Why is big-O analysis hard?

We are interested in increasing comprehension of how students understand big-O analysis. We conducted a qualitative analysis of interviews with two undergraduate students to identify sources of difficulty within the topic of big-O. This demonstrates the existence of various difficulties, which contribute to the sparse research on students' understanding of pedagogy. The students involved in the study have only minimal experience with big-O analysis, discussed within the first two introductory computer science courses. During these hour-long interviews, the students were asked to analyze code or a paragraph to find the runtime of the algorithm involved and invited students to write code that would in run a certain runtime. From these interactions, we conclude that students that have difficulties with big-O could be having trouble with the mathematical function used in the analysis and/or the techniques they used to solve the problem.