YES

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

Consider the left-linear TRS R:

  F(G(x,A(),B())) -> x
  G(F(H(C(),D())),x,y) -> H(K1(x),K2(y))
  K1(A()) -> C()
  K2(B()) -> D()

Let C be the following subset of R:

  K1(A()) -> C()
  K2(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:

  K1(A()) -> C()
  K2(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.