(VAR V1 V2 N XS X Y YS ZS X1 X2)
(RULES 
U101(tt,V1,V2) -> U102(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U102(tt,V1,V2) -> U103(isLNatKind(activate(V2)),activate(V1),activate(V2))
U103(tt,V1,V2) -> U104(isLNatKind(activate(V2)),activate(V1),activate(V2))
U104(tt,V1,V2) -> U105(isNatural(activate(V1)),activate(V2))
U105(tt,V2) -> U106(isLNat(activate(V2)))
U106(tt) -> tt
U11(tt,N,XS) -> U12(isNaturalKind(activate(N)),activate(N),activate(XS))
U111(tt,V2) -> U112(isLNatKind(activate(V2)))
U112(tt) -> tt
U12(tt,N,XS) -> U13(isLNat(activate(XS)),activate(N),activate(XS))
U121(tt,V2) -> U122(isLNatKind(activate(V2)))
U122(tt) -> tt
U13(tt,N,XS) -> U14(isLNatKind(activate(XS)),activate(N),activate(XS))
U131(tt) -> tt
U14(tt,N,XS) -> snd(splitAt(activate(N),activate(XS)))
U141(tt) -> tt
U151(tt) -> tt
U161(tt) -> tt
U171(tt,V2) -> U172(isLNatKind(activate(V2)))
U172(tt) -> tt
U181(tt,V1) -> U182(isLNatKind(activate(V1)),activate(V1))
U182(tt,V1) -> U183(isLNat(activate(V1)))
U183(tt) -> tt
U191(tt,V1) -> U192(isNaturalKind(activate(V1)),activate(V1))
U192(tt,V1) -> U193(isNatural(activate(V1)))
U193(tt) -> tt
U201(tt,V1,V2) -> U202(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U202(tt,V1,V2) -> U203(isLNatKind(activate(V2)),activate(V1),activate(V2))
U203(tt,V1,V2) -> U204(isLNatKind(activate(V2)),activate(V1),activate(V2))
U204(tt,V1,V2) -> U205(isNatural(activate(V1)),activate(V2))
U205(tt,V2) -> U206(isLNat(activate(V2)))
U206(tt) -> tt
U21(tt,X,Y) -> U22(isLNatKind(activate(X)),activate(X),activate(Y))
U211(tt) -> tt
U22(tt,X,Y) -> U23(isLNat(activate(Y)),activate(X),activate(Y))
U221(tt) -> tt
U23(tt,X,Y) -> U24(isLNatKind(activate(Y)),activate(X))
U231(tt,V2) -> U232(isLNatKind(activate(V2)))
U232(tt) -> tt
U24(tt,X) -> activate(X)
U241(tt,V1,V2) -> U242(isLNatKind(activate(V1)),activate(V1),activate(V2))
U242(tt,V1,V2) -> U243(isLNatKind(activate(V2)),activate(V1),activate(V2))
U243(tt,V1,V2) -> U244(isLNatKind(activate(V2)),activate(V1),activate(V2))
U244(tt,V1,V2) -> U245(isLNat(activate(V1)),activate(V2))
U245(tt,V2) -> U246(isLNat(activate(V2)))
U246(tt) -> tt
U251(tt,V1,V2) -> U252(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U252(tt,V1,V2) -> U253(isLNatKind(activate(V2)),activate(V1),activate(V2))
U253(tt,V1,V2) -> U254(isLNatKind(activate(V2)),activate(V1),activate(V2))
U254(tt,V1,V2) -> U255(isNatural(activate(V1)),activate(V2))
U255(tt,V2) -> U256(isLNat(activate(V2)))
U256(tt) -> tt
U261(tt,V2) -> U262(isLNatKind(activate(V2)))
U262(tt) -> tt
U271(tt,V2) -> U272(isLNatKind(activate(V2)))
U272(tt) -> tt
U281(tt,N) -> U282(isNaturalKind(activate(N)),activate(N))
U282(tt,N) -> cons(activate(N),n__natsFrom(n__s(activate(N))))
U291(tt,N,XS) -> U292(isNaturalKind(activate(N)),activate(N),activate(XS))
U292(tt,N,XS) -> U293(isLNat(activate(XS)),activate(N),activate(XS))
U293(tt,N,XS) -> U294(isLNatKind(activate(XS)),activate(N),activate(XS))
U294(tt,N,XS) -> head(afterNth(activate(N),activate(XS)))
U301(tt,X,Y) -> U302(isLNatKind(activate(X)),activate(Y))
U302(tt,Y) -> U303(isLNat(activate(Y)),activate(Y))
U303(tt,Y) -> U304(isLNatKind(activate(Y)),activate(Y))
U304(tt,Y) -> activate(Y)
U31(tt,N,XS) -> U32(isNaturalKind(activate(N)),activate(N),activate(XS))
U311(tt,XS) -> U312(isLNatKind(activate(XS)),activate(XS))
U312(tt,XS) -> pair(nil,activate(XS))
U32(tt,N,XS) -> U33(isLNat(activate(XS)),activate(N),activate(XS))
U321(tt,N,X,XS) -> U322(isNaturalKind(activate(N)),activate(N),activate(X),activate(XS))
U322(tt,N,X,XS) -> U323(isNatural(activate(X)),activate(N),activate(X),activate(XS))
U323(tt,N,X,XS) -> U324(isNaturalKind(activate(X)),activate(N),activate(X),activate(XS))
U324(tt,N,X,XS) -> U325(isLNat(activate(XS)),activate(N),activate(X),activate(XS))
U325(tt,N,X,XS) -> U326(isLNatKind(activate(XS)),activate(N),activate(X),activate(XS))
U326(tt,N,X,XS) -> U327(splitAt(activate(N),activate(XS)),activate(X))
U327(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
U33(tt,N,XS) -> U34(isLNatKind(activate(XS)),activate(N))
U331(tt,N,XS) -> U332(isNaturalKind(activate(N)),activate(XS))
U332(tt,XS) -> U333(isLNat(activate(XS)),activate(XS))
U333(tt,XS) -> U334(isLNatKind(activate(XS)),activate(XS))
U334(tt,XS) -> activate(XS)
U34(tt,N) -> activate(N)
U341(tt,N,XS) -> U342(isNaturalKind(activate(N)),activate(N),activate(XS))
U342(tt,N,XS) -> U343(isLNat(activate(XS)),activate(N),activate(XS))
U343(tt,N,XS) -> U344(isLNatKind(activate(XS)),activate(N),activate(XS))
U344(tt,N,XS) -> fst(splitAt(activate(N),activate(XS)))
U41(tt,V1,V2) -> U42(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U42(tt,V1,V2) -> U43(isLNatKind(activate(V2)),activate(V1),activate(V2))
U43(tt,V1,V2) -> U44(isLNatKind(activate(V2)),activate(V1),activate(V2))
U44(tt,V1,V2) -> U45(isNatural(activate(V1)),activate(V2))
U45(tt,V2) -> U46(isLNat(activate(V2)))
U46(tt) -> tt
U51(tt,V1,V2) -> U52(isNaturalKind(activate(V1)),activate(V1),activate(V2))
U52(tt,V1,V2) -> U53(isLNatKind(activate(V2)),activate(V1),activate(V2))
U53(tt,V1,V2) -> U54(isLNatKind(activate(V2)),activate(V1),activate(V2))
U54(tt,V1,V2) -> U55(isNatural(activate(V1)),activate(V2))
U55(tt,V2) -> U56(isLNat(activate(V2)))
U56(tt) -> tt
U61(tt,V1) -> U62(isPLNatKind(activate(V1)),activate(V1))
U62(tt,V1) -> U63(isPLNat(activate(V1)))
U63(tt) -> tt
U71(tt,V1) -> U72(isNaturalKind(activate(V1)),activate(V1))
U72(tt,V1) -> U73(isNatural(activate(V1)))
U73(tt) -> tt
U81(tt,V1) -> U82(isPLNatKind(activate(V1)),activate(V1))
U82(tt,V1) -> U83(isPLNat(activate(V1)))
U83(tt) -> tt
U91(tt,V1) -> U92(isLNatKind(activate(V1)),activate(V1))
U92(tt,V1) -> U93(isLNat(activate(V1)))
U93(tt) -> tt
afterNth(N,XS) -> U11(isNatural(N),N,XS)
fst(pair(X,Y)) -> U21(isLNat(X),X,Y)
head(cons(N,XS)) -> U31(isNatural(N),N,activate(XS))
isLNat(n__nil) -> tt
isLNat(n__afterNth(V1,V2)) -> U41(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNat(n__cons(V1,V2)) -> U51(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNat(n__fst(V1)) -> U61(isPLNatKind(activate(V1)),activate(V1))
isLNat(n__natsFrom(V1)) -> U71(isNaturalKind(activate(V1)),activate(V1))
isLNat(n__snd(V1)) -> U81(isPLNatKind(activate(V1)),activate(V1))
isLNat(n__tail(V1)) -> U91(isLNatKind(activate(V1)),activate(V1))
isLNat(n__take(V1,V2)) -> U101(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isLNatKind(n__nil) -> tt
isLNatKind(n__afterNth(V1,V2)) -> U111(isNaturalKind(activate(V1)),activate(V2))
isLNatKind(n__cons(V1,V2)) -> U121(isNaturalKind(activate(V1)),activate(V2))
isLNatKind(n__fst(V1)) -> U131(isPLNatKind(activate(V1)))
isLNatKind(n__natsFrom(V1)) -> U141(isNaturalKind(activate(V1)))
isLNatKind(n__snd(V1)) -> U151(isPLNatKind(activate(V1)))
isLNatKind(n__tail(V1)) -> U161(isLNatKind(activate(V1)))
isLNatKind(n__take(V1,V2)) -> U171(isNaturalKind(activate(V1)),activate(V2))
isNatural(n__0) -> tt
isNatural(n__head(V1)) -> U181(isLNatKind(activate(V1)),activate(V1))
isNatural(n__s(V1)) -> U191(isNaturalKind(activate(V1)),activate(V1))
isNatural(n__sel(V1,V2)) -> U201(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isNaturalKind(n__0) -> tt
isNaturalKind(n__head(V1)) -> U211(isLNatKind(activate(V1)))
isNaturalKind(n__s(V1)) -> U221(isNaturalKind(activate(V1)))
isNaturalKind(n__sel(V1,V2)) -> U231(isNaturalKind(activate(V1)),activate(V2))
isPLNat(n__pair(V1,V2)) -> U241(isLNatKind(activate(V1)),activate(V1),activate(V2))
isPLNat(n__splitAt(V1,V2)) -> U251(isNaturalKind(activate(V1)),activate(V1),activate(V2))
isPLNatKind(n__pair(V1,V2)) -> U261(isLNatKind(activate(V1)),activate(V2))
isPLNatKind(n__splitAt(V1,V2)) -> U271(isNaturalKind(activate(V1)),activate(V2))
natsFrom(N) -> U281(isNatural(N),N)
sel(N,XS) -> U291(isNatural(N),N,XS)
snd(pair(X,Y)) -> U301(isLNat(X),X,Y)
splitAt(0,XS) -> U311(isLNat(XS),XS)
splitAt(s(N),cons(X,XS)) -> U321(isNatural(N),N,X,activate(XS))
tail(cons(N,XS)) -> U331(isNatural(N),N,activate(XS))
take(N,XS) -> U341(isNatural(N),N,XS)
natsFrom(X) -> n__natsFrom(X)
s(X) -> n__s(X)
nil -> n__nil
afterNth(X1,X2) -> n__afterNth(X1,X2)
cons(X1,X2) -> n__cons(X1,X2)
fst(X) -> n__fst(X)
snd(X) -> n__snd(X)
tail(X) -> n__tail(X)
take(X1,X2) -> n__take(X1,X2)
0 -> n__0
head(X) -> n__head(X)
sel(X1,X2) -> n__sel(X1,X2)
pair(X1,X2) -> n__pair(X1,X2)
splitAt(X1,X2) -> n__splitAt(X1,X2)
activate(n__natsFrom(X)) -> natsFrom(activate(X))
activate(n__s(X)) -> s(activate(X))
activate(n__nil) -> nil
activate(n__afterNth(X1,X2)) -> afterNth(activate(X1),activate(X2))
activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
activate(n__fst(X)) -> fst(activate(X))
activate(n__snd(X)) -> snd(activate(X))
activate(n__tail(X)) -> tail(activate(X))
activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
activate(n__0) -> 0
activate(n__head(X)) -> head(activate(X))
activate(n__sel(X1,X2)) -> sel(activate(X1),activate(X2))
activate(n__pair(X1,X2)) -> pair(activate(X1),activate(X2))
activate(n__splitAt(X1,X2)) -> splitAt(activate(X1),activate(X2))
activate(X) -> X
)