Termination of rewriting with right-flat rules

Authors:
Guillem Godoy;Eduard Huntingford;Ashish Tiwari
Affiliations:
Technical University of Catalonia, Barcelona, Spain;Technical University of Catalonia, Barcelona, Spain;SRI International, Menlo Park, CA
Venue:
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Year:
2007

Citing 10
Cited 5

Counterexamples to termination for the direct sum of term rewriting systems

Information Processing Letters
Termination of Probabilistic Concurrent Program

ACM Transactions on Programming Languages and Systems (TOPLAS)
Termination of Linear Rewriting Systems (Preliminary Version)

Proceedings of the 8th Colloquium on Automata, Languages and Programming
Right-Linear Finite Path Overlapping Term Rewriting Systems Effectively Preserve Recognizability

RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Polynomial Time Termination and Constraint Satisfaction Tests

RTA '93 Proceedings of the 5th International Conference on Rewriting Techniques and Applications
Termination proofs for systems code

Proceedings of the 2006 ACM SIGPLAN conference on Programming language design and implementation
The polyranking principle

ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Termination of rewrite systems with shallow right-linear, collapsing, and right-ground rules

CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Decidability of termination for semi-constructor TRSs, left-linear shallow TRSs and related systems

RTA'06 Proceedings of the 17th international conference on Term Rewriting and Applications
The confluence problem for flat TRSs

AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation

Decidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems

Electronic Notes in Theoretical Computer Science (ENTCS)
Closure of Tree Automata Languages under Innermost Rewriting

Electronic Notes in Theoretical Computer Science (ENTCS)
Unique Normalization for Shallow TRS

RTA '09 Proceedings of the 20th International Conference on Rewriting Techniques and Applications
Multiple congruence relations, first-order theories on terms, and the frames of the applied pi-calculus

TOSCA'11 Proceedings of the 2011 international conference on Theory of Security and Applications
Non-Linear Rewrite Closure and Weak Normalization

Journal of Automated Reasoning

Quantified Score

Hi-index	0.00

Visualization

Abstract

Termination and innermost termination are shown to be decidable for term rewrite systems whose right-hand side terms are restricted to be shallow (variables occur at depth at most one) and linear. Innermost termination is also shown to be decidable for shallow rewrite systems. In all cases, we show that nontermination implies nontermination starting from flat terms. The proof is completed by using the useful enabling result that, for right shallow rewrite systems, existence of nonterminating derivations starting from a given term is decidable.We also show that termination is undecidable for shallow rewrite systems. For right-shallow systems, general and innermost termination are both undecidable.