YES

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

Consider the left-linear TRS R:

  nats() -> :(0(),inc(nats()))
  inc(:(x,y)) -> :(s(x),inc(y))
  inc(tl(nats())) -> tl(inc(nats()))
  hd(:(x,y)) -> x
  tl(:(x,y)) -> y
  d(:(x,y)) -> :(x,:(x,d(y)))

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

  phi(nats() -> :(0(),inc(nats()))) = 2
  phi(inc(:(x,y)) -> :(s(x),inc(y))) = 1
  phi(inc(tl(nats())) -> tl(inc(nats()))) = 4
  phi(hd(:(x,y)) -> x) = 1
  phi(tl(:(x,y)) -> y) = 1
  phi(d(:(x,y)) -> :(x,:(x,d(y)))) = 1

  psi(nats() -> :(0(),inc(nats()))) = 3
  psi(inc(:(x,y)) -> :(s(x),inc(y))) = 1
  psi(inc(tl(nats())) -> tl(inc(nats()))) = 4
  psi(hd(:(x,y)) -> x) = 1
  psi(tl(:(x,y)) -> y) = 1
  psi(d(:(x,y)) -> :(x,:(x,d(y)))) = 1