Intertwining of Complementary Thue-Morse Factors

We consider the positions of occurrences of a factor $x$ and its binary complement $\overline{x}$ in the Thue-Morse word ${\bf t} = {\tt 01101001} \cdots$, and show that these occurrences are "intertwined" in essentially two different ways. Our proof method consists of stating the needed properties as a first-order logic formula $φ$, and then using a theorem-prover to prove $φ$.

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