YES

linear polynomial interpretations on negative integers:

  add_A(x1,x2) = x1 + x2
  s_A(x1) = x1 + -1
  0_A = 0
  gcd_A(x1,x2) = 0
  leq_A(x1,x2) = -1
  false_A = 0



the condition leq(0(),x1) ->> false() is unsatisfiable for all substitutions.