YES

weighted path orer with linear polynomial on natural numbers:

  -_A(x1,x2) = x1 + 1
  s_A(x1) = x1 + 2
  0_A = 0


precedence:

  0 > - > s


status:
-: [1]
s: [1]
0: []

the condition -(x,x) ->> s(x) is unsatisfiable for all substitutions.