YES

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

Consider the left-linear TRS R:

  f(g(g(x))) -> a()
  f(g(h(x))) -> b()
  f(h(g(x))) -> b()
  f(h(h(x))) -> c()
  g(x) -> h(x)
  a() -> b()
  b() -> c()

Let C be the following subset of R:

  (empty)

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

  f(g(g(y0))) -> f(h(g(y0)))
  f(g(g(y0))) -> a()
  f(g(g(y0))) -> f(g(h(y0)))
  f(g(h(y0))) -> f(h(h(y0)))
  f(g(h(y0))) -> b()
  f(h(g(y0))) -> f(h(h(y0)))
  f(h(g(y0))) -> b()

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.