It is trivial that with the above scenario, INSERTION SORT is the only optimal sorting algorithm as there are no other possible alternative approaches that can satisfy all the above constraints, thus we have to relax some of the requirements—this paper assumes select does not need to run in O(1)time, meaning partial order is tolerable until all elements in X are inserted. It is essential that select should still run reasonably fast, or it will lose the purpose of being incremental.