YES # parallel critical pair closing system (Shintani and Hirokawa 2022) Consider the left-linear TRS R: F(c(x)) -> G(x) G(x) -> F(x) c(x) -> x Let C be the following subset of R: G(x) -> F(x) 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: G(x) -> F(x) 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.