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## Main Question or Discussion Point

It says that |xy| < p. But I don't understand why even after reading the proof. If I have a four state DFA, whose last state is the one that is gonna repeat for a given input string of length p, |x| is already gonna be four, since it represents the states necessary to reach the repetition state. So in this worst case scenery, |x| is already equal to p, so with |y|>0 we already have |xy|>p. SO what's wrong with my line of thought