YES

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

Consider the left-linear TRS R:

  f(b()) -> c()
  c() -> c()
  f(c()) -> b()
  a() -> b()

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

  phi(f(b()) -> c()) = 1
  phi(c() -> c()) = 1
  phi(f(c()) -> b()) = 1
  phi(a() -> b()) = 1

  psi(f(b()) -> c()) = 1
  psi(c() -> c()) = 1
  psi(f(c()) -> b()) = 1
  psi(a() -> b()) = 1