YES

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

Consider the left-linear TRS R:

  g(a()) -> f(g(a()))
  g(b()) -> c()
  a() -> b()
  f(x) -> h(x,x)
  h(x,y) -> c()

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

  phi(g(a()) -> f(g(a()))) = 2
  phi(g(b()) -> c()) = 1
  phi(a() -> b()) = 2
  phi(f(x) -> h(x,x)) = 1
  phi(h(x,y) -> c()) = 1

  psi(g(a()) -> f(g(a()))) = 2
  psi(g(b()) -> c()) = 1
  psi(a() -> b()) = 2
  psi(f(x) -> h(x,x)) = 1
  psi(h(x,y) -> c()) = 1