YES

# Compositional 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 critical pair system CPS(R,C) is:

  F(H(I(x0)),y1) -> F(I(x0),y1)
  F(H(I(x0)),y1) -> G(H(I(x0)))

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.