YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  h(a(),a()) -> g(g(a()))

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:

  h(a(),a()) -> g(g(a()))

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.