YES

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

Consider the left-linear TRS R:

  f(x) -> g(f(x))
  h(x) -> p(h(x))
  f(x) -> h(f(x))
  g(x) -> p(p(h(x)))

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

  phi(f(x) -> g(f(x))) = 2
  phi(h(x) -> p(h(x))) = 1
  phi(f(x) -> h(f(x))) = 2
  phi(g(x) -> p(p(h(x)))) = 1

  psi(f(x) -> g(f(x))) = 2
  psi(h(x) -> p(h(x))) = 1
  psi(f(x) -> h(f(x))) = 2
  psi(g(x) -> p(p(h(x)))) = 1