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