Suppose a finite deck of numeric cards 1, 2, 3, ... have been shuffled randomly. Repeat the following step: If the top card is numbered 1, the game terminates. But if it is any number n > 1, then reverse the ordering of the top n cards on the deck and iterate. Example: 42153 > 51243 > 34215 > 24315 > 42315 > 13245. Is this game guaranteed to eventually terminate? Prove your answer.