YES

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

Consider the left-linear TRS R:

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

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

  phi(g(f(f(h(x))),y) -> g(g(f(h(x)),f(f(h(x)))),y)) = 1
  phi(f(x) -> g(x,f(x))) = 2
  phi(h(x) -> g(f(x),x)) = 4
  phi(g(x,y) -> h(g(f(x),f(y)))) = 4

  psi(g(f(f(h(x))),y) -> g(g(f(h(x)),f(f(h(x)))),y)) = 4
  psi(f(x) -> g(x,f(x))) = 3
  psi(h(x) -> g(f(x),x)) = 3
  psi(g(x,y) -> h(g(f(x),f(y)))) = 3