Answer
$\gcd(12, 17) = 1$
Work Step by Step
With the given input, the algorithm uses the else clause to find that $$\gcd(12, 17) = \gcd(17 \mod 12, 12) = \gcd(5, 12)$$
It uses this clause again to find that
$$\gcd(5, 12) = \gcd(12 \mod 5, 5) = \gcd(2, 5)$$,
then to get $$\gcd(2, 5) = \gcd(5 \mod 2, 2) = \gcd(1, 2)$$,
then $$\gcd(1, 2) = \gcd(2 \mod 1, 1) = \gcd(0, 1)$$,
Finally, to find $\gcd(0, 1)$ it uses the first step with a = 0 to find that $\gcd(0, 1) = 1$.
Consequently, the algorithm finds that $\gcd(12, 17) = 1$.