Your statement about char I disagree with. A char is a byte, as you say. But that means it has numerical value as well. I could have a "identityMatrix" function

Your statement about char I disagree with. A char is a byte, as you say. But that means it has numerical value as well. I could have a "identityMatrix" function that takes a char (because I decide I won't have matrices with a dimension > 256); it would be O(n^2) in operation though. In fact, I could have a 3 dimensional identity matrix creation function, and then it would be O(n^3). I could have a brute force generation of all possible permutations of the numbers 0-input, and now it's O(256!). The input of the function does not tell you anything about the complexity of the function (though it may tell you the max value of N. But, for instance, a function of O(n!) is almost assuredly going to be far, far worse than one with O(1), even if the size of N is maximally 256). All that aside, I agree that the OP is O(1). It does 5 comparisons. It always does 5 comparisons, regardless of the input of the isVowel function. Yes, includes, evaluated out of context, is O(n), but you know something about the context it's used in to be able to give isVowel a tighter bound. That's usually what the goal of Big O is; not to define ~a~ bound, but define the most conservative.