The complexity of the functions, fun$1$ and fun$2,$ are respectively described by

A$)$ O$(2^$n$),$ O$(2^$n$)$

B$)$ O$($n$),$ O$(2^$n$)$

C$)$ O$(2^$n$),$ O$($n$)$

D$)$ O$($n$),$ O$($n$)$

E$)$ None of the above