YES

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

Consider the left-linear TRS R:

  f(0(),0()) -> f(0(),1())
  f(1(),0()) -> f(0(),0())
  f(x,y) -> f(y,x)

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

  phi(f(0(),0()) -> f(0(),1())) = 5
  phi(f(1(),0()) -> f(0(),0())) = 5
  phi(f(x,y) -> f(y,x)) = 4

  psi(f(0(),0()) -> f(0(),1())) = 1
  psi(f(1(),0()) -> f(0(),0())) = 3
  psi(f(x,y) -> f(y,x)) = 2