(VAR N XS X Y YS ZS V1 V2 X1 X2 X3 X4)
(RULES 
a__U101(tt,N,XS) -> a__fst(a__splitAt(mark(N),mark(XS)))
a__U11(tt,N,XS) -> a__snd(a__splitAt(mark(N),mark(XS)))
a__U21(tt,X) -> mark(X)
a__U31(tt,N) -> mark(N)
a__U41(tt,N) -> cons(mark(N),natsFrom(s(N)))
a__U51(tt,N,XS) -> a__head(a__afterNth(mark(N),mark(XS)))
a__U61(tt,Y) -> mark(Y)
a__U71(tt,XS) -> pair(nil,mark(XS))
a__U81(tt,N,X,XS) -> a__U82(a__splitAt(mark(N),mark(XS)),X)
a__U82(pair(YS,ZS),X) -> pair(cons(mark(X),YS),mark(ZS))
a__U91(tt,XS) -> mark(XS)
a__afterNth(N,XS) -> a__U11(a__and(a__isNatural(N),isLNat(XS)),N,XS)
a__and(tt,X) -> mark(X)
a__fst(pair(X,Y)) -> a__U21(a__and(a__isLNat(X),isLNat(Y)),X)
a__head(cons(N,XS)) -> a__U31(a__and(a__isNatural(N),isLNat(XS)),N)
a__isLNat(nil) -> tt
a__isLNat(afterNth(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
a__isLNat(cons(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
a__isLNat(fst(V1)) -> a__isPLNat(V1)
a__isLNat(natsFrom(V1)) -> a__isNatural(V1)
a__isLNat(snd(V1)) -> a__isPLNat(V1)
a__isLNat(tail(V1)) -> a__isLNat(V1)
a__isLNat(take(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
a__isNatural(0) -> tt
a__isNatural(head(V1)) -> a__isLNat(V1)
a__isNatural(s(V1)) -> a__isNatural(V1)
a__isNatural(sel(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
a__isPLNat(pair(V1,V2)) -> a__and(a__isLNat(V1),isLNat(V2))
a__isPLNat(splitAt(V1,V2)) -> a__and(a__isNatural(V1),isLNat(V2))
a__natsFrom(N) -> a__U41(a__isNatural(N),N)
a__sel(N,XS) -> a__U51(a__and(a__isNatural(N),isLNat(XS)),N,XS)
a__snd(pair(X,Y)) -> a__U61(a__and(a__isLNat(X),isLNat(Y)),Y)
a__splitAt(0,XS) -> a__U71(a__isLNat(XS),XS)
a__splitAt(s(N),cons(X,XS)) -> a__U81(a__and(a__isNatural(N),and(isNatural(X),isLNat(XS))),N,X,XS)
a__tail(cons(N,XS)) -> a__U91(a__and(a__isNatural(N),isLNat(XS)),XS)
a__take(N,XS) -> a__U101(a__and(a__isNatural(N),isLNat(XS)),N,XS)
mark(U101(X1,X2,X3)) -> a__U101(mark(X1),X2,X3)
mark(fst(X)) -> a__fst(mark(X))
mark(splitAt(X1,X2)) -> a__splitAt(mark(X1),mark(X2))
mark(U11(X1,X2,X3)) -> a__U11(mark(X1),X2,X3)
mark(snd(X)) -> a__snd(mark(X))
mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
mark(natsFrom(X)) -> a__natsFrom(mark(X))
mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3)
mark(head(X)) -> a__head(mark(X))
mark(afterNth(X1,X2)) -> a__afterNth(mark(X1),mark(X2))
mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
mark(U71(X1,X2)) -> a__U71(mark(X1),X2)
mark(U81(X1,X2,X3,X4)) -> a__U81(mark(X1),X2,X3,X4)
mark(U82(X1,X2)) -> a__U82(mark(X1),X2)
mark(U91(X1,X2)) -> a__U91(mark(X1),X2)
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNatural(X)) -> a__isNatural(X)
mark(isLNat(X)) -> a__isLNat(X)
mark(isPLNat(X)) -> a__isPLNat(X)
mark(tail(X)) -> a__tail(mark(X))
mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
mark(tt) -> tt
mark(cons(X1,X2)) -> cons(mark(X1),X2)
mark(s(X)) -> s(mark(X))
mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
mark(nil) -> nil
mark(0) -> 0
a__U101(X1,X2,X3) -> U101(X1,X2,X3)
a__fst(X) -> fst(X)
a__splitAt(X1,X2) -> splitAt(X1,X2)
a__U11(X1,X2,X3) -> U11(X1,X2,X3)
a__snd(X) -> snd(X)
a__U21(X1,X2) -> U21(X1,X2)
a__U31(X1,X2) -> U31(X1,X2)
a__U41(X1,X2) -> U41(X1,X2)
a__natsFrom(X) -> natsFrom(X)
a__U51(X1,X2,X3) -> U51(X1,X2,X3)
a__head(X) -> head(X)
a__afterNth(X1,X2) -> afterNth(X1,X2)
a__U61(X1,X2) -> U61(X1,X2)
a__U71(X1,X2) -> U71(X1,X2)
a__U81(X1,X2,X3,X4) -> U81(X1,X2,X3,X4)
a__U82(X1,X2) -> U82(X1,X2)
a__U91(X1,X2) -> U91(X1,X2)
a__and(X1,X2) -> and(X1,X2)
a__isNatural(X) -> isNatural(X)
a__isLNat(X) -> isLNat(X)
a__isPLNat(X) -> isPLNat(X)
a__tail(X) -> tail(X)
a__take(X1,X2) -> take(X1,X2)
a__sel(X1,X2) -> sel(X1,X2)
)