YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  (empty)

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

  +(0(),0()) -> 0()
  +(0(),s(y1)) -> s(y1)
  +(0(),s(y1)) -> s(+(0(),y1))
  +(s(x0),0()) -> s(+(x0,0()))
  +(s(x0),0()) -> s(x0)
  +(s(x0),s(y1)) -> s(+(x0,s(y1)))
  +(s(x0),s(y1)) -> s(+(s(x0),y1))
  +(s(y0),0()) -> s(y0)
  +(s(y0),0()) -> s(+(y0,0()))
  +(0(),s(x1)) -> s(+(0(),x1))
  +(0(),s(x1)) -> s(x1)
  +(s(y0),s(x1)) -> s(+(s(y0),x1))
  +(s(y0),s(x1)) -> s(+(y0,s(x1)))

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.