YES

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

Consider the left-linear TRS R:

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

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

  phi(f(a(),b()) -> c()) = 1
  phi(a() -> a'()) = 3
  phi(b() -> b'()) = 7
  phi(c() -> f(a'(),b())) = 2
  phi(c() -> f(a(),b'())) = 8
  phi(c() -> f(a(),b())) = 8

  psi(f(a(),b()) -> c()) = 3
  psi(a() -> a'()) = 6
  psi(b() -> b'()) = 4
  psi(c() -> f(a'(),b())) = 5
  psi(c() -> f(a(),b'())) = 4
  psi(c() -> f(a(),b())) = 9