YES

# parallel critical pair closing system (Shintani and Hirokawa 2022)

Consider the left-linear TRS R:

  f(g(h(x))) -> g(f(h(g(x))))
  f(x) -> x
  g(x) -> x
  h(x) -> x

Let C be the following subset of R:

  f(x) -> x
  g(x) -> x
  h(x) -> 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:

  f(x) -> x
  g(x) -> x
  h(x) -> 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.