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Let's have this language:

$ L= \{ w_1 @ w_2 | w_1,w_2 \in \Sigma^*, \#_1(w_1)+(2*\#_2(w_1))=\#_1(w_2) + (2*\#_2(w_2)) \}$

$\Sigma = \{0,1,2\} \cup \{@\} $

I need to prove that this language is not regular by using pumping lemma. Where $\#_1(w_1) $ means count of symbols "1" in string $w_1$. I bet there is some easy solution with that symbol "@" in the middle of string, which we could possibly omit when pumping(maybe).

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Just consider the string $111\cdots111 @ 111\cdots 111$, where the number of $1$'s is the same on both sides and is large: longer than the pumping length. Then the decomposition into $xyz$ must be such that $y$ contains only $1$'s, and so repeating it any number of times (other than exactly once) will make $\#_1(w_1) \neq \#_1(w_2)$.

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