International Mathematical Olympiad 1986 Problem 3

To each vertex of a regular pentagon an integer is assigned in such a way that the sum of all five numbers is positive. If three consecutive vertices are assigned the numbers $x, y, z$ respectively and $y < 0$ then the following operation is allowed: the numbers $x, y, z$ are replaced by $x + y, -y, z + y$ respectively. Such an operation is performed repeatedly as long as at least one of the five numbers is negative. Determine whether this procedure necessarily comes to and end after a finite number of steps.