YES

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

Consider the left-linear TRS R:

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

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

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

  psi(a(a(x)) -> a(b(a(x)))) = 3
  psi(b(a(b(x))) -> a(c(a(x)))) = 2