YES

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

Consider the left-linear TRS R:

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

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

  phi(c(c(x)) -> a(c(x))) = 8
  phi(c(b(x)) -> c(c(x))) = 2
  phi(b(a(x)) -> c(b(x))) = 7
  phi(a(b(x)) -> b(a(x))) = 14
  phi(c(a(x)) -> c(a(x))) = 1
  phi(b(c(x)) -> c(c(x))) = 10
  phi(c(c(x)) -> b(c(x))) = 13
  phi(c(a(x)) -> b(c(x))) = 6

  psi(c(c(x)) -> a(c(x))) = 12
  psi(c(b(x)) -> c(c(x))) = 1
  psi(b(a(x)) -> c(b(x))) = 4
  psi(a(b(x)) -> b(a(x))) = 9
  psi(c(a(x)) -> c(a(x))) = 2
  psi(b(c(x)) -> c(c(x))) = 5
  psi(c(c(x)) -> b(c(x))) = 11
  psi(c(a(x)) -> b(c(x))) = 3