YES

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

Consider the left-linear TRS R:

  W(W(x)) -> W(x)
  B(I(x)) -> W(x)
  W(B(x)) -> B(x)
  F(H(x),y) -> F(H(x),G(y))
  F(x,I(y)) -> F(G(x),I(y))
  G(x) -> x

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

  phi(W(W(x)) -> W(x)) = 1
  phi(B(I(x)) -> W(x)) = 2
  phi(W(B(x)) -> B(x)) = 2
  phi(F(H(x),y) -> F(H(x),G(y))) = 5
  phi(F(x,I(y)) -> F(G(x),I(y))) = 2
  phi(G(x) -> x) = 3

  psi(W(W(x)) -> W(x)) = 1
  psi(B(I(x)) -> W(x)) = 2
  psi(W(B(x)) -> B(x)) = 2
  psi(F(H(x),y) -> F(H(x),G(y))) = 6
  psi(F(x,I(y)) -> F(G(x),I(y))) = 4
  psi(G(x) -> x) = 1