Your misreading: the turtle doesn't move at all. It teleports to the rabbit's location. (Counting following a link as a move, which seems to be the costly operation being optimized for.)<p>For every full iteration of the loop, TH (tortoise and hare) follows 3 links, while TT (teleporting turtle) follows 1 link. In the loop case, where the loop of length n is linked in at k steps, the there must be at least k iterations of both loops (the turtle or tortoise must reach the loop). In the no-loop case, there must be at least n iterations of the TT case but TH can get away with n/2 iterations. Unfortunately, each iteration of TH has more than twice the cost of an iteration of TT, when optimizing for following loops.