YES

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

  f(g(h(y1))) -> g(h(y1))
  f(g(h(y1))) -> g(f(h(g(y1))))
  f(g(h(y1))) -> f(h(y1))
  f(g(h(y1))) -> f(g(y1))
  f(g(h(x0_1))) -> g(f(h(g(x0_1))))
  f(g(h(x0_1))) -> g(h(x0_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.