YES

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

Consider the left-linear TRS R:

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

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

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

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