Use the procedure described in Lemma $1\mathrm{.}60$ to convert the following NFAs to regular expressions:

$($a$)$ start state q$1,$ accepting state q$2$

$||$ a $|$ b $|\backslash$epsi $|$

$|------|-----------|------|-----|$

$|->|$ q$1|\{$q$1,$ q$2\}\text{'}||$

$|*$q$2||\{$q$1\}||$

$($b$)$ start state q$1,$ accepting state q$2$

$||$ a $|$ b $|\backslash$epsi $|$

$|------|-------|------|-----|$

$|->|$ q$1||\{$q$2\}|$

$|*$q$2|\{$q$2,$ q$3\}|\{$q$3\}||$

$|$ q$3|\{$q$3\}|\{$q$2\}|\{$q$2\}|$

Show your work $($including GNFA and intermediate results after each state removal$).$