(VAR V1 V2 N XS Y X YS ZS X1 X2 X3 X4)
(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)
)