YES

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

Consider the left-linear TRS R:

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

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

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

  psi(a(a(b(b(x)))) -> b(b(b(b(b(a(a(a(a(a(x))))))))))) = 1