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...a termination prover for TRS, which is available at http://www.trs.cm.is.nagoya-u.ac.jp/NaTT/ NaTT is powerful and fast; its power comes from the novel implementation of the weighted path order (WPO) =-=[25, 26]-=- that subsumes most of the existing reduction pairs, and its efficiency comes from the strong cooperation with stateof-the-art satisfiability modulo theory (SMT) solvers. In principle, any solver that...

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...implementation issues are discussed in Section 6. In Section 7 we verify the significance of our work through experiments and we conclude in Section 8. A preliminary version of this paper appeared in =-=[28]-=-. The results for the reduction orders of Section 3 are basically the same as in [28]. The definition of WPO as a reduction pair in Section 4 is new, and hence most of the results in Section 4 are new...

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... Takeuti [12], are one of the most powerful syntactic notations of ordinals that have been devised. They are related to the Friedman’s [11] and Kříž’s [6] gap version of Kruskal’s famous Tree Theorem =-=[7, 8]-=-, in that the well-orderedness of diagrams follows from the Gap Tree Theorem. Partially ordered versions of ordinal diagrams are only possible in restricted cases; see [10, 5, 4]. We reformulate ordin...