Problem 1. (12 marks) Consider the following program: procedure Foo(A. I.) "Precondition: Alf ...!] is an array of integers, ,1 are two naturals 2 1 with fs L if (f = 1) then return Alf] else return max(Foo(A, J,m), Foo(A,m+1,1) end if a. (4 marks) Suppose A = [7, 12, 8, 4, 4, 8, 10, 12.6] and consider the call Foo(A,1,9). Show all recursive calls by drawing a tree, and for each call, indicate what is returned b. (4 marks) Give a formal statement about what Foo does, and prove it. c. (4 marks) Write a recurrence relation to describe the number of max-operations run by Foo in terms of the size of array A, and using the master theorem, give a bound on the complexity of this program