Solved Forms for Path Ordering Constraints

A usual technique in symbolic constraint solving is to apply transformation rules until a solved form is reached for which the problem becomes trivial. Ordering constraints are well-known to be reducible to a disjunction of solved forms, but unfortunately no polynomial algorithm deciding the satissability of these solved forms is known. Surprisingly, it turns out that this is no longer the case for a slightly diierent notion of solved form, where fundamental properties of orderings like transitivity and monotonicity are taken into account. This leads to a new family of constraint solving algorithms for the full recursive path ordering with status (RPOS), and hence as well for other path orderings like LPO, MPO, KNS and RDO. Apart from simplicity and elegance from the theoretical point of view, the main contribution of these algorithms is on eeciency in practice. Since guessing is minimized, and, in particular, no linear orderings between the subterms are guessed, a practical improvement in performance of several orders of magnitude over previous algorithms is obtained, as shown by our experiments.