YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

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

The parallel critical pair system PCPS(R,C) is:

  -(-(+(x1_1,x1_2))) -> -(+(-(x1_1),-(x1_2)))
  -(-(+(x1_1,x1_2))) -> +(x1_1,x1_2)

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

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

  phi(-(+(x,y)) -> +(-(x),-(y))) = 1
  phi(+(+(x,y),z) -> +(x,+(y,z))) = 3
  phi(+(x,y) -> +(y,x)) = 4

  psi(-(+(x,y)) -> +(-(x),-(y))) = 2
  psi(+(+(x,y),z) -> +(x,+(y,z))) = 6
  psi(+(x,y) -> +(y,x)) = 5