My question is: can you add more context to it's use at the Circle- K? I don't quite remember how this logic is sued there. I haven't seen the film in a while.
In the movie Bill and Ted are at the Circle-K working on their report when Rufus and the phone-booth arrive. Rufus is talking to them about the booth and their report when
another phone booth arrives. This one is damaged and carrying Bill, Ted and the historical figures. "Future Bill and Ted" come out of it and talk with themselves (the whole, "What number am I thinking of?"/"69!" bit). Rufus leads them away, much to the confusion of our Bill and Ted. "Future Bill" instructs "our" Bill to say "Hi!" to the princesses (much to OB's confusion). As Rufus is talking to Future Bill and Ted our Bill and Ted remain confused.
"Future" Ted shouts to Our Ted to remember to wind his watch (Why Ted owns a watch that needs winding is a mystery) and they depart. Rufus returns to our Bill and Ted and the story begins.
Later in the movie after their adventures through time we see the other end of this encounter ("Our" Bill and Ted now being the "Future" Bill and Ted talking to their past selves.) The scene plays out exactly the same. (Though we skip part of it, for the sake of brevity.) We also get to see the other end of the conversation where Rufus checks in on the boys, they find out it's "already tomorrow" and they need to dial a number higher in order to get back into the present. (Why they can't simply stay there and have all night to work on the report is another mystery.) Ted reminds his past-self to wind his watch (which, obviously, is a pointless exercise because it won't and CANNOT work) then Bill and Ted set off for "tomorrow" and the rest of the movie. Once departed Rufus offers the new booth to Bill and Ted.
It's just a beautiful, beautiful scene showing how I believe time travel works. In a closed loop system. The past comes first so the past HAPPENS first even if that past happens to include events from the future. It's a predestination paradox sort of thing and also says a LOT about free-will (at least in the B&T Universe or a universe with a closed timeline.)
Like I said, no matter what happens Ted will forget to wind his watch! Reminding himself to do it had no impact on anything, he forgot to do it. That cannot be changed. In the B&T universe these historical figures were ALWAYS kidnapped by B&T and taken into the future to do this report and everything that the world is built on is BASED on this. Taking the princesses from the past doesn't change anything, they ALWAYS disappeared from the past even if the time they were taken from happened centuries before Bill and Ted get the time machine which they get centuries before it's even invented!
It's just a beautiful, beautiful use of time travel. The keys thing also being a great point in it as well as other tricks they use to "set-up" events. (Like how they managed to get everyone out of jail.) I need to watch that movie again now.