YES

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

Consider the left-linear TRS R:

  f(a(),f(x,a())) -> f(a(),f(f(a(),a()),a()))

Let C be the following subset of R:

  (empty)

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

  (empty)

The TRS R is locally confluent and CPS(R,C)/R is terminating.
Therefore, the confluence of R follows from that of C.

# Emptiness.

The empty TRS is confluent.