YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (?,1) Signature: {(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (1,1) Signature: {(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (1,1) Signature: {(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1},1->{1,2},2->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (?,1) 3. f5(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (?,1) 3. f5(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B) -> f5(2,4) True (1,1) 1. f5(A,B) -> f5(2 + A,4 + A) [19 >= A] (?,1) 2. f5(A,B) -> f8(A,B) [A >= 20] (?,1) 3. f5(A,B) -> exitus616(A,B) True (?,1) Signature: {(exitus616,2);(f0,2);(f5,2);(f8,2)} Flow Graph: [0->{1,3},1->{1,2,3},2->{},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,0.0] f0 ~> f5 [A <= 2*K, B <= 4*K] f5 ~> f5 [A <= 2*K + A, B <= 4*K + A] f5 ~> f8 [A <= A, B <= B] f5 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 20*K + A] f5 ~> f5 [A <= 2*K + A, B <= 4*K + A] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f0 ~> f5 [K ~=> A,K ~=> B] f5 ~> f5 [A ~+> A,A ~+> B,K ~*> A,K ~*> B] f5 ~> f8 [] f5 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f5 ~> f5 [A ~+> A,A ~+> B,K ~*> A,K ~*> B] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] f0 ~> f8 [K ~=> A ,K ~=> B ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] + f5> [A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,A ~*> A ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> tick] YES(?,O(1))