YES

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

Consider the left-linear TRS R:

  Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))
  Ap(Ap(K(),x),y) -> x
  Ap(I(),x) -> x

Let C be the following subset of R:

  (empty)

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

  (empty)

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.