In the Futurama movie Bender's Big Score, after finding the key to time travel tattooed on Fry and sending Bender to rob history of its treasures (and incidentally to encounter himself), the Scammers decide to eliminate the existence of the code by destroying Fry. Fry uses the code to escape to the past, and Bender is sent to terminate him, and a merry chase ensues. It is a complicated and convoluted chase, as both parties use the time code again, and then interact with their own duplicates.
Fry goes to half past midnight New Year's Day 2000, moments after he originally fell into the cryo machine that preserved him for the future. Shortly after Fry's departure, Bender leaves, arriving two minutes before Fry; but that does not mean Bender is already waiting when Fry arrives. Before Bender can leave from the future, time must resolve between Fry's 2000 arrival and the moment of Bender's departure. During that time, Fry goes to the pizza parlor, realizes he can't get pizza, returns to the cryo lab where there is cold pizza waiting, and then uses the code to go back an hour to seconds after his original arrival so he can get hot pizza. This means that before Bender can leave the future, there are two Frys in the past. They meet; they do not encounter Bender. The one who has not yet been to the pizza parlor goes there, arriving a minute later, and apparently deciding that a place to live was more important than a slice of pizza--but the other had not already arrived there, because this is a new history. The double back at the cryo lab remembers that the original has money in his wallet, and in attempting to take it falls into the cryo machine, where he remains until the original Fry gets out and accidently resets the machine for another eight years.
Because the Fry who in our view arrived "second" never made the one hour trip back for hot pizza, the Fry who arrived "first" now cannot exist. This should create an infinity loop, preventing the future beyond an hour after Fry's arrival, and undoing everything that ever happened in Futurama. Some would call that a good thing. However, Futurama has ignored this aspect of its doppelgangers, and so we will follow the thread as if there were a way for a doppelganger to exist by not making the same time trip made by the original.
Before those eight years can elapse, Bender makes most of his trips and begins his terminator hunt. He arrives two minutes before Fry, but then needs to leave the room unattended for a moment, and so uses the time code to copy himself, meeting the version of himself just arriving from the future. There are now two Benders; and since they arrived from the future in which there are two Frys, both Frys will arrive momentarily.
(It is at this moment that Tuxedo Bender appears with the tattoo, but he is not relevant to the chase.)
The Fry from a millennium away arrives first, and confronts the Bender who was left on guard; that Bender goes into self-destruct mode and is pushed into a cryo capsule. The other Fry watches. Then they talk about the pizza, and the Fry who has not yet been to the pizza parlor goes there and again chooses getting an apartment over getting a slice.
At this point there are two doppelgangers, one of Fry and one of Bender. One of each pair is in cryo--but it is the opposite one of each. The "doomed" Bender is in stasis (his doom delayed, although why cryonic suspension would stop a self destruct sequence on a robot is another of those side points that should snap your disbelief suspenders), but the "doomed" Fry is staying in an apartment over a pizza parlor. Each of those should have caused an infinity loop, but instead Futurama choose to assume that the one who did not travel to the past is doomed, awaiting his fate.
No one likes a cliffhanger, but the chase is the most complicated aspect of the time travel in the movie, and as Bender pursues a doomed duplicate Fry, more nonsense lies ahead next time.
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