YES

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

Consider the left-linear TRS R:

  0(1(2(3(4(x))))) -> 0(2(1(3(4(x)))))
  0(5(1(2(4(3(x)))))) -> 0(5(2(1(4(3(x))))))
  0(5(2(4(1(3(x)))))) -> 0(1(5(2(4(3(x))))))
  0(5(3(1(2(4(x)))))) -> 0(1(5(3(2(4(x))))))
  0(5(4(1(3(2(x)))))) -> 0(5(4(3(1(2(x))))))

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

  phi(0(1(2(3(4(x))))) -> 0(2(1(3(4(x)))))) = 1
  phi(0(5(1(2(4(3(x)))))) -> 0(5(2(1(4(3(x))))))) = 1
  phi(0(5(2(4(1(3(x)))))) -> 0(1(5(2(4(3(x))))))) = 1
  phi(0(5(3(1(2(4(x)))))) -> 0(1(5(3(2(4(x))))))) = 1
  phi(0(5(4(1(3(2(x)))))) -> 0(5(4(3(1(2(x))))))) = 1

  psi(0(1(2(3(4(x))))) -> 0(2(1(3(4(x)))))) = 1
  psi(0(5(1(2(4(3(x)))))) -> 0(5(2(1(4(3(x))))))) = 1
  psi(0(5(2(4(1(3(x)))))) -> 0(1(5(2(4(3(x))))))) = 1
  psi(0(5(3(1(2(4(x)))))) -> 0(1(5(3(2(4(x))))))) = 1
  psi(0(5(4(1(3(2(x)))))) -> 0(5(4(3(1(2(x))))))) = 1