$6$ Recursive Algorithm and Induction

$1.$ Give a recursive algorithm that takes as input two non$-$negative integers x and y and

returns their sum, x $+$ y$.$ However, the only arithmetic operation your algorithm is

allowed to perform is incrementing an integer value, e$.$g$.$ x$++,$ and decrementing an

integer value, e$.$g$.$ x$.$

$2.$ Use induction to prove that your algorithm always returns a correct answer.

$3.$ State a correct claim about the number of increment and decrement operations your

algorithm makes to compute x $+$ y and use induction to prove that your claim is correct.