Given the alphabet $\Sigma = \left\{ 1,2,3,4 \right\}$, I have to find a NFA that accepts the language: $$L=\left\{awb\mid a,b\in \Sigma \wedge a<b \wedge w \in \Sigma^*\right\}$$.
I don't know how build a general NFA for all case. Indeed I thought to do a NFA for every case and then joining all the costructions but I don't think is the better way... Can somebody help me?
Label the arrows as below:
$q_0\rightarrow q_1$ as $1$
$q_0\rightarrow q_2$ as $1, 2$
$q_0\rightarrow q_3$ as $1, 2, 3$
$q_1\rightarrow q_4$ as $2$
$q_2\rightarrow q_5$ as $3$
$q_3\rightarrow q_6$ as $4$
and $q_1, q_2, q_3$ have self loops labelled $1, 2, 3, 4$.