YES

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

Consider the left-linear TRS R:

  f(a()) -> f(g(b(),b()))
  a() -> g(c(),c())
  c() -> d()
  d() -> b()
  b() -> d()

Let C be the following subset of R:

  c() -> d()
  b() -> d()

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() -> d()
  b() -> d()

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.