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.