YES

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

Consider the left-linear TRS R:

  b(w(x)) -> w(w(w(b(x))))
  w(b(x)) -> b(x)
  b(b(x)) -> w(w(w(w(x))))
  w(w(x)) -> w(x)

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

  phi(b(w(x)) -> w(w(w(b(x))))) = 6
  phi(w(b(x)) -> b(x)) = 4
  phi(b(b(x)) -> w(w(w(w(x))))) = 6
  phi(w(w(x)) -> w(x)) = 1

  psi(b(w(x)) -> w(w(w(b(x))))) = 5
  psi(w(b(x)) -> b(x)) = 5
  psi(b(b(x)) -> w(w(w(w(x))))) = 2
  psi(w(w(x)) -> w(x)) = 3