Why is $\{a^nb^n \mid n \geq 1\}$ not type 3 (regular)?
$S\Rightarrow bS\Rightarrow baS\Rightarrow bab$.

However, $bab$ is not $a^nb^n$ for any $n$.



(Exercise.) Is the following grammar a grammar for $L_1$?

$S \to Sa \mid Sb \mid a$