YES

# Compositional parallel critical pair 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:

  (empty)

The parallel critical pair system PCPS(R,C) is:

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

All pairs in PCP(R) are joinable and PCPS(R,C)/R is terminating.
Therefore, the confluence of R follows from that of C.

# emptiness

The empty TRS is confluent.