$14\mathrm{.}10$ R$.$E$.-$NFA Normal Form Rules

Let D be a DFA with alphabet $\{$a$,$ b$\},$ state set $\{$p$,$ q$,$ r$\},$ start state p$,$ and final state set $\{$q$,$ r$\}.$ The transition function has $\backslash$delta $($p$,$ a$)=$ q$,\backslash$delta $($p$,$ b$)=$ r$,\backslash$delta $($q$,$ a$)=$ r$,\backslash$delta $($q$,$ b$)=$ p$,\backslash$delta $($r$,$ a$)=$ p$,$ and $\backslash$delta $($r$,$ b$)=$ q$.$ Then the first r$.$e$.-$NFA made from D according to our rules has five states and three $\backslash$lambda $-$moves $($before any states are eliminated$).$