YES

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

  f(f(f(x1_1,x1_2),y2),y3) -> f(f(x1_1,f(x1_2,y2)),y3)
  f(f(f(x1_1,x1_2),y2),y3) -> f(f(x1_1,x1_2),f(y2,y3))
  f(f(1(),y2),y3) -> f(y2,y3)
  f(f(1(),y2),y3) -> f(1(),f(y2,y3))

All pairs in PCP(R) are joinable and PCPS(R,C)/R is terminating.
Therefore, the confluence of R follows from that of C.

# Parallel rule labeling (Zankl et al. 2015).

Consider the left-linear TRS R:

  (empty)

All parallel critical peaks (except C's) are decreasing wrt rule labeling: