Hi

I am trying to prove if language is not regular. my language is {a^i b^j c^l | where i=j}.

I assume this language is regular and that there exist constant p

I am trying to pick my string w but i don't know what are constrains on l.

So if i pick my string on at least p length it will be w = a^p b^p c^?

Do I have to consider 3 cases such as :

w = a^p b^p c^(l<p)

w = a^p b^p c^(l>p)

w = a^p b^p c^(l=p)

Thanks