# Show that the language L = {www : w ∈ {0, 1} ∗} is not regular [duplicate]

Hey was wondering if I'm applying the pumping lemma correctly for this proof or if this proof could be improved?

Suppose $$L = \{www:w\in\{0,1\}^*\}$$ is a regular language. Let $$p$$ be the number from the Pumping Lemma. Consider $$s = 0^p10^p10^p1$$, since $$s \in L$$ the conditions of the pumping lemma must hold for $$s = xyz$$. Now let $$x= 0^p$$, $$y = 1$$, and $$z = 0^p10^p1$$. Then since $$|xy|\le p$$ and if we let $$i = 2$$ then $$s’=0^p110^p10^p1$$. But clearly $$s’ \notin L$$ which is a contradiction to the Pumping Lemma so $$L$$ is not regular.