Consider the following pseudocode.$($a$)(5$ points$)$ Describe the running time T$($n$)$ of Alg$($n$)$ as a recurrence relation.$($b$)(15$ points$)$ Use the substitution method to prove that T$($n$)=$O$(((1+$sqrt$5)/(2))^(|\_\_($n$)/(2)\_\_|)).($Useful Fact: $\{$:$((1+$sqrt$5)/(2))^(2)=((1+$sqrt$5)/(2))+1)$