$(10)$ Consider the following two algorithms A and B$.$ For A$($n$),$ let its time be tA$($n$).$ Give a recurrence for

tA$($n$)($don$$t forget the initial condition$)$ and solve it$.$ For B$($n$),$ let its time be tB$($n$).$ What is tB$($n$)$ and why?

Correct solution to incorrect recurrence will get little credit.

A$($x$,$ n$)$

if n $=0$

return x$*$x

else

return x$*$x$*$x$*$A$($x$,$ n$-1)$

end A

B$($n$)$

for i$=1$ to n

for j$=1$ to i

print A$($n$,$ n$*$n$)$

print A$($n$,$ n$*$n$)$

end B