YES

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

Consider the left-linear TRS R:

  c() -> b()
  a() -> a()
  b() -> b()
  f(f(a())) -> c()

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

  phi(c() -> b()) = 1
  phi(a() -> a()) = 1
  phi(b() -> b()) = 1
  phi(f(f(a())) -> c()) = 1

  psi(c() -> b()) = 1
  psi(a() -> a()) = 1
  psi(b() -> b()) = 1
  psi(f(f(a())) -> c()) = 1