Binary equality sets are generated by two words

@article{Holub2012BinaryES,
  title={Binary equality sets are generated by two words},
  author={Stepan Holub},
  journal={CoRR},
  year={2012},
  volume={abs/1209.4061}
}
We show that the equality set Eq(g, h) of two non-periodic binary morphisms g, h : A∗ → Σ∗ is generated by at most two words. If the rank of Eq(g, h) = {α, β}∗ is two, then α and β start (and end) with different letters. This in particular implies that any binary language has a test set of cardinality at most two. 

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