(VAR L N V V1 V2 X X1 X2 )
(RULES 
        zeros -> cons(0, n__zeros)
        U11(tt, V1) -> U12(isNatList(activate(V1)))
        U12(tt) -> tt
        U21(tt, V1) -> U22(isNat(activate(V1)))
        U22(tt) -> tt
        U31(tt, V) -> U32(isNatList(activate(V)))
        U32(tt) -> tt
        U41(tt, V1, V2) -> U42(isNat(activate(V1)), activate(V2))
        U42(tt, V2) -> U43(isNatIList(activate(V2)))
        U43(tt) -> tt
        U51(tt, V1, V2) -> U52(isNat(activate(V1)), activate(V2))
        U52(tt, V2) -> U53(isNatList(activate(V2)))
        U53(tt) -> tt
        U61(tt, L) -> s(length(activate(L)))
        and(tt, X) -> activate(X)
        isNat(n__0) -> tt
        isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)), activate(V1))
        isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
        isNatIList(V) -> U31(isNatIListKind(activate(V)), activate(V))
        isNatIList(n__zeros) -> tt
        isNatIList(n__cons(V1, V2)) -> U41(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2))
        isNatIListKind(n__nil) -> tt
        isNatIListKind(n__zeros) -> tt
        isNatIListKind(n__cons(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2)))
        isNatKind(n__0) -> tt
        isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
        isNatKind(n__s(V1)) -> isNatKind(activate(V1))
        isNatList(n__nil) -> tt
        isNatList(n__cons(V1, V2)) -> U51(and(isNatKind(activate(V1)), n__isNatIListKind(activate(V2))), activate(V1), activate(V2))
        length(nil) -> 0
        length(cons(N, L)) -> U61(and(and(isNatList(activate(L)), n__isNatIListKind(activate(L))), n__and(n__isNat(N), n__isNatKind(N))), activate(L))
        zeros -> n__zeros
        0 -> n__0
        length(X) -> n__length(X)
        s(X) -> n__s(X)
        cons(X1, X2) -> n__cons(X1, X2)
        isNatIListKind(X) -> n__isNatIListKind(X)
        nil -> n__nil
        and(X1, X2) -> n__and(X1, X2)
        isNat(X) -> n__isNat(X)
        isNatKind(X) -> n__isNatKind(X)
        activate(n__zeros) -> zeros
        activate(n__0) -> 0
        activate(n__length(X)) -> length(activate(X))
        activate(n__s(X)) -> s(activate(X))
        activate(n__cons(X1, X2)) -> cons(activate(X1), X2)
        activate(n__isNatIListKind(X)) -> isNatIListKind(X)
        activate(n__nil) -> nil
        activate(n__and(X1, X2)) -> and(activate(X1), X2)
        activate(n__isNat(X)) -> isNat(X)
        activate(n__isNatKind(X)) -> isNatKind(X)
        activate(X) -> X
        
)