Problem 33. Prove that the language A= {x {0,1}* | #(01, x) = #(10,x)} is regular. (Here, for a, b {0,1}, #(ab, x) is the number of as in x that are immediately followed by b.) Recall that the canonical equivalence relation of a language AC * is the binary relation =on * defined by X =A y if and only if, for all z E 2*, [xZ E A Ayz E A]