YES

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

Consider the left-linear TRS R:

  Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))
  Ap(Ap(K(),x),y) -> x
  Ap(I(),x) -> x

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

  phi(Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))) = 1
  phi(Ap(Ap(K(),x),y) -> x) = 1
  phi(Ap(I(),x) -> x) = 1

  psi(Ap(Ap(Ap(S(),x),y),z) -> Ap(Ap(x,z),Ap(y,z))) = 1
  psi(Ap(Ap(K(),x),y) -> x) = 1
  psi(Ap(I(),x) -> x) = 1