Words without Near-Repetitions

We find an infinite word w on four symbols with the following property: Two occurrences of any block in w must be separated by more than the length of the block. That is, in any subword of w of the form xyx, the length of y is greater than the length of x. This answers a question of C. Edmunds connected to the Burnside problem for groups.The research of the first author was supported by an NSERC Operating Grant. The second author was supported by an NSERC Undergraduate Summer Research Award.https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/words-without-nearrepetitions/F86509D865F222F1FC63ACA8545C069