Show how a partial$-$order regression planner works by deriving a plan for the Blocks World

problem described below. The available operators are as follows.

Action$($Move$($b$,$ x$,$ y$),$

P recond : On$($b$,$ x$)$ Clear$($b$)$ Clear$($y$),$

Effect : On$($b$,$ y$)$ Clear$($x$)$On$($b$,$ x$)$Clear$($y$))$

Action$($MoveT oT able$($b$,$ x$),$

P recond : On$($b$,$ x$)$ Clear$($b$),$

Effect : On$($b$,$ T able$)$ Clear$($x$)$On$($b$,$ x$))$

You may assume that the interpretation of Clear$($b$)$ means that there is a clear space on b

to place a block, and so Clear$($T able$)$ will always be true.

The initial state for the problem is

On$($C$,$ A$),$ On$($A$,$ T able$),$ On$($B$,$ T able$),$ Clear$($B$),$ Clear$($C$)$

and the goal state that your plan should achieve is

On$($A$,$ B$),$ On$($B$,$ C$),$ On$($C$,$ T able$),$ Clear$($A$).$