  We implement four algorithms for solving linear Diophantine equations in the
naturals: a lexicographic enumeration algorithm, a completion procedure, a
graph-based algorithm, and the Slopes algorithm. As already known, the
lexicographic enumeration algorithm and the completion procedure are slower
than the other two algorithms. We compare in more detail the graph-based
algorithm and the Slopes algorithm. In contrast to previous comparisons, our
work suggests that they are equally fast on small inputs, but the graph-based
algorithm gets much faster as the input grows. We conclude that implementations
of AC-unification algorithms should use the graph-based algorithm for maximum
efficiency.
