Last Puzzles (Famous 13 Cave Logic Problem)

A thief was running from the police after the biggest theft the town saw. He took his guard in one of the thirteen caves arranged in a circle. Each day, the thief moves either to the adjacent cave or stay in the same cave. Two cops goes there daily and have enough time to enter any two of the caves out of them. How will the cop make sure to catch the thief in minimum number of days and what are the minimum number of days?

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