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