716.3. Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.
Example: In a two-player game, the active player controls a creature with the ability “{0}: gains flying,” the nonactive player controls a permanent with the ability “{0}: Target creature loses flying,” and nothing in the game cares how many times an ability has been activated. Say the active player activates his creature’s ability, it resolves, then the nonactive player activates her permanent’s ability targeting that creature, and it resolves. This returns the game to a game state it was at before. The active player must make a different game choice (in other words, anything other than activating that creature’s ability again). The creature doesn’t have flying. Note that the nonactive player could have prevented the fragmented loop simply by not activating her permanent’s ability, in which case the creature would have had flying. The nonactive player always has the final choice and is therefore able to determine whether the creature has flying.