YES

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

Consider the left-linear TRS R:

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

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

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

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