YES

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

Consider the left-linear TRS R:

  a() -> c()
  b() -> c()
  f(a(),b()) -> d()
  f(x,c()) -> f(c(),c())
  f(c(),x) -> f(c(),c())
  d() -> f(a(),c())
  d() -> f(c(),b())

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

  phi(a() -> c()) = 2
  phi(b() -> c()) = 3
  phi(f(a(),b()) -> d()) = 5
  phi(f(x,c()) -> f(c(),c())) = 1
  phi(f(c(),x) -> f(c(),c())) = 2
  phi(d() -> f(a(),c())) = 5
  phi(d() -> f(c(),b())) = 5

  psi(a() -> c()) = 4
  psi(b() -> c()) = 4
  psi(f(a(),b()) -> d()) = 6
  psi(f(x,c()) -> f(c(),c())) = 1
  psi(f(c(),x) -> f(c(),c())) = 1
  psi(d() -> f(a(),c())) = 4
  psi(d() -> f(c(),b())) = 4