5. Suppose we must solve planning problems for cleaning a house. Various rooms can be dusted

(making the room dust-free) or swept (making the room have a clean floor), but the robot can only sweep or dust a room if it is in that room. Sweeping causes a room to become dusty (i.e., not dust-free). The robot can only dust a room if the dustcloth is clean; but dusting rooms that are extra-dusty, like the garage, cause the dustcloth to become dirty. The robot can move directly from any room to any other room.

Assume there are only two rooms, the garage – which, if it is dusty, is extra-dusty – and the living room – which is not extra-dusty. Assume the following features