YES # Compositional parallel critical pair system (Shintani and Hirokawa 2022). Consider the left-linear TRS R: from(x) -> :(x,from(s(x))) sel(0(),:(y,z)) -> y sel(s(x),:(y,z)) -> sel(x,z) Let C be the following subset of R: (empty) The parallel critical pair system PCPS(R,C) is: (empty) All pairs in PCP(R) are joinable and PCPS(R,C)/R is terminating. Therefore, the confluence of R follows from that of C. # emptiness The empty TRS is confluent.