YES

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

Consider the left-linear TRS R:

  f(a(),f(a(),f(a(),f(a(),y)))) -> f(a(),f(a(),f(a(),g(y,f(a(),y)))))
  f(x,y) -> g(y,f(x,y))

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

  phi(f(a(),f(a(),f(a(),f(a(),y)))) -> f(a(),f(a(),f(a(),g(y,f(a(),y)))))) = 3
  phi(f(x,y) -> g(y,f(x,y))) = 2

  psi(f(a(),f(a(),f(a(),f(a(),y)))) -> f(a(),f(a(),f(a(),g(y,f(a(),y)))))) = 3
  psi(f(x,y) -> g(y,f(x,y))) = 1