Exercise ${17}_{?}$ Conversion of finite automata to regular expressions

$(6$ points$)$

Let the following non$-$deterministic automata $N_1$ and $N_2$ be given:

Convert both non$-$deterministic automata $N_1$ and $N_2$ to regular expressions $$ and $.$ Use the procedure

from the lecture! The regular expressions $$ and $$ have to describe the same languages that are

accepted by the automata $N_1$ and $N_2.$ Thus the following should hold:

$L(N_1)=L(),$ and $,L(N_2)=L().$

Indicate all intermediate steps of your transformation.

$($Note: If you apply the rule $S($deletion of loops$)$ as late as possible, the resulting regular expressions

will be smaller.$)$