YES

linear polynomial interpretations on negative integers:

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



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