YES

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

Consider the left-linear TRS R:

  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  s(s(x)) -> x

Let C be the following subset of R:

  (empty)

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

  +(s(s(x0)),y1) -> +(x0,y1)
  +(s(s(x0)),y1) -> s(+(s(x0),y1))
  s(s(s(x0))) -> s(x0)

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.