YES proof: The input problem is infeasible because [1] the following set of Horn clauses is satisfiable: +(s(x), y) = s(+(x, y)) +(0, x) = x +(x, a) = 0 ==> true__ = false__ true__ = false__ ==> \bottom This holds because [2] the following E does not entail the following G (Claessen-Smallbone's transformation (2018)): E: +(0, x) = x +(s(x), y) = s(+(x, y)) t1(+(x, a)) = true__ t1(0) = 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: t1(0) -> false__ t1(a) -> true__ t2(false__) -> true__ t2(true__) -> false__ with the LPO induced by t2 > a > t1 > 0 > + > s > false__ > true__ with the following interpretations: + returns 2nd variable s returns 1st variable