Equational problems anddisunification
Journal of Symbolic Computation
A new method for undecidability proofs of first order theories
Journal of Symbolic Computation
Simple LPO constraint solving methods
Information Processing Letters
Equational formulae with membership constraints
Information and Computation
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
The first-order theory of lexicographic path orderings is undecidable
Theoretical Computer Science
Term rewriting and all that
A decision procedure for term algebras with queues
ACM Transactions on Computational Logic (TOCL)
Knuth-Bendix Constraint Solving Is NP-Complete
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
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
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
Solved Forms for Path Ordering Constraints
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
The Theory of Total Unary RPO Is Decidable
CL '00 Proceedings of the First International Conference on Computational Logic
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
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
Structural Subtyping of Non-Recursive Types is Decidable
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Presburger arithmetic with bounded quantifier alternation
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Decision procedures for term algebras with integer constraints
Information and Computation - Special issue: Combining logical systems
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Decision procedures for algebraic data types with abstractions
Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Decision procedures for automating termination proofs
VMCAI'11 Proceedings of the 12th international conference on Verification, model checking, and abstract interpretation
A Combined Superposition and Model Evolution Calculus
Journal of Automated Reasoning
Meta-interpretive learning of higher-order dyadic datalog: predicate invention revisited
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Two kinds of orderings are widely used in term rewriting and theorem proving, namely recursive path ordering (RPO) and Knuth-Bendix ordering (KBO). They provide powerful tools to prove the termination of rewriting systems. They are also applied in ordered resolution to prune the search space without compromising refutational completeness. Solving ordering constraints is therefore essential to the successful application of ordered rewriting and ordered resolution. Besides the needs for decision procedures for quantifier-free theories, situations arise in constrained deduction where the truth value of quantified formulas must be decided. Unfortunately, the full first-order theory of recursive path orderings is undecidable. This leaves an open question whether the first-order theory of KBO is decidable. In this paper, we give a positive answer to this question using quantifier elimination. In fact, we shall show the decidability of a theory that is more expressive than the theory of KBO.