A new polynomial-time algorithm for linear programming
Combinatorica
A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
Automating the Knuth Bendix ordering
Acta Informatica
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Termination Proofs and the Length of Derivations (Preliminary Version)
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Extensions and Comparison of Simplification Orderings
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
Orienting rewrite rules with the Knuth--Bendix order
Information and Computation - RTA 2001
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
IEA/AIE'2004 Proceedings of the 17th international conference on Innovations in applied artificial intelligence
Mechanizing and Improving Dependency Pairs
Journal of Automated Reasoning
Tyrolean termination tool: Techniques and features
Information and Computation
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
SAT solving for termination analysis with polynomial interpretations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Termination by quasi-periodic interpretations
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
SAT solving for argument filterings
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Derivational complexity of knuth-bendix orders revisited
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
AProVE 1.2: automatic termination proofs in the dependency pair framework
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving and disproving termination of higher-order functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Solving partial order constraints for LPO termination
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Lazy abstraction for size-change termination
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Satisfiability of non-linear (Ir)rational arithmetic
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
On transfinite Knuth-Bendix orders
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Proving Termination by Dependency Pairs and Inductive Theorem Proving
Journal of Automated Reasoning
Decreasing Diagrams and Relative Termination
Journal of Automated Reasoning
Decreasing diagrams and relative termination
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Ordinals and knuth-bendix orders
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
SAT Solving for Termination Proofs with Recursive Path Orders and Dependency Pairs
Journal of Automated Reasoning
Unifying the Knuth-Bendix, recursive path and polynomial orders
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
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This article presents three new approaches to prove termination of rewrite systems with the Knuth---Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic or linear arithmetic and the resulting formula is tested for satisfiability using dedicated solvers. Any satisfying assignment represents a weight function and a precedence such that the induced Knuth---Bendix order orients the rules of the encoded rewrite system from left to right. This means that in contrast to the dedicated methods our approach does not directly solve the problem but transforms it to equivalent formulations for which sophisticated back-ends exist. In order to make all approaches complete we present a method to compute upper bounds on the weights. Furthermore, our encodings take dependency pairs into account to increase the applicability of the order.