  The Pollard Rho algorithm is a widely used algorithm for solving discrete
logarithms on general cyclic groups, including elliptic curves. Recently the
first nontrivial runtime estimates were provided for it, culminating in a sharp
O(sqrt(n)) bound for the collision time on a cyclic group of order n. In this
paper we show that for n satisfying a mild arithmetic condition, the collisions
guaranteed by these results are nondegenerate with high probability: that is,
the Pollard Rho algorithm successfully finds the discrete logarithm.
