Mechanizing Weakly Ground Termination Proving of Term Rewriting Systems by Structural and Cover-Set Inductions
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The paper presents three formal proving methods for generalized weakly ground terminating property, i.e., weakly terminating property in a restricted domain of a term rewriting system, one with structural induction, one with cover-set induction, and the third without induction, and describes their mechanization based on a meta-computation model for term rewriting systems—dynamic term rewriting calculus. The methods can be applied to non-terminating, non-confluent and/or non-left-linear term rewriting systems. They can do “forward proving” by applying propositions in the proof, as well as “backward proving” by discovering lemmas during the proof.
Keywordsautomated formal proving cover-set induction dynamic term rewriting calculus term rewriting system weakly ground termination
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