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I agree with everything you said, but I don't see how it leads the OP's formulation being silly or wrong or not useful. Here's another example (of my own) where you can pick an upper bound for `n` and base your complexity analysis around it. In this case, we're trying to provide an API guarantee that a search takes O(m+n) time despite wanting to use an O(mn) algorithm in some subset of cases. We can still meet the O(m+n) bound by reasoning that the O(mn) algorithm is only used in a finite set of cases, and thus collapses to O(1) time. Therefore, the O(m+n) time bound is preserved. And this isn't a trick either. That really is the scaling behavior of the implementation. See: https://github.com/BurntSushi/memchr/blob/ce7b8e606410f6c81a...
> If an algorithm is defined as being unscalable (fixed input), what sense does it make to describe that it scales constantly with input size?
I'll answer your question with another: in what cases does it make sense to describe the scaling behavior of algorithm with O(1)?