YES

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

Consider the left-linear TRS R:

  f(i(x),g(a())) -> f(j(x,x),g(b()))
  b() -> a()
  i(x) -> j(x,x)

Let C be the following subset of R:

  (empty)

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

  f(i(y0),g(a())) -> f(j(y0,y0),g(a()))
  f(i(y0),g(a())) -> f(j(y0,y0),g(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.