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A behavioral specification is a description of what is supposed to happen. Two states are said to be behaviourally equivalent on a behavioral specification if they are observationally indistinguishable. A proof method based on implicit induction principle have been proposed as an automatic proof method for behavioral equivalence. However it is a problem that the method sometimes fails to prove when two terms that represent states cannnot be ordered by the given reduction order. This paper proposes an implicit induction proof-method based on equational rewriting in order to solve the above problem. 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