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# Article

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Keywords:
combinatorics on words; binary equality languages
Summary:
Let $w$ be an equality word of two binary non-periodic morphisms $g,h: \{a,b\}^* \to \Delta^*$ with unique overflows. It is known that if $w$ contains at least 25 occurrences of each of the letters $a$ and $b$, then it has to have one of the following special forms: up to the exchange of the letters $a$ and $b$ either $w=(ab)^ia$, or $w=a^ib^j$ with $\operatorname{gcd} (i,j)=1$. We will generalize the result, justify this bound and prove that it can be lowered to nine occurrences of each of the letters $a$ and $b$.
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