How to prove that $L = \{w \in \{a,b,c\}^* \mid w \text{ contains } abc \}$ is regular using the Nerode theorem?
Attempt
If I show that there are a finite number of equivalence classes for this language then by Nerode theorem it's regular.
I found two equivalence classes: $S_0 = L[(b+ac+abb)^*]$, $S_1 = L[((b+ac+abb)^*a(a+ab+abb)^*)^*]$ but got stuck on $S_2, S_3$.
Also, here is an image of the language automata:
