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:

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

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

  (empty)

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

# Parallel rule labeling (Zankl et al. 2015).

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()

All parallel critical peaks (except C's) are decreasing wrt rule labeling:

  phi(F(G(x,A(),B())) -> x) = 2
  phi(G(F(H(C(),D())),x,y) -> H(K1(x),K2(y))) = 2
  phi(K1(A()) -> C()) = 1
  phi(K2(B()) -> D()) = 1

  psi(F(G(x,A(),B())) -> x) = 2
  psi(G(F(H(C(),D())),x,y) -> H(K1(x),K2(y))) = 2
  psi(K1(A()) -> C()) = 1
  psi(K2(B()) -> D()) = 1