YES

# Compositional parallel rule labeling (Shintani and Hirokawa 2022).

Consider the left-linear TRS R:

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

Let C be the following subset of R:

  (empty)

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

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

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


Therefore, the confluence of R follows from that of C.

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

Consider the left-linear TRS R:

  (empty)

Let C be the following subset of R:

  (empty)

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.

# emptiness

The empty TRS is confluent.