A new method for undecidability proofs of first order theories
Journal of Symbolic Computation
Simple LPO constraint solving methods
Information Processing Letters
The first-order theory of lexicographic path orderings is undecidable
Theoretical Computer Science
Term rewriting and all that
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
A New Method for Undecidability Proofs of First Order Theories
Proceedings of the Tenth Conference 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
Verifying Orientability of Rewrite Rules Using the Knuth-Bendix Order
RTA '01 Proceedings of the 12th 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
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
Knuth--bendix constraint solving is NP-complete
ACM Transactions on Computational Logic (TOCL)
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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We show that the first-order theory of any Knuth-Bendix order in the case of the signatures consisting of unary function symbols and constants is decidable. Our decision procedure uses interpretation of unary terms as trees and uses decidability of the weak monadic second-order theory of binary trees. One area of applications of our result is automated deduction, since using the first-order theory of the Knuth-Bendix orders we can decide an important class of ordering constraints.