Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Handbook of logic in computer science (vol. 2)
Termination of term rewriting using dependency pairs
Theoretical Computer Science - Trees in algebra and programming
Automated termination analysis for Haskell: from term rewriting to programming languages
RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
Levels of undecidability in rewriting
Information and Computation
Least upper bounds on the size of church-rosser diagrams in term rewriting and λ-calculus
FLOPS'10 Proceedings of the 10th international conference on Functional and Logic Programming
Highlights in infinitary rewriting and lambda calculus
Theoretical Computer Science
ACM Transactions on Computational Logic (TOCL)
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Undecidability of various properties of first order term rewriting systems is well-known. An undecidable property can be classified by the complexity of the formula defining it. This gives rise to a hierarchy of distinct levels of undecidability, starting from the arithmetical hierarchy classifying properties using first order arithmetical formulas and continuing into the analytic hierarchy, where also quantification over function variables is allowed. In this paper we consider properties of first order term rewriting systems and classify them in this hierarchy. Most of the standard properties are Π20 -complete, that is, of the same level as uniform halting of Turing machines. In this paper we show two exceptions. Weak confluence is Σ10- complete, and therefore essentially easier than ground weak confluence which is Π20-complete. The most surprising result is on dependency pair problems: we prove this to be Π11-complete, which means that this property exceeds the arithmetical hierarchy and is essentially analytic. A minor variant, dependency pair problems with minimality flag, turns out be Π20-complete again, just like the original termination problem for which dependency pair analysis was developed.