E$)(*+5$GCD$($x$,$ y$)$: if x $=$ y return x else if x $>$ y return E$)(*+5$GCD$($x $\text{'}$ y$,$ y$)$ else return E$)(*+5$GCD$($x$,$ y $\text{'}$ x$)($a$)$ Prove that E$)(*+5$GCD correctly computes gcd$($x$,$ y$)."$$Specifically: i$.$ Prove that E$)(*+5$GCD$($x$,$ y$)$ divides both x and y$.$ ii$.$ Prove that every divisor of x and y is a divisor of E$)(*+5$GCD$($x$,$ y$).($b$)$ What is the worst$-$case running time of E$)(*+5$GCD$($x$,$ y$),$ as a function of x and y$?($Assume that computing x $\text{'}$ y requires O$($log x $+$ log y$)$ time.$)$

Unknown. $01-$recursion $($p$.38).$ Kindle Edition.