YES

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

Consider the left-linear TRS R:

  +(x,0()) -> x
  +(x,s(y)) -> s(+(x,y))
  +(0(),y) -> y
  +(s(x),y) -> s(+(x,y))
  dbl(x) -> +(x,x)
  +(+(x,y),z) -> +(x,+(y,z))
  +(x,y) -> +(y,x)

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

  phi(+(x,0()) -> x) = 4
  phi(+(x,s(y)) -> s(+(x,y))) = 4
  phi(+(0(),y) -> y) = 4
  phi(+(s(x),y) -> s(+(x,y))) = 4
  phi(dbl(x) -> +(x,x)) = 1
  phi(+(+(x,y),z) -> +(x,+(y,z))) = 6
  phi(+(x,y) -> +(y,x)) = 3

  psi(+(x,0()) -> x) = 2
  psi(+(x,s(y)) -> s(+(x,y))) = 7
  psi(+(0(),y) -> y) = 4
  psi(+(s(x),y) -> s(+(x,y))) = 2
  psi(dbl(x) -> +(x,x)) = 1
  psi(+(+(x,y),z) -> +(x,+(y,z))) = 5
  psi(+(x,y) -> +(y,x)) = 1