YES

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

Consider the left-linear TRS R:

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

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

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

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