(VAR M N V1 V2 X X1 X2 )
(RULES 
        U11(tt, V1, V2) -> U12(isNat(activate(V1)), activate(V2))
        U12(tt, V2) -> U13(isNat(activate(V2)))
        U13(tt) -> tt
        U21(tt, V1) -> U22(isNat(activate(V1)))
        U22(tt) -> tt
        U31(tt, N) -> activate(N)
        U41(tt, M, N) -> s(plus(activate(N), activate(M)))
        and(tt, X) -> activate(X)
        isNat(n__0) -> tt
        isNat(n__plus(V1, V2)) -> U11(and(isNatKind(activate(V1)), n__isNatKind(activate(V2))), activate(V1), activate(V2))
        isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
        isNatKind(n__0) -> tt
        isNatKind(n__plus(V1, V2)) -> and(isNatKind(activate(V1)), n__isNatKind(activate(V2)))
        isNatKind(n__s(V1)) -> isNatKind(activate(V1))
        plus(N, 0) -> U31(and(isNat(N), n__isNatKind(N)), N)
        plus(N, s(M)) -> U41(and(and(isNat(M), n__isNatKind(M)), n__and(isNat(N), n__isNatKind(N))), M, N)
        0 -> n__0
        plus(X1, X2) -> n__plus(X1, X2)
        isNatKind(X) -> n__isNatKind(X)
        s(X) -> n__s(X)
        and(X1, X2) -> n__and(X1, X2)
        activate(n__0) -> 0
        activate(n__plus(X1, X2)) -> plus(X1, X2)
        activate(n__isNatKind(X)) -> isNatKind(X)
        activate(n__s(X)) -> s(X)
        activate(n__and(X1, X2)) -> and(X1, X2)
        activate(X) -> X
        
)