YES

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

Consider the left-linear TRS R:

  f(a()) -> f(g(b(),b()))
  a() -> g(c(),c())
  c() -> d()
  d() -> b()
  b() -> d()

Let C be the following subset of R:

  (empty)

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

  f(a()) -> f(g(c(),c()))
  f(a()) -> f(g(b(),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.