YES

linear polynomial interpretations on negative integers:

  odd_A(x1) = 0
  s_A(x1) = -2
  false_A = -2
  true_A = -1
  even_A(x1) = 0
  zero_A(x1) = x1
  0_A = -1



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