How can I prove that the language $L=\{110^n 10^{n-m} 1^m \mid 1 \le m < n \}$ is not regular using pumping lemma?
I chose the word $w = 110^{2p} 10^{2p-q} 1^q$ to prove the non-regularity. Then I started partitioning the word to $xyz$ with $|y| \ge 1$, $|xy| \le p$ and for each $i\ge 0$, $xy^iz$:
\begin{align*} x &= 110^r\\ y &= 0^s\\ z &= 10^{2p - q} 1^q\,, \end{align*} where $r + s = p$ and $s > 0$.
The second partition: \begin{align*} x &= 1\\ y &= 10^{2p}\\ z &= 10^{2p-q}1^q\,. \end{align*}
However, I got stuck at this point because I am not really sure how to find the other partitions and how the choose the correct $i$ for those which I already have. Any help with this will be appreciated.