YES

linear polynomial interpretations on natural numbers:

  min_A(x1) = x1
  cons_A(x1,x2) = x1 + x2
  nil_A = 1
  le_A(x1,x2) = x2
  s_A(x1) = x1 + 1
  0_A = 2
  false_A = 2
  true_A = 0



the condition le(x1,min(nil())) ->> false() is unsatisfiable for all substitutions.