Before revision:  We then show that information complexity of treasure hunt for the class of arbitrary terrains (even for non-convex polygons without obstacles, and even for those with only horizontal or vertical sides) is exponentially larger than for regular terrains.
After revision:  We then show that advice complexity of treasure hunt for the class of arbitrary terrains (even for non-convex polygons without obstacles, and even for those with only horizontal or vertical sides) is exponentially larger than for regular terrains.