Is there a competition to solve 3x3 cube using only Kociemba's Algorithm?

The way you ask makes me feel you don't understand how Kociemba's 2-phase algorithm works.

It is good for computer speedsolving, bad (or at least not great) for computer FMC, and not designed to human solving.

Computer algorithms are not much useful in human speedsolving. In human FMC, humans have been mimicking 4-phase Thistlethwaite's algorithm.

 
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