YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

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

The parallel critical pair system PCPS(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.

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

Consider the left-linear TRS R:

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

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

  phi(-(+(x,y)) -> +(-(x),-(y))) = 1
  phi(+(-(x),-(y)) -> -(+(x,y))) = 1

  psi(-(+(x,y)) -> +(-(x),-(y))) = 2
  psi(+(-(x),-(y)) -> -(+(x,y))) = 2