Project Problem: Simplification of Context$-$Free Grammars We learned three context free grammar $($CFG$)$ simplification techniques in our classes removing e$-$rules, unit rules, and useless rules. In this project, read a CFG from a txt ble simplify it by removing rules and useless rules, October $27,2021$ Project $2$ of CSC $471($F$21.$ Dr$.$ Zu$)$ Page $2$ of $2$ and print out the simplified equivalent CEG. No need to care or remove unit$-$rules, For example, given the following CFG in a text file $($O denotes empty string and denotes arrow head"$)$ S$-$ABB A$-$AAA B$-$B bbc C$-$ After processing your program should print out the following simplified equivalent CFG: S$-$aAa A$-$aa The following are a few more examples you can use to test your program $($I highly recommend that you come up with more examples to make sure the correctness of your program$)$: $(1)$ S$.$ABCD A$-0$a B$-6$b COC D$-$Old For the above CE$,$ the print out should be S$-$aubah Bat$/$AaBaba AlbaBach$/$AaBabwbb$/$AshD$|$RahD$|$AaBubDCBD:AACHDBachd AaBach A$-$a B$-$b Cc D$-$d $(2)$ S$-$AaB A$-0$ B$-$bu$\backslash$Lambda $\backslash$Iota $\backslash$Omicron For the above CFG$,$ the print out should be S$-$a Balaa B$-$ha $(3)$ S$-$ASAB A$-$BS B$-60$ For the above part of the transition table of a NFA, the print out should be S$-$ASAB SAAS A$-$BS a B$-$b Note that your program must be able to work for any CPG$,$ not only just for the above given examples