YES

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

Consider the left-linear TRS R:

  a() -> b()
  a() -> c()
  a() -> e()
  b() -> d()
  c() -> a()
  d() -> a()
  d() -> e()
  g(x) -> h(a())
  h(x) -> e()

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

  phi(a() -> b()) = 4
  phi(a() -> c()) = 4
  phi(a() -> e()) = 2
  phi(b() -> d()) = 1
  phi(c() -> a()) = 1
  phi(d() -> a()) = 4
  phi(d() -> e()) = 1
  phi(g(x) -> h(a())) = 1
  phi(h(x) -> e()) = 1

  psi(a() -> b()) = 3
  psi(a() -> c()) = 5
  psi(a() -> e()) = 2
  psi(b() -> d()) = 1
  psi(c() -> a()) = 1
  psi(d() -> a()) = 3
  psi(d() -> e()) = 1
  psi(g(x) -> h(a())) = 1
  psi(h(x) -> e()) = 1