YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: d = x & e = x ==> c = d d = x & e = x ==> b = d b = x & c = x ==> a = a d = x & e = x ==> true__ = false__ true__ = false__ ==> \bottom This holds because [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): E: g1(d) = b g1(d) = c g1(e) = d t1(b) = a t1(c) = a t2(d) = false__ t2(e) = 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: a -> t1(g1(g1(e))) a -> t1(g1(g1(e))) b -> g1(g1(e)) c -> g1(g1(e)) d -> g1(e) t2(e) -> true__ t2(g1(e)) -> false__ t3(false__) -> true__ t3(true__) -> false__ with the LPO induced by t3 > a > b > c > d > e > g1 > t2 > t1 > false__ > true__