Two people start in the same cell in an orthogonal grid of infinite size.
Each cell has four edges, and hence, a maximum of four ways to enter or exit it.
Every edge in the grid is either a wall or not a wall.
Each person will choose to execute a series of moves, which will consist of 'north', 'south', 'east' and 'west' instructions.
If a wall exists in a direction your instruction indicates, the instruction will be skipped.
You can assume that there are an infinite number of cells that are accessible from the starting cell; i.e. walls do not box you into some non-infinite subset of cells.
The two persons can reside on the same cell or cross each other; their movement ignores each other's existence.
Find a pair of sequences of instructions (of minimum possible total length) - the first to be executed by the first person and the second to be executed by the second person, such that no matter the details of the maze, you can guarantee that atleast one of the two persons doesn't end up at the starting cell, once execution completes.
P.S. I'm not sure this can be done; if it can't, prove that.