YES # parallel critical pair closing system (Shintani and Hirokawa 2022) Consider the left-linear TRS R: h(a(),b()) -> a() f(c()) -> f(c()) c() -> h(a(),h(b(),b())) Let C be the following subset of R: c() -> h(a(),h(b(),b())) The TRS R is left-linear and all parallel critical pairs are joinable by C. Therefore, the confluence of R follows from that of C. # parallel critical pair closing system (Shintani and Hirokawa 2022) Consider the left-linear TRS R: c() -> h(a(),h(b(),b())) Let C be the following subset of R: (empty) The TRS R is left-linear and all parallel critical pairs are joinable by C. Therefore, the confluence of R follows from that of C. # emptiness The empty TRS is confluent.