Suppose we play a chess-variant, where any finite number of pieces are allowed, and the board is as large as we wish, but only two kings in total. And there is no 50 move-rule, no castling and no captures and no pawn-moves.
Then is it possible to have a a pair of positions A and B, such that we can go from configuration A to B by legal moves, but not from B to A?
No stalemates or checkmates allowed, the game must be extendable atleast two moves in both direction from both A and B.
Two configurations are different also if the pieces are in the same places but it is a different player to move.