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Relative Termination via Dependency Pairs.

José Iborra1, Naoki Nishida2, Germán Vidal3

  • 1London, UK.

Journal of Automated Reasoning
|September 4, 2018
PubMed
Summary
This summary is machine-generated.

This study introduces a new method to prove relative termination in term rewrite systems by converting the problem into dependency pairs. This novel technique addresses a long-standing open problem in the field.

Keywords:
Dependency pairsTerm rewritingTermination

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Area of Science:

  • Theoretical Computer Science
  • Formal Methods
  • Automated Reasoning

Background:

  • Termination is crucial for analyzing computational systems.
  • Relative termination is a generalization allowing some infinite reductions.
  • This concept is vital for confluence analysis and narrowing in rewrite systems.

Purpose of the Study:

  • To introduce a novel technique for proving relative termination.
  • To address Problem #106 of the RTA List of Open Problems.
  • To reduce the problem of relative termination to dependency pair problems.

Main Methods:

  • Developed a general approach for relative termination.
  • Instantiated the approach into a concrete technique.
  • Utilized dependency pair problems as a reduction target.

Main Results:

  • Successfully reduced the problem of proving relative termination to dependency pair problems.
  • Presented a novel technique for relative termination analysis.
  • Demonstrated the practical significance through experimental evaluation.

Conclusions:

  • The proposed method offers a new way to tackle relative termination.
  • This work provides the first significant contribution to RTA List of Open Problems #106.
  • The technique is effective and practically relevant for rewrite system analysis.