Representability of a finite relation algebra is determined by playing a certain two player game over `atomic -networks'. It can be shown that the second player in this game has a winning strategy if and only if is representable.
Let be a finite set of square tiles, where each edge of each tile has a colour. Suppose includes a special tile whose four edges are all the same colour, a colour not used by any other tile. The tiling problem we use is this: is it the case that for each tile there is a tiling of the plane using only tiles from in which edge colours of adjacent tiles match and with placed at ? It is not hard to show that this problem is undecidable.
From an instance of this tiling problem , we construct a finite relation algebra and show that the second player has a winning strategy in if and only if is a yes-instance. This reduces the tiling problem to the representation problem and proves the latter's undecidability.