YES

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

Consider the left-linear TRS R:

  a() -> b()
  a() -> d()
  b() -> a()
  c() -> a()
  c() -> b()

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

  phi(a() -> b()) = 3
  phi(a() -> d()) = 2
  phi(b() -> a()) = 1
  phi(c() -> a()) = 4
  phi(c() -> b()) = 4

  psi(a() -> b()) = 3
  psi(a() -> d()) = 2
  psi(b() -> a()) = 1
  psi(c() -> a()) = 4
  psi(c() -> b()) = 4