A Characterization of Quasi-Decreasingness

In 2010 Schernhammer and Gramlich [10] showed that quasi-decreasingness of a DCTRS R is equivalent to μ-termination of its context-sensitive unraveling UCS(R) on original terms. While the direction that quasi-decreasingness ofR implies μ-termination of UCS(R) on original terms is shown directly; the converse – facilitating the use of context-sensitive termination tools like MU-TERM [1] and VMTL [9] – employs the additional notion of context-sensitive quasi-reductivity of R. In the following, we give a direct proof of the fact that μ-termination of UCS(R) on original terms implies quasi-decreasingness of R. Moreover, we report our experimental findings on DCTRSs from the confluence problems database (Cops),1 extending the experiments of Schernhammer and Gramlich.