YES

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

Consider the left-linear TRS R:

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

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

  phi(f(f(f(f(x)))) -> f(f(f(g(x,f(x)))))) = 3
  phi(f(x) -> g(x,f(x))) = 2

  psi(f(f(f(f(x)))) -> f(f(f(g(x,f(x)))))) = 3
  psi(f(x) -> g(x,f(x))) = 1