YES

weighted path orer with linear polynomial on natural numbers:

  g_A(x1) = x1 + 1
  f_A(x1) = x1
  h_A(x1) = x1


precedence:

  f > h > g


status:
g: [1]
f: [1]
h: [1]

the condition f(x) ->> f(h(x)) is unsatisfiable for all substitutions.