(VAR M N V1 V2 X X1 X2 )
(RULES 
        U11(tt, V2) -> U12(isNat(activate(V2)))
        U12(tt) -> tt
        U21(tt) -> tt
        U31(tt, N) -> activate(N)
        U41(tt, M, N) -> U42(isNat(activate(N)), activate(M), activate(N))
        U42(tt, M, N) -> s(plus(activate(N), activate(M)))
        isNat(n__0) -> tt
        isNat(n__plus(V1, V2)) -> U11(isNat(activate(V1)), activate(V2))
        isNat(n__s(V1)) -> U21(isNat(activate(V1)))
        plus(N, 0) -> U31(isNat(N), N)
        plus(N, s(M)) -> U41(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
        
)