YES

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

Consider the left-linear TRS R:

  a(x) -> x
  a(b(x)) -> c(b(b(a(a(x)))))
  b(x) -> c(x)
  c(c(x)) -> x

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

  phi(a(x) -> x) = 2
  phi(a(b(x)) -> c(b(b(a(a(x)))))) = 4
  phi(b(x) -> c(x)) = 2
  phi(c(c(x)) -> x) = 1

  psi(a(x) -> x) = 3
  psi(a(b(x)) -> c(b(b(a(a(x)))))) = 4
  psi(b(x) -> c(x)) = 3
  psi(c(c(x)) -> x) = 1