(VAR M N V1 V2 X X1 X2 )
(RULES 
        U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2))
        U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2))
        U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2))
        U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2))
        U15(tt, V2) -> U16(isNat(activate(V2)))
        U16(tt) -> tt
        U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1))
        U22(tt, V1) -> U23(isNat(activate(V1)))
        U23(tt) -> tt
        U31(tt, V2) -> U32(isNatKind(activate(V2)))
        U32(tt) -> tt
        U41(tt) -> tt
        U51(tt, N) -> U52(isNatKind(activate(N)), activate(N))
        U52(tt, N) -> activate(N)
        U61(tt, M, N) -> U62(isNatKind(activate(M)), activate(M), activate(N))
        U62(tt, M, N) -> U63(isNat(activate(N)), activate(M), activate(N))
        U63(tt, M, N) -> U64(isNatKind(activate(N)), activate(M), activate(N))
        U64(tt, M, N) -> s(plus(activate(N), activate(M)))
        isNat(n__0) -> tt
        isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2))
        isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1))
        isNatKind(n__0) -> tt
        isNatKind(n__plus(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V2))
        isNatKind(n__s(V1)) -> U41(isNatKind(activate(V1)))
        plus(N, 0) -> U51(isNat(N), N)
        plus(N, s(M)) -> U61(isNat(M), M, N)
        0 -> n__0
        plus(X1, X2) -> n__plus(X1, X2)
        s(X) -> n__s(X)
        activate(n__0) -> 0
        activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2))
        activate(n__s(X)) -> s(activate(X))
        activate(X) -> X
        
)