YES

weighted path orer with linear polynomial on natural numbers:

  c_A = 0
  g_A(x1) = x1 + 1
  a_A = 0
  h_A(x1) = 1
  b_A = 2


precedence:

  h > b > a > g > c


status:
c: []
g: [1]
a: []
h: []
b: []

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