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We will prove that the word a i b j a k is periodicity forcing if j ≥ 3 and i + k ≥ 3, where i and k are positive integers. Also we will give examples showing that both bounds are optimal.

Let w be an equality word of two nonperiodic binary mor-phisms g, h : {a, b} * → ∆ *. Suppose that no overflow occurs twice in w and that w contains at least 9 occurrences of a and at least 9 occurrences of b. Then either w = (ab) i a, or w = a i b j with gcd(i, j) = 1, up to the exchange of letters a and b.

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