YES

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

Consider the left-linear TRS R:

  h(f(),a(),a()) -> h(g(),a(),a())
  h(g(),a(),a()) -> h(f(),a(),a())
  a() -> a'()
  h(x,a'(),y) -> h(x,y,y)
  g() -> f()
  f() -> g()

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

  phi(h(f(),a(),a()) -> h(g(),a(),a())) = 4
  phi(h(g(),a(),a()) -> h(f(),a(),a())) = 7
  phi(a() -> a'()) = 5
  phi(h(x,a'(),y) -> h(x,y,y)) = 1
  phi(g() -> f()) = 1
  phi(f() -> g()) = 2

  psi(h(f(),a(),a()) -> h(g(),a(),a())) = 2
  psi(h(g(),a(),a()) -> h(f(),a(),a())) = 8
  psi(a() -> a'()) = 5
  psi(h(x,a'(),y) -> h(x,y,y)) = 7
  psi(g() -> f()) = 7
  psi(f() -> g()) = 6