YES

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

Consider the left-linear TRS R:

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

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

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

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