YES

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

Consider the left-linear TRS R:

  f(g(x)) -> h(g(x),g(x))
  f(s(x)) -> h(s(x),s(x))
  g(x) -> s(x)

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

  phi(f(g(x)) -> h(g(x),g(x))) = 2
  phi(f(s(x)) -> h(s(x),s(x))) = 1
  phi(g(x) -> s(x)) = 3

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