Termination proofs and the length of derivations
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
Termination proofs by multiset path orderings imply primitive recursive derivation lengths
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
Term rewriting and all that
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Tyrolean termination tool: Techniques and features
Information and Computation
Matrix Interpretations for Proving Termination of Term Rewriting
Journal of Automated Reasoning
Arctic Termination ...Below Zero
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Automated Complexity Analysis Based on the Dependency Pair Method
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Complexity, Graphs, and the Dependency Pair Method
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Automating the dependency pair method
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Derivational complexity of knuth-bendix orders revisited
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Termination Of Term Rewriting By Semantic Labelling
Fundamenta Informaticae
Cdiprover3: a tool for proving derivational complexities of term rewriting systems
ESSLLI'08/09 Proceedings of the 2008 international conference on Interfaces: explorations in logic, language and computation
Characterising space complexity classes via Knuth-Bendix orders
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
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We study the derivational complexity induced by the (basic) dependency pair method. Suppose the derivational complexity induced by a termination method is closed under elementary functions. We show that the derivational complexity induced by the dependency pair method based on this termination technique is the same as for the direct technique. Therefore, the derivational complexity induced by the dependency pair method based on lexicographic path orders or multiset path orders is multiple recursive or primitive recursive, respectively. Moreover for the dependency pair method based on Knuth-Bendix orders, we obtain that the derivational complexity function is majorised by the Ackermann function. These characterisations are essentially optimal.