The Repetition Threshold for Rote Sequences

We consider Rote words, which are infinite binary words with factor complexity $2n$. We prove that the repetition threshold for this class is $5/2$. Our technique is purely computational, using the Walnut theorem prover and a new technique for generating automata from morphisms due to the first author and his co-authors.
Comment: The attached html and ipynb files illustrate the ideas and give the Walnut code