$($a$)$ Convert the null$-$stack PDA $P=(\{q\},\{a,b\},\{A,B,Z_0\},,q,Z_0),$ where

$(q,lon,Z_0)=\{(q,lon)\}$

$(q,a,Z_0)=\{(q,A{Z}_0)\}$

$(q,a,A)=\{(q,AA)\}$

$(q,b,A)=\{(q,lon)\}$

$(q,B,Z_0)=\{(q,B{Z}_0)\}$

$(q,b,B)=\{(q,BB)\}$

$(q,a,B)=\{(q,lon)\}$

to a CFG $G,$ such that $L(G)=N(P).$

$($b$)$ Show the derivation of string aababb in the resulting grammar.