Bob is busy saving the world on Puzzling Stack Exchange by tracking down yet another super-villain. Alice rushes in holding a long paper.
A: I made a discovery you will like.
B: I am not on Facebook.
A: Whatever. You have probably seen 3-D or 4-D labyrinths. But have you seen a 1-D labyrinth?
B: 1-D? That cannot be much of a challenge, can it?
A: It can. Look here, I have a map.
ab A bcefgi B acdfghi C bcfgi D bcdg E cefh F efghi G begi H dehi I bcdfgij J j
B: That's a map? A single line?
A: What did you expect? It is a 1-D labyrinth!
B: Hm... OK, maybe. How does it work?
A: It is the access to an abandoned top-secret operations base.
B: These things don't exist!
A: Exactly that type! The access is a long tunnel. There are plenty of checkpoints and heavy doors controlled by buttons. The buttons are all over the place. Normally they are operated by guards. But they are gone.
B: If they are gone, how are you going to open the doors?
A: That is why I need you. Look at the map. The uppercase letters are the heavy doors. The lowercase letters are the buttons operating the corresponding door. You lift a door by pressing the button. You must keep pressing the button or the door slams shut immediately. Some buttons can be operated from outside. I need you to press these buttons so I can cross the first doors. Then I press some other buttons inside and you cross the doors.
B: Isn't it, like, dangerous?
A: No.... I don't think so... And it is exciting! I want to see if together we manage to pass all the doors. Every time you open a door it gives access to new buttons. It is bound to lead somewhere. Let's go and have a try!
B: I have a better idea. I will just put the "map" on Stackexchange and they will crack it in no time.
So dear puzzler, care to help Alice and Bob cross the tunnel?
ab A bcefgi B acdfghi C bcfgi D bcdg E cefh F efghi G begi H dehi I bcdfgij J j
Alice and Bob enter from the left. One of them moves one position at a time. To pass a door (an uppercase letter), the other player must stand at a corresponding button (the lowercase letter). If a player leaves a button it shuts the door, possibly killing anyone standing under the door. The goal is to bring Alice and Bob safely to the right.