Proving $L = \{0^i1^j0^i1^j\ |\ i+j > 0\}$ is not a context-free language
You do not need to express $i$ and $j$ in terms of $n$.

Now suppose $L$ were context-free; then there would exist an $n \geq 0$ such that for every $s \in L$ with $|s| \geq n$ there would be a partition of $s = uvwxy$ such that


$|vwx| \leq n$
$|vx| &gt; 0$
$uv^iwx^iy \in L$ for all $i \geq 0$


Consider the example string $s = 0^n1^n0^n1^n$. Clearly, $s \in L$, and obviously $|s| \geq n$. You must now examine all the possible partitions of $s$ and show that none of them can satisfy all three of the above conditions.