Please show all the work. Thank you. (ANALYSIS OF ALGORITHM)

FIND-MAX: Consider the problem of finding the maximal number in a sequence of numbers. Describe the problem in a mathematical way based on Input - Output relation as the Textbook does for the sorting problem at the beginning of Section 2.1. Write the pseudo-code for an algorithm called FIND-MAX that takes in input an array of numbers and returns the maximal element. The algorithm must be non-recursive