YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  (empty)

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

  f(a()) -> f(c())
  f(a()) -> b()
  f(a()) -> f(d())
  f(d()) -> f(c())
  f(d()) -> 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.