YES

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

Consider the left-linear TRS R:

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

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

  phi(f(f(x,y),z) -> f(x,f(y,z))) = 3
  phi(f(x,y) -> f(y,x)) = 2

  psi(f(f(x,y),z) -> f(x,f(y,z))) = 1
  psi(f(x,y) -> f(y,x)) = 1