Can the String, $0^p 0^p 0^p$, be Used with the Pumping Lemma to Show that $w^r w w^r$ is Not Context Free?
For $p&gt;0$, you can always split $0^{3p}$ into $uvxyz$ such that $u=x=\varepsilon$, $v=0$, $y=0^2$, and $z=0^{3p-3}$. Such a split clearly satisfies $|vxy|\leq p$, $|vy|\geq1$. Finally, for all $n\geq0$, $uv^nxy^nz=0^{3(p-1+n)}$, which is in $L$, since $0^{3m}\in L$ for all $m$.

Since you want to show, that for an arbitrary split satisfying the length conditions, there is some $n$ for which $uv^nxy^nz\notin L$, the choice of $0^{3p}$ is unfortunate.