Explain precisely how to modify the AND-OR-GRAPH-SEARCH algorithm to generate a cyclic plan if no acyclic plan exists. You will need to deal with three issues: labeling the plan steps so that a cyclic plan can point back tc~a n earlier part of the plan, modifying OR-SEARCH so that it continues to look for acyclic plans after finding a cyclic plan, and augmenting the plan representation to indicate whether a plan is cyclic. Show how your algorithm works on

(a) the triple Murphy vacuum world, and

(b) the alternate double Murphy vacuum world. You might wish to use a computer implementation to check your results. Can the plan for case

(b) be written using standard loop syntax?