W1 Using our rules for Hoare logic, prove the correctness of the following program that computes the integer n'th power of integer r. Although you might want to figure out the proof using tree lavout, give vour solution in linear form similar to the proofs of division given in the textbook. We give the initial assumption In20} and final goal TL in the program below: // Slow Exponentiation while (k>0) do k:= k-1 done Bonus points Why is this called slow exponentiation? To get one bonus point, give code that is exponentially faster in n, and to get the second bonus point, argue convincingly that your speedup is exponential W1 Using our rules for Hoare logic, prove the correctness of the following program that computes the integer n'th power of integer r. Although you might want to figure out the proof using tree lavout, give vour solution in linear form similar to the proofs of division given in the textbook. We give the initial assumption In20} and final goal TL in the program below: // Slow Exponentiation while (k>0) do k:= k-1 done Bonus points Why is this called slow exponentiation? To get one bonus point, give code that is exponentially faster in n, and to get the second bonus point, argue convincingly that your speedup is exponential