YES

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

Consider the left-linear TRS R:

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

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

  phi(f(f(f(x))) -> a()) = 6
  phi(f(f(a())) -> a()) = 5
  phi(f(a()) -> a()) = 4
  phi(f(f(g(g(x)))) -> f(a())) = 6
  phi(g(f(a())) -> a()) = 7
  phi(g(a()) -> a()) = 2

  psi(f(f(f(x))) -> a()) = 6
  psi(f(f(a())) -> a()) = 1
  psi(f(a()) -> a()) = 3
  psi(f(f(g(g(x)))) -> f(a())) = 7
  psi(g(f(a())) -> a()) = 7
  psi(g(a()) -> a()) = 6