YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: a = b y' = y & y'' = y ==> f(g(y'), y'') = h(y, f(g(y), a)) x' = x & x'' = x ==> f(x', x'') = h(x, f(x, b)) g(x1) = x & x2 = x & x1 = x3 & x2 = x3 ==> 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 = b f(g(y), y) = h(y, f(g(y), a)) f(x, x) = h(x, f(x, b)) t1(g(x3), x3) = true__ t1(x3, x3) = false__ 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: b -> a h(Y0, f(Y0, a)) -> f(Y0, Y0) h(y, f(g(y), a)) -> f(g(y), y) t1(g(x3), x3) -> true__ t1(x3, x3) -> false__ t2(false__) -> true__ t2(true__) -> false__ with the LPO induced by h > f > g > t1 > t2 > b > a > false__ > true__