Express the recurrence relation in the form $T(n)=rT(\frac{n}{b})+O(g(n)),$ which describes the time complexity of the

following algorithm. Assume that basic operations, $+,-,*,/,$ and element comparisons $(a<mtext\; id="EditorElement\_613362"></mtext><mi\; id="EditorElement\_613363">b</mi>$ 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

$ifb==1$ :

return $a$

$d=b^{****}b$

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

result $=$ process$($d$,$ half$)$

if mod$($b$,2)==0$

return result

return a $*$ result