YES

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

Consider the left-linear TRS R:

  f(g(h(x))) -> g(f(h(g(x))))
  f(x) -> x
  g(x) -> x
  h(x) -> x

Let C be the following subset of R:

  (empty)

The critical pair system CPS(R,C) is:

  f(g(h(x0))) -> g(f(h(g(x0))))
  f(g(h(x0))) -> g(h(x0))
  f(g(h(y0))) -> g(h(y0))
  f(g(h(y0))) -> g(f(h(g(y0))))
  f(g(h(y0))) -> f(h(y0))
  f(g(h(y0))) -> f(g(y0))

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.