YES

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

Consider the left-linear TRS R:

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

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

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

  psi(f(a()) -> f(f(a()))) = 3
  psi(a() -> b()) = 2
  psi(f(x) -> f(b())) = 1