YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: a = c f(a, b, x) = f(x, x, x) F(x, x, x) = F(a, b, y) ==> true__ = false__ true__ = false__ ==> \bottom This holds because [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): E: a = c t1(F(a, b, y), y) = false__ t1(F(x, x, x), y) = true__ t2(false__) = true__ t2(true__) = false__ G: true__ = false__ This holds because [3] the following ground-complete ordered TRS entails E but does not entail G: a -> c t1(F(c, b, Y0), Y0) -> false__ t1(F(x, x, x), y) -> true__ t2(false__) -> true__ t2(true__) -> false__ with the LPO induced by b > F > t1 > t2 > a > c > false__ > true__