YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: a = b ==> a = b a = 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: t1(a) = a t1(b) = b t2(a) = true__ t2(b) = false__ 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: t1(a) -> a t1(b) -> b t2(a) -> true__ t2(b) -> false__ t3(false__) -> true__ t3(true__) -> false__ with the LPO induced by t3 > t2 > b > a > t1 > false__ > true__