YES(?,O(1)) * Step 1: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 199 p(f1) = -101 + x1 Following rules are strictly oriented: [300 + -1*A >= 0 && A >= 102] ==> f1(A) = -101 + A > -102 + A = f1(-1 + A) Following rules are weakly oriented: True ==> f0(A) = 199 >= 199 = f1(300) * Step 2: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] (199,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))