YES

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

Consider the left-linear TRS R:

  F(x,y) -> c(y)
  G(x) -> x
  f(x) -> g(x)
  g(x) -> c(x)

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

  phi(F(x,y) -> c(y)) = 1
  phi(G(x) -> x) = 1
  phi(f(x) -> g(x)) = 1
  phi(g(x) -> c(x)) = 1

  psi(F(x,y) -> c(y)) = 1
  psi(G(x) -> x) = 1
  psi(f(x) -> g(x)) = 1
  psi(g(x) -> c(x)) = 1