Question: 5. Consider the following program specification and implementation that for, two positive integers a and d, finds q and r such that a=dq+r and 0

5. Consider the following program specification and implementation that for, two

5. Consider the following program specification and implementation that for, two positive integers a and d, finds q and r such that a=dq+r and 0 d (4) rer-d (5) 9+9+1 (6) return q and r (a) Trace the execution of these calls to division, that is, for each iteration of the loop on line (3), show what r and q are: division(11,4) division (20,7) division (30,5) (b) Prove that a = dq+r and r >0 are loop invariants. (c) Prove the correctness of division by arguing (i) partial correctness and (ii) termination

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