YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(0,C) True (1,1) 1. f6(A,B) -> f6(1 + A,B) [A >= 0 && 49 >= A] (?,1) 2. f6(A,B) -> f14(A,B) [A >= 0 && A >= 50] (?,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(0,C) True (1,1) 1. f6(A,B) -> f6(1 + A,B) [A >= 0 && 49 >= A] (?,1) 2. f6(A,B) -> f14(A,B) [A >= 0 && A >= 50] (?,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(0,C) True (1,1) 1. f6(A,B) -> f6(1 + A,B) [A >= 0 && 49 >= A] (?,1) 2. f6(A,B) -> f14(A,B) [A >= 0 && A >= 50] (1,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(f0) = 50 p(f14) = 50 + -1*x1 p(f6) = 50 + -1*x1 Following rules are strictly oriented: [A >= 0 && 49 >= A] ==> f6(A,B) = 50 + -1*A > 49 + -1*A = f6(1 + A,B) Following rules are weakly oriented: True ==> f0(A,B) = 50 >= 50 = f6(0,C) [A >= 0 && A >= 50] ==> f6(A,B) = 50 + -1*A >= 50 + -1*A = f14(A,B) * Step 4: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f6(0,C) True (1,1) 1. f6(A,B) -> f6(1 + A,B) [A >= 0 && 49 >= A] (50,1) 2. f6(A,B) -> f14(A,B) [A >= 0 && A >= 50] (1,1) Signature: {(f0,2);(f14,2);(f6,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))