YES

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

Consider the left-linear TRS R:

  f(f(x,y),z) -> f(x,f(y,z))
  f(1(),x) -> x

Let C be the following subset of R:

  (empty)

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

  f(f(f(x0,x1),y1),y2) -> f(f(x0,f(x1,y1)),y2)
  f(f(f(x0,x1),y1),y2) -> f(f(x0,x1),f(y1,y2))
  f(f(1(),y1),y2) -> f(y1,y2)
  f(f(1(),y1),y2) -> f(1(),f(y1,y2))

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.