Undecidability and the representation theory of $K<X,Y>$

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The question comes from the problem here: https://mathoverflow.net/questions/73940/are-wild-problems-related-to-undecidable-ones It has already been proven that the representation theory of $K<X,Y>$ is undecidable. May I ask what does that mean? Does it mean that it is inherently impossible for the indecomposable representations of $K<X,Y>$ to ever be classified? Or the classification, albeit hard, is still theoretically possible?