YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: c = c h(x) = b ==> g(x) = a g(x) = x h(x) = a h(x) = b ==> true__ = false__ true__ = false__ ==> \bottom This holds because [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): E: g(x) = x h(x) = a t1(b, x) = a t1(h(x), x) = g(x) t2(b) = false__ t2(h(x)) = true__ t3(false__) = true__ t3(true__) = false__ G: true__ = false__ This holds because [3] the following ground-complete ordered TRS entails E but does not entail G: g(x) -> x h(x) -> a t1(a, Y0) -> Y0 t1(b, x) -> a t2(a) -> true__ t2(b) -> false__ t3(false__) -> true__ t3(true__) -> false__ with the LPO induced by b > h > a > g > t1 > t3 > t2 > true__ > false__