Problem $7(6$ points$)$

Suppose you were trying to prove that the language $\{a{b}^{n+1}{c}^{n}d|ninN\}$ is not regular and you are using the proof by contradiction using the pumping lemma style proof we discussed in class.

You decide to prove this using the string $S=a{b}^{m+1}{C}^{m}d$ where $m$ is the number from the pumping lemma.

In your proof you state that $s$ can be split into $3$ pieces, $x,y,$ and $z$ as described in the pumping lemma. Now I am going to ask you some questions about what $x,y$ and $z$ look like.

Circle the best answer for each line of the table below $($in other words: circle "yes" if the answer is definitely yes; circle $"$no$"$ if the answer is definitely no; and circle "maybe" if the answer could be yes but also could be no$.)(15$ parts, $0\mathrm{.}4$ points each$)$

$\backslash$table$[[$Is it possible that x might be ${?}^{{?}^{?}}?,$Yes,No$,],[$Does x contain the symbol a$?,$Yes,Maybe,No$],[$Does x contain the symbol b$?,$Yes,Maybe,No$],[$Does x contain the symbol c$?,$Yes,Maybe,No$],[$Does x contain the symbol d$?,$Yes,Maybe,No$],[$Is it possible that y might be ${?}^{{?}^{?}}?,$Yes,No$,],[$Does y contain the symbol a$?,$Yes,Maybe,No$],[$Does y contain the symbol b$?,$Yes,Maybe,No$],[$Does y contain the symbol c$?,$Yes,Maybe,No$],[$Does y contain the symbol d$?,$Yes,Maybe,No$],[$Is it possible that z might be ${?}^{{?}^{?}}?,$Yes,No$,],[$Does z contain the symbol a$?,$Yes,Maybe,No$],[$Does z contain the symbol b$?,$Yes,Maybe,No$],[$Does z contain the symbol c$?,$Yes,Maybe,No$],[$Does z contain the symbol d$?,$Yes,Maybe,No$]]$