CS321 Automata theory. Please don't use the method that chegg study already has, the method is not correct. Please give me a correct proof. This is the second time I have posted the same question. Thank you

Def: num(x, y) means the number of times x appears as a substring in y 1. Using the pumping lemma technique, prove that the following languages are not regular. For reference, here is the pumping lemma game: 1. Adversary picks a positive integer p 2. You pick w A with [wl 2 p 3. Adversary splits up w into w- xyz with lxyl s p and lyl>0 4. You pick a nonnegative integer i You win the game if xy'z A. If you can describe a strategy in which you always win, then A is not regular. (a) {w {a, b)' I num(aa, w)-num(bbb, w)) Note: Be careful in your counting: bbbb contains the substring bbb two times. (b) {w {a, b)' : lwl is a square number} Hint: choose i so you can argue that the length of the resulting string is strictly between adjacent squares, ie.,