>From the analysis of problem C of the qualification round:

For example, we can find the shortest prefix and the shortest suffix that 
reduce to i and k, respectively. If the prefix does not overlap with the 
suffix, then we can reduce the rest to j. Care must be taken as the 
multiplication operator is not commutative. 
Exercise: Can the prefix-suffix pair actually overlap? Answer: No.

I'm probably reading this wrong, but isn't "kjjji" a counter-example?

The shortest prefix that equals "i" is "kjjj" and the shortest suffix that 
equals "k" is "jjji", and these overlap.

Thanks!

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