Let M be a PDA in normal form with Q $=\{$q$0,$ q$1,$ q$2\}$ and start state q$0$ and accepting state q$0$ and with transitions listed below: $($q$0,$ a$,$ $)=\{($q$1,$ X$)\},$ $($q$0,$ b$,$ $)=\{($q$2,$ X$)\},$ $($q$1,$ b$,$ X$)=\{($q$0,$ $)\},$ $($q$2,$ a$,$ X$)=\{($q$0,$ $)\},$ $($q$1,$ a$,$ $)=\{($q$1,$ Y$)\},$ $($q$1,$ b$,$ Y$)=\{($q$0,$ $)\},$ $($q$2,$ b$,$ $)=\{($q$2,$ Y$)\},$ $($q$2,$ a$,$ Y$)=\{($q$2,$ $)\}.$ If M is converted to an equivalent CFG G$\_$M using the algorithm presented in class, which of the following rules will be added to G$\_$M$?$

$$a$)$A$22-->$ b A$22$ a$$b$)$A$12-->$ $$c$)$A$00-->$a A$00$ b$$d$)$A$12-->$ A$10$ A$20$