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 b = x & c = 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: f1(d) = c f1(e) = d f2(d) = b f2(e) = d f3(b) = a f3(c) = a f4(b) = true__ f4(c) = false__ f5(false__) = false__ f5(true__) = true__ G: true__ = false__ This holds because [3] the following ground-complete ordered TRS entails E but does not entail G: a -> f3(f1(f1(e))) b -> f2(f1(e)) c -> f1(f1(e)) d -> f1(e) f2(e) -> f1(e) f3(f2(f1(e))) -> f3(f1(f1(e))) f4(f1(f1(e))) -> false__ f4(f2(f1(e))) -> true__ f5(false__) -> false__ f5(true__) -> true__ with the LPO induced by f5 > f4 > c > a > b > f2 > d > f1 > e > f3 > false__ > true__