YES

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

Consider the left-linear TRS R:

  f(f(x)) -> f(g(f(x),f(x)))

Let C be the following subset of R:

  (empty)

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

  f(f(f(x1_1))) -> f(f(g(f(x1_1),f(x1_1))))
  f(f(f(x1_1))) -> f(g(f(f(x1_1)),f(f(x1_1))))

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.