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Pop-Stack Sorting is an algorithm that takes a permutation as an input andsorts its elements. It consists of several steps. At one step, the algorithmreads the permutation it has to process from left to right and reverses each ofits maximal decreasing subsequences of consecutive elements. It terminates atthe first step that outputs the identity permutation.  In this note, we answer a question of Defant on the running time of Pop-StackSorting on the uniform random permutation $\sigma_n$. More precisely, we showthat there is a constant $c > 0.5$ such that asymptotically almost surely, thealgorithm needs at least $cn$ steps to terminate on $\sigma_n$.

Lower bound on the running time of Pop-Stack Sorting on a random permutation