YES

# Compositional parallel critical pair system (Shintani and Hirokawa 2022).

Consider the left-linear TRS R:

  F(H(x),y) -> G(H(x))
  H(I(x)) -> I(x)
  F(I(x),y) -> G(I(x))

Let C be the following subset of R:

  (empty)

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

  F(H(I(x1_1)),y2) -> F(I(x1_1),y2)
  F(H(I(x1_1)),y2) -> G(H(I(x1_1)))

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.