Termination of the minimum expected cost algorithm

Let Algorithm~ be the algorithm defined in the paper, let $M$ denote its termination parameter, and let $\epsilon>0$. Termination conjecture. Algorithm~ will terminate with $M=\infty$ for any $\epsilon>0$. The conjecture concerns convergence of the algorithm used to compute a minimum expected search cost; the supplied text gives no resolution or further conditions, so its status remains open.