Dealing with Non-orientable Equations in Rewriting Induction
Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order. Thus, when the given conjecture is not orientable by the reduction order in use, any proof attempts for that conjecture fails; also conjectures such as a commutativity equation are out of the scope of the rewriting induction because they can not be oriented by any reduction order. In this paper, we give an enhanced rewriting induction which can deal with non-orientable conjectures. We also present an extension which intends an incremental use of our enhanced rewriting induction.
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