(VAR IL L M N V V1 V2 X X1 X2 )
(RULES 
        zeros -> cons(0, n__zeros)
        U11(tt, L) -> s(length(activate(L)))
        U21(tt) -> nil
        U31(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL)))
        and(tt, X) -> activate(X)
        isNat(n__0) -> tt
        isNat(n__length(V1)) -> isNatList(activate(V1))
        isNat(n__s(V1)) -> isNat(activate(V1))
        isNatIList(V) -> isNatList(activate(V))
        isNatIList(n__zeros) -> tt
        isNatIList(n__cons(V1, V2)) -> and(isNat(activate(V1)), n__isNatIList(activate(V2)))
        isNatList(n__nil) -> tt
        isNatList(n__cons(V1, V2)) -> and(isNat(activate(V1)), n__isNatList(activate(V2)))
        isNatList(n__take(V1, V2)) -> and(isNat(activate(V1)), n__isNatIList(activate(V2)))
        length(nil) -> 0
        length(cons(N, L)) -> U11(and(isNatList(activate(L)), n__isNat(N)), activate(L))
        take(0, IL) -> U21(isNatIList(IL))
        take(s(M), cons(N, IL)) -> U31(and(isNatIList(activate(IL)), n__and(isNat(M), n__isNat(N))), activate(IL), M, N)
        zeros -> n__zeros
        take(X1, X2) -> n__take(X1, X2)
        0 -> n__0
        length(X) -> n__length(X)
        s(X) -> n__s(X)
        cons(X1, X2) -> n__cons(X1, X2)
        isNatIList(X) -> n__isNatIList(X)
        nil -> n__nil
        isNatList(X) -> n__isNatList(X)
        isNat(X) -> n__isNat(X)
        and(X1, X2) -> n__and(X1, X2)
        activate(n__zeros) -> zeros
        activate(n__take(X1, X2)) -> take(X1, X2)
        activate(n__0) -> 0
        activate(n__length(X)) -> length(X)
        activate(n__s(X)) -> s(X)
        activate(n__cons(X1, X2)) -> cons(X1, X2)
        activate(n__isNatIList(X)) -> isNatIList(X)
        activate(n__nil) -> nil
        activate(n__isNatList(X)) -> isNatList(X)
        activate(n__isNat(X)) -> isNat(X)
        activate(n__and(X1, X2)) -> and(X1, X2)
        activate(X) -> X
        
)