Counterexamples to termination for the direct sum of term rewriting systems
Information Processing Letters
Thue systems as rewriting systems
Journal of Symbolic Computation
Journal of Symbolic Computation
The Church-Rosser property for ground term-rewriting systems is decidable
Theoretical Computer Science
A note on a canonical theory with undecidable unification and matching problem
Journal of Automated Reasoning
On ground-confluence of term rewriting systems
Information and Computation
Modularity of simple termination of term rewriting systems with shared constructors
Theoretical Computer Science
Confluence, ground confluence, and termination of monadic term rewriting systems
Journal of Information Processing and Cybernetics
On termination of one rule rewrite systems
Theoretical Computer Science
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Modular proofs for completeness of hierarchical term rewriting systems
Selected papers of the thirteenth conference on Foundations of software technology and theoretical computer science
Termination for direct sums of left-linear complete term rewriting systems
Journal of the ACM (JACM)
On the modularity of decidability of completeness and termination
Journal of Automata, Languages and Combinatorics
Computing in Systems Described by Equations
Computing in Systems Described by Equations
Introduction to Mathematical Theory of Computation
Introduction to Mathematical Theory of Computation
Relative undecidability in term rewriting: I. the termination Hierarchy
Information and Computation
Relative undecidability in term rewriting: II. the confluence hierarchy
Information and Computation
Termination of Linear Rewriting Systems (Preliminary Version)
Proceedings of the 8th Colloquium on Automata, Languages and Programming
Term Rewriting Systems: From Church-Rosser to Knuth-Bendix and Beyond
ICALP '90 Proceedings of the 17th International Colloquium on Automata, Languages and Programming
Termination Proofs and the Length of Derivations (Preliminary Version)
RTA '89 Proceedings of the 3rd International Conference on Rewriting Techniques and Applications
On Proving Termination by Innermost Termination
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
CTRS '94 Proceedings of the 4th International Workshop on Conditional and Typed Rewriting Systems
General size-change termination and lexicographic descent
The essence of computation
Characterizing Confluence by Rewrite Closure and Right Ground Term Rewrite Systems
Applicable Algebra in Engineering, Communication and Computing
Termination of rewrite systems with shallow right-linear, collapsing, and right-ground rules
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Confluence of shallow right-linear rewrite systems
CSL'05 Proceedings of the 19th international conference on Computer Science Logic
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Undecidability results in rewriting have usually been proved by reduction from undecidable problems of Turing machines or, more recently, from Post's Correspondence Problem. Another natural candidate for proofs regarding term rewriting is Recursion Theory, a direction we promote in this contribution. We present some undecidability results for “primitive” term rewriting systems, which encode primitive-recursive definitions, in the manner suggested by Klop. We also reprove some undecidability results for orthogonal and non-orthogonal rewriting by applying standard results in recursion theory.