YES

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

Consider the left-linear TRS R:

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

Let C be the following subset of R:

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

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

  (empty)

The TRS R is locally confluent 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:

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

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

  phi(+(0(),x) -> x) = 1
  phi(+(s(x),y) -> s(+(x,y))) = 1

  psi(+(0(),x) -> x) = 1
  psi(+(s(x),y) -> s(+(x,y))) = 1