An elementary point is a point in complex n space, which is an isolated, nonsingular solution of и equations in n variables, each equation being either of the form p = 0, where p is a polynomial in Q[x_1,..., x_n], or of the form x_j — е^(x_i) = 0. An elementary number is the polynomial image of an elementary point. In this article a semi algorithm is given to decide whether or not a given elementary number is zero. It is proved that this semi algorithm is an algorithm, i.e. that it always terminates, unless it is given a problem containing a counterexample to SchanucPs conjecture.