Austrian-Japanese Workshop on Symbolic Computation in Software Science

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 and the original rewriting induction is not capable of proving theorems which are not orientable by that reduction order. To deal with such theorems, Bouhoula (1995) as well as Dershowitz & Reddy (1993) used the ordered rewriting. However, even using ordered rewriting, the weak capability of non-orientable theorems is considered one of the weakness of rewriting induction approach compared to other automated methods for proving inductive theorems. We present a refined system of rewriting induction with an increased capability of non-orientable theorems and a capability of disproving incorrect conjectures. Soundness for proving/disproving are shown and effectiveness of our system is demonstrated through some examples.

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