YES(?,O(1)) * Step 1: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [A >= 0 && 99 >= A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 0 && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f5,7)} 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,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [A >= 0 && 99 >= A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 0 && A >= 100] (?,1) Signature: {(f0,7);(f13,7);(f5,7)} 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,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [A >= 0 && 99 >= A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 0 && A >= 100] (1,1) Signature: {(f0,7);(f13,7);(f5,7)} 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) = 100 p(f13) = 100 + -1*x1 p(f5) = 100 + -1*x1 Following rules are strictly oriented: [A >= 0 && 99 >= A] ==> f5(A,B,C,D,E,F,G) = 100 + -1*A > 99 + -1*A = f5(1 + A,B,C,D,E,F,G) Following rules are weakly oriented: True ==> f0(A,B,C,D,E,F,G) = 100 >= 100 = f5(0,B,C,D,E,F,G) [A >= 0 && A >= 100] ==> f5(A,B,C,D,E,F,G) = 100 + -1*A >= 100 + -1*A = f13(A,B,C,-2 + A,E,F,G) * Step 4: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E,F,G) -> f5(0,B,C,D,E,F,G) True (1,1) 1. f5(A,B,C,D,E,F,G) -> f5(1 + A,B,C,D,E,F,G) [A >= 0 && 99 >= A] (100,1) 2. f5(A,B,C,D,E,F,G) -> f13(A,B,C,-2 + A,E,F,G) [A >= 0 && A >= 100] (1,1) Signature: {(f0,7);(f13,7);(f5,7)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: KnowledgePropagation + Details: The problem is already solved. YES(?,O(1))