YES

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

Consider the left-linear TRS R:

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

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

  phi(f(a(),a()) -> g(f(a(),a()))) = 4
  phi(a() -> b()) = 2
  phi(f(b(),x) -> g(f(x,x))) = 1
  phi(f(x,b()) -> g(f(x,x))) = 1

  psi(f(a(),a()) -> g(f(a(),a()))) = 4
  psi(a() -> b()) = 3
  psi(f(b(),x) -> g(f(x,x))) = 1
  psi(f(x,b()) -> g(f(x,x))) = 1