The iteration bound for the algorithm cref{alg:Px}

Let $n$ be the dimension parameter, and let $(C,c)$ be the randomly sampled input used by algorithm. The algorithm repeatedly applies Step~. The iteration-bound conjecture. terminates after repeating Step~ at most $2n$ times. The claim is motivated by the reported experiments, which found termination in fewer than $2n$ iterations for all tested instances; no proof or resolution is provided here.