YES

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

Consider the left-linear TRS R:

  f(g(x,a(),b())) -> x
  g(f(h(c(),d())),x,y) -> h(k1(x),k2(y))
  k1(a()) -> c()
  k2(b()) -> d()
  f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
  f(h(c(),k2(b()))) -> f(h(c(),d()))
  f(h(k1(a()),d())) -> f(h(c(),d()))

Let C be the following subset of R:

  (empty)

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

  f(g(f(h(c(),d())),a(),b())) -> f(h(k1(a()),k2(b())))
  f(g(f(h(c(),d())),a(),b())) -> f(h(c(),d()))
  f(h(k1(a()),k2(b()))) -> f(h(c(),k2(b())))
  f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
  f(h(k1(a()),k2(b()))) -> f(h(k1(a()),d()))

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.