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We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of interpretations. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we obtain an instance of WPO that unifies KBO, LPO and POLO. In order to fit WPO in the modern dependency pair framework, we further provide a reduction pair based on WPO and partial statuses. As a reduction pair, WPO also subsumes matrix interpretations. We finally present SMT encodings of our techniques, and demonstrate the significance of our work through experiments.

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This paper describes the implementation and techniques of the Nagoya Termination Tool, a termination prover for term rewrite systems. The main features of the tool are: the first implementation of the weighted path order which subsumes most of the existing reduction pairs, and the efficiency due to the strong cooperation with external SMT solvers. We present some new ideas that contribute to the efficiency and power of the tool. The Dependency Pair FrameworkThe overall procedure of NaTT is illustrated in Figure 1. NaTT is based on the ⋆ Full version of the paper which is