When applying the pumping lemma to prove that a language is irregular, is it allowed to start by operating on the language to make applying the pumping lemma easier?
For example, when attempting to disprove:
L = {0^i 1^j | j <= i and i, j > 0}
Can I first reverse the language like so:
L = {1^j 0^i | j <= i and i, j > 0}
and reason that "if the language were regular, reversing (or performing any operation that's closed under regular languages) it wouldn't make it irregular," then continue to pump so that j must be greater than i?