Journal of Symbolic Computation
On the recursive decomposition ordering with lexicographical status and other related orderings
Journal of Automated Reasoning
Simple LPO constraint solving methods
Information Processing Letters
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Satisfiability of Systems of Ordinal Notations with the Subterm Property is Decidable
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
RPO Constraint Solving Is in NP
Proceedings of the 12th International Workshop on Computer Science Logic
CAAP '94 Proceedings of the 19th International Colloquium on Trees in Algebra and Programming
Decision Problems in Ordered Rewriting
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
The Decidability of the First-Order Theory of the Knuth-Bendix Order in the Case of Unary Signatures
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
Algorithms, Datastructures, and other Issues in Efficient Automated Deduction
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Invited Talk: Rewrite-based Deduction and Symbolic Constraints
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
CCE: Testing Ground Joinability
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
A Decision Procedure for the Existential Theory of Term Algebras with the Knuth-Bendix Ordering
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
The decidability of the first-order theory of knuth-bendix order
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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A usual technique in symbolic constraint solving is to apply transformation rules until a solved form is reached for which the problem becomes simple. Ordering constraints are well-known to be reducible to (a disjunction of) solved forms, but unfortunately no polynomial algorithm deciding the satisfiability of these solved forms is known. Here we deal with a different 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, and for all possible total precedences and signatures. Apart from simplicity and elegance from the theoretical point of view, the main contribution of these algorithms is on efficiency 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.