Abstract
This paper is the fourth in a series on the structure of sets of solutions to systems of equations in a free group, projections of such sets, and the structure of elementary sets defined over a free group. In the fourth paper we present an iterative procedure that validates the correctness of anAE sentence defined over a free group. The terminating procedure presented in this paper is the basis for our analysis of elementary sets defined over a free group presented in the next papers in the series.
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