Express the recurrence relation in the form T$($n$)=$rT$($n$/$b$)+$O$($g$($n$)),$ which describes the time complexity of the following algorithm. Assume that basic operations, $+,,,/,$ and element comparisons $($a $<$ b and a $=$ b$),$ take constant time, and the functions mod$($a$,$ b$)$ and floor$($x$)$ have the same values as their corresponding mathematical functions.

def process$(a,b)$ :

# Precondition: a and $b$ are positive integers

if $b==1$ :

return a

$d=b**b$

half $=$ floor $(\frac{b}{2})$

result $,$ half