YES

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

Consider the left-linear TRS R:

  f(x) -> f(f(x))
  g(x) -> f(x)
  f(x) -> g(x)

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

  phi(f(x) -> f(f(x))) = 5
  phi(g(x) -> f(x)) = 4
  phi(f(x) -> g(x)) = 3

  psi(f(x) -> f(f(x))) = 2
  psi(g(x) -> f(x)) = 1
  psi(f(x) -> g(x)) = 6