Argument Filtering Transformation

To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this paper, we show that the argument filtering method combining with the dependency pair technique is essential in all the above elimination methods. We present remarkable simple proofs for the soundness of these elimination methods based on this observation. Moreover, we propose a new elimination method, called the argument filtering transformation, which is not only more powerful than all the other elimination methods but also especially useful to make clear the essential relation hidden behind these methods.

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