Notes on the Polish Algorithm

Abstract

We study, with the help of a computer program, the Polish Algorithm for finite terms satisfying various algebraic laws, e.g., left distributivity a(bc) = (ab)(ac). While the termination of the algorithm for left distributivity remains open in general, we can establish some partial results, which might be useful towards a positive solution. In contrast, we show the divergence of the algorithm for the laws a(bc) = (ab)(cc) and a(bc) = (ab)(a(ac)).