YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  (empty)

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

  p(s(p(x0))) -> p(x0)
  +(y0,s(p(x0))) -> +(y0,x0)
  +(y0,s(p(x0))) -> s(+(y0,p(x0)))
  -(y0,s(p(x0))) -> -(y0,x0)
  -(y0,s(p(x0))) -> p(-(y0,p(x0)))
  s(p(s(x0))) -> s(x0)
  +(y0,p(s(x0))) -> +(y0,x0)
  +(y0,p(s(x0))) -> p(+(y0,s(x0)))
  -(y0,p(s(x0))) -> -(y0,x0)
  -(y0,p(s(x0))) -> s(-(y0,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.