YES

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

Consider the left-linear TRS R:

  f(a(),x) -> f(a(),g(x))
  a() -> b()
  g(x) -> x

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

  phi(f(a(),x) -> f(a(),g(x))) = 2
  phi(a() -> b()) = 2
  phi(g(x) -> x) = 1

  psi(f(a(),x) -> f(a(),g(x))) = 2
  psi(a() -> b()) = 2
  psi(g(x) -> x) = 1