(VAR IL L M N T X X1 X2 )
(RULES 
        and(tt, T) -> T
        isNatIList(IL) -> isNatList(activate(IL))
        isNat(n__0) -> tt
        isNat(n__s(N)) -> isNat(activate(N))
        isNat(n__length(L)) -> isNatList(activate(L))
        isNatIList(n__zeros) -> tt
        isNatIList(n__cons(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
        isNatList(n__nil) -> tt
        isNatList(n__cons(N, L)) -> and(isNat(activate(N)), isNatList(activate(L)))
        isNatList(n__take(N, IL)) -> and(isNat(activate(N)), isNatIList(activate(IL)))
        zeros -> cons(0, n__zeros)
        take(0, IL) -> uTake1(isNatIList(IL))
        uTake1(tt) -> nil
        take(s(M), cons(N, IL)) -> uTake2(and(isNat(M), and(isNat(N), isNatIList(activate(IL)))), M, N, activate(IL))
        uTake2(tt, M, N, IL) -> cons(activate(N), n__take(activate(M), activate(IL)))
        length(cons(N, L)) -> uLength(and(isNat(N), isNatList(activate(L))), activate(L))
        uLength(tt, L) -> s(length(activate(L)))
        0 -> n__0
        s(X) -> n__s(X)
        length(X) -> n__length(X)
        zeros -> n__zeros
        cons(X1, X2) -> n__cons(X1, X2)
        nil -> n__nil
        take(X1, X2) -> n__take(X1, X2)
        activate(n__0) -> 0
        activate(n__s(X)) -> s(X)
        activate(n__length(X)) -> length(X)
        activate(n__zeros) -> zeros
        activate(n__cons(X1, X2)) -> cons(X1, X2)
        activate(n__nil) -> nil
        activate(n__take(X1, X2)) -> take(X1, X2)
        activate(X) -> X
        
)