Ordering, AC-theories and symbolic constraint solving

We design combination techniques for symbolic constraint solving in the presence of associative and commutative (AC) function symbols. This yields an algorithm for solving AC-RPO constraints (where AC-RPO is the AC-compatible total reduction ordering of Rubio and Nieuwenhuis, 1994), which was a missing ingredient for automated deduction strategies with AC-constraint inheritance. As in the AC-unification case, for this purpose we first study the pure case, i.e. we show how to solve AC-ordering constraints built over a single AC function symbol and variables. Since AC-RPO is an interpretation-based ordering, our algorithm also requires the combination of algorithms for solving interpreted constraints and non-interpreted constraints.