YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  (empty)

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

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

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.