFrom(V1))) → MARK(isNaturalKind(V1))
ACTIVE(U151(tt, V1, V2)) → ISNATURAL(V1)
MARK(head(X)) → HEAD(mark(X))
ACTIVE(U201(tt, N, X, XS)) → MARK(U202(splitAt(N, XS), X))
ACTIVE(U171(tt, N, XS)) → MARK(head(afterNth(N, XS)))
ACTIVE(U71(tt, V1)) → ISNATURAL(V1)
U202¹(X1, active(X2)) → U202¹(X1, X2)
ACTIVE(isPLNat(splitAt(V1, V2))) → U151¹(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
ACTIVE(tail(cons(N, XS))) → ISLNATKIND(XS)
U153¹(mark(X)) → U153¹(X)
ACTIVE(isPLNat(splitAt(V1, V2))) → ISLNATKIND(V2)
ACTIVE(isPLNat(splitAt(V1, V2))) → ISNATURALKIND(V1)
ACTIVE(isNatural(0)) → MARK(tt)
U82¹(mark(X)) → U82¹(X)
U201¹(X1, X2, X3, active(X4)) → U201¹(X1, X2, X3, X4)
ACTIVE(splitAt(s(N), cons(X, XS))) → ISNATURAL(N)
U81¹(X1, active(X2)) → U81¹(X1, X2)
ACTIVE(and(tt, X)) → MARK(X)
ACTIVE(isLNatKind(afterNth(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
ACTIVE(U42(tt, V2)) → MARK(U43(isLNat(V2)))
U201¹(X1, X2, X3, mark(X4)) → U201¹(X1, X2, X3, X4)
ACTIVE(isNatural(sel(V1, V2))) → MARK(U131(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
MARK(U92(X)) → U92¹(mark(X))
MARK(U211(X1, X2)) → MARK(X1)
MARK(U43(X)) → U43¹(mark(X))
ACTIVE(isPLNat(pair(V1, V2))) → ISLNATKIND(V1)
MARK(U153(X)) → MARK(X)
U111¹(X1, active(X2)) → U111¹(X1, X2)
ACTIVE(isLNatKind(take(V1, V2))) → ISNATURALKIND(V1)
MARK(s(X)) → MARK(X)
ACTIVE(U132(tt, V2)) → U133¹(isLNat(V2))
MARK(U151(X1, X2, X3)) → U151¹(mark(X1), X2, X3)
ACTIVE(U91(tt, V1)) → U92¹(isLNat(V1))
ACTIVE(U201(tt, N, X, XS)) → SPLITAT(N, XS)
ACTIVE(isPLNatKind(splitAt(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
U152¹(X1, active(X2)) → U152¹(X1, X2)
ACTIVE(fst(pair(X, Y))) → AND(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y)))
U41¹(active(X1), X2, X3) → U41¹(X1, X2, X3)
MARK(splitAt(X1, X2)) → ACTIVE(splitAt(mark(X1), mark(X2)))
MARK(U103(X)) → MARK(X)
U131¹(X1, X2, active(X3)) → U131¹(X1, X2, X3)
ACTIVE(U121(tt, V1)) → U122¹(isNatural(V1))
MARK(U211(X1, X2)) → ACTIVE(U211(mark(X1), X2))
U21¹(active(X1), X2) → U21¹(X1, X2)
ACTIVE(U202(pair(YS, ZS), X)) → PAIR(cons(X, YS), ZS)
ACTIVE(U81(tt, V1)) → U82¹(isPLNat(V1))
MARK(U102(X1, X2)) → ACTIVE(U102(mark(X1), X2))
U111¹(X1, mark(X2)) → U111¹(X1, X2)
ACTIVE(U141(tt, V1, V2)) → MARK(U142(isLNat(V1), V2))
U211¹(X1, mark(X2)) → U211¹(X1, X2)
U101¹(X1, active(X2), X3) → U101¹(X1, X2, X3)
MARK(U92(X)) → MARK(X)
ACTIVE(U161(tt, N)) → NATSFROM(s(N))
U142¹(mark(X1), X2) → U142¹(X1, X2)
ACTIVE(splitAt(s(N), cons(X, XS))) → AND(isNatural(N), isNaturalKind(N))
MARK(U211(X1, X2)) → U211¹(mark(X1), X2)
MARK(U152(X1, X2)) → ACTIVE(U152(mark(X1), X2))
U201¹(X1, X2, active(X3), X4) → U201¹(X1, X2, X3, X4)
MARK(U202(X1, X2)) → U202¹(mark(X1), X2)
ACTIVE(U72(tt)) → MARK(tt)
MARK(afterNth(X1, X2)) → AFTERNTH(mark(X1), mark(X2))
ACTIVE(splitAt(0, XS)) → MARK(U191(and(isLNat(XS), isLNatKind(XS)), XS))
U53¹(mark(X)) → U53¹(X)
U161¹(mark(X1), X2) → U161¹(X1, X2)
ACTIVE(U151(tt, V1, V2)) → U152¹(isNatural(V1), V2)
MARK(tt) → ACTIVE(tt)
U152¹(X1, mark(X2)) → U152¹(X1, X2)
MARK(U101(X1, X2, X3)) → U101¹(mark(X1), X2, X3)
U201¹(X1, mark(X2), X3, X4) → U201¹(X1, X2, X3, X4)
AND(X1, mark(X2)) → AND(X1, X2)
ACTIVE(splitAt(0, XS)) → U191¹(and(isLNat(XS), isLNatKind(XS)), XS)
ACTIVE(isLNat(natsFrom(V1))) → MARK(U71(isNaturalKind(V1), V1))
HEAD(mark(X)) → HEAD(X)
ACTIVE(isLNat(natsFrom(V1))) → ISNATURALKIND(V1)
U191¹(active(X1), X2) → U191¹(X1, X2)
ACTIVE(head(cons(N, XS))) → ISLNATKIND(XS)
ACTIVE(tail(cons(N, XS))) → AND(isNatural(N), isNaturalKind(N))
MARK(U132(X1, X2)) → MARK(X1)
U211¹(X1, active(X2)) → U211¹(X1, X2)
ACTIVE(U202(pair(YS, ZS), X)) → CONS(X, YS)
MARK(U53(X)) → MARK(X)
ACTIVE(isLNat(cons(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
ACTIVE(U11(tt, N, XS)) → SND(splitAt(N, XS))
ISLNAT(mark(X)) → ISLNAT(X)
PAIR(X1, active(X2)) → PAIR(X1, X2)
U43¹(active(X)) → U43¹(X)
MARK(U221(X1, X2, X3)) → ACTIVE(U221(mark(X1), X2, X3))
ACTIVE(isLNat(take(V1, V2))) → ISLNATKIND(V2)
ACTIVE(splitAt(0, XS)) → AND(isLNat(XS), isLNatKind(XS))
U181¹(X1, mark(X2)) → U181¹(X1, X2)
U141¹(X1, mark(X2), X3) → U141¹(X1, X2, X3)
ACTIVE(splitAt(s(N), cons(X, XS))) → ISLNATKIND(XS)
MARK(pair(X1, X2)) → MARK(X1)
MARK(isNatural(X)) → ACTIVE(isNatural(X))
MARK(U91(X1, X2)) → U91¹(mark(X1), X2)
MARK(U21(X1, X2)) → MARK(X1)
TAKE(mark(X1), X2) → TAKE(X1, X2)
U202¹(mark(X1), X2) → U202¹(X1, X2)
MARK(U181(X1, X2)) → ACTIVE(U181(mark(X1), X2))
MARK(U42(X1, X2)) → ACTIVE(U42(mark(X1), X2))
MARK(U42(X1, X2)) → MARK(X1)
ACTIVE(U92(tt)) → MARK(tt)
ACTIVE(isNatural(s(V1))) → U121¹(isNaturalKind(V1), V1)
ACTIVE(sel(N, XS)) → AND(isNatural(N), isNaturalKind(N))
U71¹(X1, active(X2)) → U71¹(X1, X2)
U21¹(X1, active(X2)) → U21¹(X1, X2)
ACTIVE(isLNatKind(afterNth(V1, V2))) → ISLNATKIND(V2)
ACTIVE(isPLNatKind(pair(V1, V2))) → AND(isLNatKind(V1), isLNatKind(V2))
SEL(X1, active(X2)) → SEL(X1, X2)
ACTIVE(U221(tt, N, XS)) → FST(splitAt(N, XS))
ACTIVE(U91(tt, V1)) → MARK(U92(isLNat(V1)))
MARK(U31(X1, X2)) → MARK(X1)
ACTIVE(isLNatKind(cons(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
ACTIVE(U51(tt, V1, V2)) → U52¹(isNatural(V1), V2)
U71¹(X1, mark(X2)) → U71¹(X1, X2)
U52¹(X1, mark(X2)) → U52¹(X1, X2)
ACTIVE(U81(tt, V1)) → MARK(U82(isPLNat(V1)))
ACTIVE(take(N, XS)) → ISNATURALKIND(N)
MARK(U152(X1, X2)) → U152¹(mark(X1), X2)
U62¹(mark(X)) → U62¹(X)
ACTIVE(sel(N, XS)) → AND(isLNat(XS), isLNatKind(XS))
MARK(U161(X1, X2)) → ACTIVE(U161(mark(X1), X2))
MARK(pair(X1, X2)) → MARK(X2)
MARK(snd(X)) → MARK(X)
ACTIVE(U41(tt, V1, V2)) → U42¹(isNatural(V1), V2)
ACTIVE(U71(tt, V1)) → MARK(U72(isNatural(V1)))
MARK(s(X)) → S(mark(X))
U161¹(X1, active(X2)) → U161¹(X1, X2)
ACTIVE(isLNat(take(V1, V2))) → ISNATURALKIND(V1)
MARK(U72(X)) → U72¹(mark(X))
ACTIVE(U61(tt, V1)) → U62¹(isPLNat(V1))
ACTIVE(U82(tt)) → MARK(tt)
MARK(U52(X1, X2)) → U52¹(mark(X1), X2)
MARK(U153(X)) → U153¹(mark(X))
PAIR(active(X1), X2) → PAIR(X1, X2)
ACTIVE(U52(tt, V2)) → MARK(U53(isLNat(V2)))
MARK(U142(X1, X2)) → U142¹(mark(X1), X2)
ACTIVE(isNaturalKind(head(V1))) → ISLNATKIND(V1)
ACTIVE(U171(tt, N, XS)) → AFTERNTH(N, XS)
ACTIVE(sel(N, XS)) → ISNATURALKIND(N)
ACTIVE(U133(tt)) → MARK(tt)
MARK(pair(X1, X2)) → PAIR(mark(X1), mark(X2))
MARK(0) → ACTIVE(0)
U41¹(X1, X2, mark(X3)) → U41¹(X1, X2, X3)
MARK(U103(X)) → ACTIVE(U103(mark(X)))
U201¹(active(X1), X2, X3, X4) → U201¹(X1, X2, X3, X4)
MARK(U142(X1, X2)) → MARK(X1)
U11¹(mark(X1), X2, X3) → U11¹(X1, X2, X3)
U91¹(mark(X1), X2) → U91¹(X1, X2)
ACTIVE(isLNat(snd(V1))) → MARK(U81(isPLNatKind(V1), V1))
MARK(U202(X1, X2)) → MARK(X1)
U71¹(mark(X1), X2) → U71¹(X1, X2)
ACTIVE(isLNatKind(afterNth(V1, V2))) → ISNATURALKIND(V1)
ACTIVE(U161(tt, N)) → S(N)
ACTIVE(U153(tt)) → MARK(tt)
MARK(U81(X1, X2)) → MARK(X1)
CONS(X1, mark(X2)) → CONS(X1, X2)
MARK(U171(X1, X2, X3)) → U171¹(mark(X1), X2, X3)
ACTIVE(isNaturalKind(sel(V1, V2))) → MARK(and(isNaturalKind(V1), isLNatKind(V2)))
MARK(U161(X1, X2)) → U161¹(mark(X1), X2)
U152¹(active(X1), X2) → U152¹(X1, X2)
MARK(U151(X1, X2, X3)) → MARK(X1)
ACTIVE(isNaturalKind(sel(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
ISPLNAT(active(X)) → ISPLNAT(X)
ACTIVE(isLNatKind(natsFrom(V1))) → ISNATURALKIND(V1)
ACTIVE(isLNat(afterNth(V1, V2))) → MARK(U41(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
ACTIVE(isPLNat(pair(V1, V2))) → U141¹(and(isLNatKind(V1), isLNatKind(V2)), V1, V2)
ACTIVE(afterNth(N, XS)) → ISNATURAL(N)
ACTIVE(snd(pair(X, Y))) → ISLNATKIND(Y)
U171¹(X1, X2, mark(X3)) → U171¹(X1, X2, X3)
MARK(U82(X)) → MARK(X)
U31¹(X1, mark(X2)) → U31¹(X1, X2)
ACTIVE(isLNatKind(take(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
U141¹(X1, X2, mark(X3)) → U141¹(X1, X2, X3)
U91¹(X1, active(X2)) → U91¹(X1, X2)
ACTIVE(snd(pair(X, Y))) → U181¹(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), Y)
ACTIVE(U161(tt, N)) → CONS(N, natsFrom(s(N)))
ACTIVE(isLNat(snd(V1))) → U81¹(isPLNatKind(V1), V1)
SND(mark(X)) → SND(X)
MARK(U191(X1, X2)) → MARK(X1)
ACTIVE(isLNat(tail(V1))) → MARK(U91(isLNatKind(V1), V1))
CONS(mark(X1), X2) → CONS(X1, X2)
MARK(take(X1, X2)) → MARK(X2)
ACTIVE(isLNatKind(afterNth(V1, V2))) → MARK(and(isNaturalKind(V1), isLNatKind(V2)))
ACTIVE(isLNat(tail(V1))) → U91¹(isLNatKind(V1), V1)
ACTIVE(U221(tt, N, XS)) → MARK(fst(splitAt(N, XS)))
U133¹(mark(X)) → U133¹(X)
ACTIVE(isLNat(snd(V1))) → ISPLNATKIND(V1)
ACTIVE(head(cons(N, XS))) → AND(isNatural(N), isNaturalKind(N))
ACTIVE(afterNth(N, XS)) → ISLNAT(XS)
ACTIVE(sel(N, XS)) → U171¹(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS)
ACTIVE(isLNat(cons(V1, V2))) → U51¹(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2)
PAIR(mark(X1), X2) → PAIR(X1, X2)
ACTIVE(U142(tt, V2)) → MARK(U143(isLNat(V2)))
ACTIVE(afterNth(N, XS)) → MARK(U11(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
U51¹(X1, active(X2), X3) → U51¹(X1, X2, X3)
ISPLNATKIND(mark(X)) → ISPLNATKIND(X)
ACTIVE(U11(tt, N, XS)) → MARK(snd(splitAt(N, XS)))
U72¹(active(X)) → U72¹(X)
SPLITAT(mark(X1), X2) → SPLITAT(X1, X2)
MARK(U111(X1, X2)) → MARK(X1)
U142¹(active(X1), X2) → U142¹(X1, X2)
ACTIVE(splitAt(0, XS)) → ISLNAT(XS)
MARK(U102(X1, X2)) → U102¹(mark(X1), X2)
MARK(isLNat(X)) → ACTIVE(isLNat(X))
MARK(U133(X)) → U133¹(mark(X))
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))
U61¹(X1, active(X2)) → U61¹(X1, X2)
U131¹(X1, active(X2), X3) → U131¹(X1, X2, X3)
U122¹(mark(X)) → U122¹(X)
U41¹(X1, active(X2), X3) → U41¹(X1, X2, X3)
ACTIVE(isLNat(cons(V1, V2))) → ISLNATKIND(V2)
ACTIVE(U121(tt, V1)) → ISNATURAL(V1)
MARK(cons(X1, X2)) → ACTIVE(cons(mark(X1), X2))
MARK(U103(X)) → U103¹(mark(X))
U151¹(X1, X2, mark(X3)) → U151¹(X1, X2, X3)
MARK(U111(X1, X2)) → U111¹(mark(X1), X2)
ACTIVE(isLNatKind(snd(V1))) → MARK(isPLNatKind(V1))
U151¹(X1, active(X2), X3) → U151¹(X1, X2, X3)
MARK(U72(X)) → MARK(X)
ACTIVE(U171(tt, N, XS)) → HEAD(afterNth(N, XS))
MARK(U61(X1, X2)) → U61¹(mark(X1), X2)
MARK(U43(X)) → MARK(X)
U221¹(active(X1), X2, X3) → U221¹(X1, X2, X3)
U102¹(active(X1), X2) → U102¹(X1, X2)
ACTIVE(afterNth(N, XS)) → AND(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS)))
ACTIVE(U61(tt, V1)) → MARK(U62(isPLNat(V1)))
U181¹(mark(X1), X2) → U181¹(X1, X2)
U42¹(X1, mark(X2)) → U42¹(X1, X2)
U141¹(X1, X2, active(X3)) → U141¹(X1, X2, X3)
ACTIVE(U101(tt, V1, V2)) → U102¹(isNatural(V1), V2)
MARK(U111(X1, X2)) → ACTIVE(U111(mark(X1), X2))
U43¹(mark(X)) → U43¹(X)
U82¹(active(X)) → U82¹(X)
ACTIVE(isLNatKind(nil)) → MARK(tt)
U143¹(active(X)) → U143¹(X)
ACTIVE(U102(tt, V2)) → ISLNAT(V2)
MARK(take(X1, X2)) → MARK(X1)
MARK(U92(X)) → ACTIVE(U92(mark(X)))
MARK(U43(X)) → ACTIVE(U43(mark(X)))
ACTIVE(U181(tt, Y)) → MARK(Y)
ACTIVE(snd(pair(X, Y))) → ISLNAT(Y)
U31¹(X1, active(X2)) → U31¹(X1, X2)
S(active(X)) → S(X)
MARK(sel(X1, X2)) → MARK(X1)
U171¹(mark(X1), X2, X3) → U171¹(X1, X2, X3)
U11¹(active(X1), X2, X3) → U11¹(X1, X2, X3)
MARK(tail(X)) → ACTIVE(tail(mark(X)))
U102¹(X1, mark(X2)) → U102¹(X1, X2)
U112¹(active(X)) → U112¹(X)
NATSFROM(mark(X)) → NATSFROM(X)
MARK(U91(X1, X2)) → MARK(X1)
ACTIVE(take(N, XS)) → ISNATURAL(N)
ACTIVE(U41(tt, V1, V2)) → ISNATURAL(V1)
MARK(U131(X1, X2, X3)) → ACTIVE(U131(mark(X1), X2, X3))
U221¹(X1, X2, active(X3)) → U221¹(X1, X2, X3)
U181¹(X1, active(X2)) → U181¹(X1, X2)
ACTIVE(isLNatKind(fst(V1))) → ISPLNATKIND(V1)
AND(active(X1), X2) → AND(X1, X2)
ACTIVE(sel(N, XS)) → ISLNAT(XS)
SEL(mark(X1), X2) → SEL(X1, X2)
U141¹(active(X1), X2, X3) → U141¹(X1, X2, X3)
ACTIVE(take(N, XS)) → ISLNAT(XS)
MARK(U62(X)) → MARK(X)
NATSFROM(active(X)) → NATSFROM(X)
U101¹(X1, X2, active(X3)) → U101¹(X1, X2, X3)
MARK(U202(X1, X2)) → ACTIVE(U202(mark(X1), X2))
MARK(natsFrom(X)) → MARK(X)
ACTIVE(isNaturalKind(sel(V1, V2))) → ISLNATKIND(V2)
U131¹(X1, X2, mark(X3)) → U131¹(X1, X2, X3)
ACTIVE(isPLNat(splitAt(V1, V2))) → MARK(U151(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
U52¹(X1, active(X2)) → U52¹(X1, X2)
ACTIVE(head(cons(N, XS))) → AND(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS)))
U191¹(mark(X1), X2) → U191¹(X1, X2)
U141¹(mark(X1), X2, X3) → U141¹(X1, X2, X3)
ACTIVE(tail(cons(N, XS))) → AND(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS)))
ACTIVE(U202(pair(YS, ZS), X)) → MARK(pair(cons(X, YS), ZS))
U201¹(X1, active(X2), X3, X4) → U201¹(X1, X2, X3, X4)
U61¹(mark(X1), X2) → U61¹(X1, X2)
U133¹(active(X)) → U133¹(X)
MARK(take(X1, X2)) → ACTIVE(take(mark(X1), mark(X2)))
U121¹(X1, active(X2)) → U121¹(X1, X2)
ACTIVE(splitAt(s(N), cons(X, XS))) → ISLNAT(XS)
MARK(U91(X1, X2)) → ACTIVE(U91(mark(X1), X2))
ACTIVE(isLNat(take(V1, V2))) → AND(isNaturalKind(V1), isLNatKind(V2))
ACTIVE(U102(tt, V2)) → U103¹(isLNat(V2))
MARK(U171(X1, X2, X3)) → ACTIVE(U171(mark(X1), X2, X3))
MARK(and(X1, X2)) → AND(mark(X1), X2)
U11¹(X1, X2, mark(X3)) → U11¹(X1, X2, X3)
U101¹(X1, X2, mark(X3)) → U101¹(X1, X2, X3)
MARK(U53(X)) → ACTIVE(U53(mark(X)))
ACTIVE(afterNth(N, XS)) → U11¹(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS)
ISPLNATKIND(active(X)) → ISPLNATKIND(X)
U151¹(active(X1), X2, X3) → U151¹(X1, X2, X3)
MARK(U101(X1, X2, X3)) → MARK(X1)
ACTIVE(take(N, XS)) → ISLNATKIND(XS)
MARK(U181(X1, X2)) → U181¹(mark(X1), X2)
U171¹(X1, mark(X2), X3) → U171¹(X1, X2, X3)
ACTIVE(U221(tt, N, XS)) → SPLITAT(N, XS)
ACTIVE(head(cons(N, XS))) → ISNATURAL(N)
U142¹(X1, mark(X2)) → U142¹(X1, X2)
U101¹(mark(X1), X2, X3) → U101¹(X1, X2, X3)
ACTIVE(isNatural(sel(V1, V2))) → ISNATURALKIND(V1)
ACTIVE(tail(cons(N, XS))) → U211¹(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), XS)
ACTIVE(isLNat(fst(V1))) → U61¹(isPLNatKind(V1), V1)
MARK(U133(X)) → MARK(X)
ACTIVE(U191(tt, XS)) → PAIR(nil, XS)
MARK(fst(X)) → ACTIVE(fst(mark(X)))
U153¹(active(X)) → U153¹(X)
ACTIVE(isNatural(head(V1))) → U111¹(isLNatKind(V1), V1)
MARK(U151(X1, X2, X3)) → ACTIVE(U151(mark(X1), X2, X3))
ACTIVE(fst(pair(X, Y))) → MARK(U21(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), X))
U201¹(X1, X2, mark(X3), X4) → U201¹(X1, X2, X3, X4)
ACTIVE(U81(tt, V1)) → ISPLNAT(V1)
ACTIVE(U122(tt)) → MARK(tt)
U161¹(X1, mark(X2)) → U161¹(X1, X2)
ACTIVE(U52(tt, V2)) → ISLNAT(V2)
ACTIVE(U21(tt, X)) → MARK(X)
U31¹(active(X1), X2) → U31¹(X1, X2)
MARK(U82(X)) → ACTIVE(U82(mark(X)))
ACTIVE(fst(pair(X, Y))) → ISLNAT(X)
ACTIVE(tail(cons(N, XS))) → ISLNAT(XS)
ACTIVE(splitAt(s(N), cons(X, XS))) → ISNATURALKIND(X)
ACTIVE(snd(pair(X, Y))) → MARK(U181(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), Y))
MARK(U171(X1, X2, X3)) → MARK(X1)
MARK(take(X1, X2)) → TAKE(mark(X1), mark(X2))
ACTIVE(afterNth(N, XS)) → ISLNATKIND(XS)
U21¹(mark(X1), X2) → U21¹(X1, X2)
ACTIVE(U131(tt, V1, V2)) → U132¹(isNatural(V1), V2)
MARK(fst(X)) → MARK(X)
U52¹(active(X1), X2) → U52¹(X1, X2)
ACTIVE(snd(pair(X, Y))) → AND(isLNat(Y), isLNatKind(Y))
MARK(U101(X1, X2, X3)) → ACTIVE(U101(mark(X1), X2, X3))
MARK(U142(X1, X2)) → ACTIVE(U142(mark(X1), X2))
ISPLNAT(mark(X)) → ISPLNAT(X)
U142¹(X1, active(X2)) → U142¹(X1, X2)
MARK(isLNatKind(X)) → ACTIVE(isLNatKind(X))
ACTIVE(U111(tt, V1)) → U112¹(isLNat(V1))
ACTIVE(isLNat(cons(V1, V2))) → ISNATURALKIND(V1)
U171¹(X1, active(X2), X3) → U171¹(X1, X2, X3)
MARK(U201(X1, X2, X3, X4)) → MARK(X1)
U211¹(mark(X1), X2) → U211¹(X1, X2)
ACTIVE(U131(tt, V1, V2)) → ISNATURAL(V1)
ACTIVE(isLNat(take(V1, V2))) → MARK(U101(and(isNaturalKind(V1), isLNatKind(V2)), V1, V2))
ACTIVE(splitAt(s(N), cons(X, XS))) → ISNATURALKIND(N)
ACTIVE(head(cons(N, XS))) → ISLNAT(XS)
U42¹(active(X1), X2) → U42¹(X1, X2)
ACTIVE(snd(pair(X, Y))) → AND(isLNat(X), isLNatKind(X))
U151¹(X1, mark(X2), X3) → U151¹(X1, X2, X3)
U61¹(active(X1), X2) → U61¹(X1, X2)
U131¹(mark(X1), X2, X3) → U131¹(X1, X2, X3)
MARK(snd(X)) → ACTIVE(snd(mark(X)))
ISNATURALKIND(active(X)) → ISNATURALKIND(X)
ACTIVE(isLNat(fst(V1))) → MARK(U61(isPLNatKind(V1), V1))
MARK(pair(X1, X2)) → ACTIVE(pair(mark(X1), mark(X2)))
MARK(U82(X)) → U82¹(mark(X))
ACTIVE(take(N, XS)) → U221¹(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS)
U141¹(X1, active(X2), X3) → U141¹(X1, X2, X3)
SND(active(X)) → SND(X)
U103¹(mark(X)) → U103¹(X)
MARK(U132(X1, X2)) → ACTIVE(U132(mark(X1), X2))
CONS(X1, active(X2)) → CONS(X1, X2)
MARK(and(X1, X2)) → MARK(X1)
ACTIVE(isLNatKind(fst(V1))) → MARK(isPLNatKind(V1))
U92¹(active(X)) → U92¹(X)
ACTIVE(U53(tt)) → MARK(tt)
ACTIVE(U191(tt, XS)) → MARK(pair(nil, XS))
ACTIVE(U41(tt, V1, V2)) → MARK(U42(isNatural(V1), V2))
ACTIVE(splitAt(s(N), cons(X, XS))) → AND(and(isNatural(N), isNaturalKind(N)), and(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS))))
ACTIVE(isNatural(s(V1))) → ISNATURALKIND(V1)
U111¹(active(X1), X2) → U111¹(X1, X2)
U71¹(active(X1), X2) → U71¹(X1, X2)
ACTIVE(U132(tt, V2)) → MARK(U133(isLNat(V2)))
ACTIVE(fst(pair(X, Y))) → U21¹(and(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y))), X)
U191¹(X1, mark(X2)) → U191¹(X1, X2)
MARK(U131(X1, X2, X3)) → U131¹(mark(X1), X2, X3)
ACTIVE(U152(tt, V2)) → MARK(U153(isLNat(V2)))
ACTIVE(afterNth(N, XS)) → AND(isLNat(XS), isLNatKind(XS))
U221¹(X1, mark(X2), X3) → U221¹(X1, X2, X3)
MARK(U61(X1, X2)) → MARK(X1)
MARK(fst(X)) → FST(mark(X))
ACTIVE(U111(tt, V1)) → MARK(U112(isLNat(V1)))
AND(mark(X1), X2) → AND(X1, X2)
U171¹(X1, X2, active(X3)) → U171¹(X1, X2, X3)
U102¹(mark(X1), X2) → U102¹(X1, X2)
U221¹(X1, X2, mark(X3)) → U221¹(X1, X2, X3)
ACTIVE(snd(pair(X, Y))) → ISLNAT(X)
ACTIVE(tail(cons(N, XS))) → ISNATURAL(N)
ACTIVE(isLNatKind(take(V1, V2))) → MARK(and(isNaturalKind(V1), isLNatKind(V2)))
MARK(sel(X1, X2)) → MARK(X2)
ACTIVE(U151(tt, V1, V2)) → MARK(U152(isNatural(V1), V2))
MARK(U132(X1, X2)) → U132¹(mark(X1), X2)
ACTIVE(sel(N, XS)) → ISLNATKIND(XS)
TAKE(X1, active(X2)) → TAKE(X1, X2)
MARK(U122(X)) → U122¹(mark(X))
MARK(U71(X1, X2)) → ACTIVE(U71(mark(X1), X2))
ACTIVE(fst(pair(X, Y))) → ISLNAT(Y)
MARK(U102(X1, X2)) → MARK(X1)
MARK(tail(X)) → MARK(X)
MARK(head(X)) → MARK(X)
MARK(cons(X1, X2)) → MARK(X1)
U41¹(mark(X1), X2, X3) → U41¹(X1, X2, X3)
MARK(U71(X1, X2)) → U71¹(mark(X1), X2)
U143¹(mark(X)) → U143¹(X)
U42¹(mark(X1), X2) → U42¹(X1, X2)
MARK(U122(X)) → ACTIVE(U122(mark(X)))
U121¹(mark(X1), X2) → U121¹(X1, X2)
ACTIVE(isLNatKind(snd(V1))) → ISPLNATKIND(V1)
U132¹(active(X1), X2) → U132¹(X1, X2)
MARK(U51(X1, X2, X3)) → ACTIVE(U51(mark(X1), X2, X3))
SPLITAT(active(X1), X2) → SPLITAT(X1, X2)
MARK(U121(X1, X2)) → U121¹(mark(X1), X2)
ACTIVE(U161(tt, N)) → MARK(cons(N, natsFrom(s(N))))
ACTIVE(isLNat(afterNth(V1, V2))) → ISNATURALKIND(V1)
MARK(U121(X1, X2)) → MARK(X1)
U81¹(active(X1), X2) → U81¹(X1, X2)
MARK(afterNth(X1, X2)) → MARK(X2)
MARK(U21(X1, X2)) → U21¹(mark(X1), X2)
MARK(U41(X1, X2, X3)) → U41¹(mark(X1), X2, X3)
U201¹(mark(X1), X2, X3, X4) → U201¹(X1, X2, X3, X4)
AFTERNTH(mark(X1), X2) → AFTERNTH(X1, X2)
HEAD(active(X)) → HEAD(X)
ACTIVE(tail(cons(N, XS))) → MARK(U211(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), XS))
ACTIVE(splitAt(s(N), cons(X, XS))) → AND(isNatural(X), isNaturalKind(X))
ACTIVE(take(N, XS)) → MARK(U221(and(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS))), N, XS))
U221¹(X1, active(X2), X3) → U221¹(X1, X2, X3)
U81¹(X1, mark(X2)) → U81¹(X1, X2)
U103¹(active(X)) → U103¹(X)
U202¹(active(X1), X2) → U202¹(X1, X2)
PAIR(X1, mark(X2)) → PAIR(X1, X2)
ACTIVE(snd(pair(X, Y))) → AND(and(isLNat(X), isLNatKind(X)), and(isLNat(Y), isLNatKind(Y)))
ACTIVE(splitAt(0, XS)) → ISLNATKIND(XS)
ACTIVE(isNatural(head(V1))) → MARK(U111(isLNatKind(V1), V1))
SPLITAT(X1, mark(X2)) → SPLITAT(X1, X2)
ACTIVE(U111(tt, V1)) → ISLNAT(V1)
ACTIVE(U61(tt, V1)) → ISPLNAT(V1)
MARK(U112(X)) → U112¹(mark(X))
ACTIVE(isNaturalKind(0)) → MARK(tt)
MARK(natsFrom(X)) → NATSFROM(mark(X))
MARK(U81(X1, X2)) → U81¹(mark(X1), X2)
ACTIVE(take(N, XS)) → AND(and(isNatural(N), isNaturalKind(N)), and(isLNat(XS), isLNatKind(XS)))
ACTIVE(splitAt(s(N), cons(X, XS))) → AND(and(isNatural(X), isNaturalKind(X)), and(isLNat(XS), isLNatKind(XS)))
MARK(U31(X1, X2)) → ACTIVE(U31(mark(X1), X2))
MARK(and(X1, X2)) → ACTIVE(and(mark(X1), X2))
ACTIVE(isPLNatKind(pair(V1, V2))) → MARK(and(isLNatKind(V1), isLNatKind(V2)))
U92¹(mark(X)) → U92¹(X)
U41¹(X1, X2, active(X3)) → U41¹(X1, X2, X3)
U51¹(X1, X2, mark(X3)) → U51¹(X1, X2, X3)
SPLITAT(X1, active(X2)) → SPLITAT(X1, X2)
FST(active(X)) → FST(X)
ACTIVE(U112(tt)) → MARK(tt)
ACTIVE(isLNatKind(tail(V1))) → ISLNATKIND(V1)
ACTIVE(natsFrom(N)) → MARK(U161(and(isNatural(N), isNaturalKind(N)), N))
U62¹(active(X)) → U62¹(X)
U171¹(active(X1), X2, X3) → U171¹(X1, X2, X3)
ACTIVE(U43(tt)) → MARK(tt)
U11¹(X1, mark(X2), X3) → U11¹(X1, X2, X3)
MARK(isPLNatKind(X)) → ACTIVE(isPLNatKind(X))
ACTIVE(U51(tt, V1, V2)) → ISNATURAL(V1)
ACTIVE(U52(tt, V2)) → U53¹(isLNat(V2))
ACTIVE(natsFrom(N)) → AND(isNatural(N), isNaturalKind(N))
MARK(U221(X1, X2, X3)) → MARK(X1)
U52¹(mark(X1), X2) → U52¹(X1, X2)
ACTIVE(U103(tt)) → MARK(tt)
MARK(head(X)) → ACTIVE(head(mark(X)))
U51¹(mark(X1), X2, X3) → U51¹(X1, X2, X3)
TAKE(X1, mark(X2)) → TAKE(X1, X2)
MARK(U153(X)) → ACTIVE(U153(mark(X)))
MARK(U143(X)) → U143¹(mark(X))
ACTIVE(isLNatKind(cons(V1, V2))) → MARK(and(isNaturalKind(V1), isLNatKind(V2)))
ACTIVE(splitAt(s(N), cons(X, XS))) → ISNATURAL(X)
MARK(U141(X1, X2, X3)) → U141¹(mark(X1), X2, X3)
ACTIVE(head(cons(N, XS))) → AND(isLNat(XS), isLNatKind(XS))
MARK(nil) → ACTIVE(nil)