KöMaL 2009 A475

To each vertex of a regular $n$-gon a real number is assigned in such a way that the sum of all $n$ 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 $n$ numbers is negative. Determine whether this procedure necessarily terminates after a finite number of steps.