YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (?,1) Signature: {(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + 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) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (1,1) Signature: {(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (1,1) Signature: {(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (?,1) 4. f3(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,3)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (?,1) 4. f3(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [2] | `- p:[1] c: [1] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A) -> f3(0) True (1,1) 1. f3(A) -> f3(1 + A) [41 >= A] (?,1) 2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1) 3. f3(A) -> f13(A) [A >= 42] (?,1) 4. f3(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f13,1);(f3,1)} Flow Graph: [0->{1,2,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}] ,We construct a looptree: P: [0,1,2,3,4] | `- p:[1,2] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,0.0,0.0.0] f0 ~> f3 [A <= 0*K] f3 ~> f3 [A <= K + A] f3 ~> f3 [A <= K + A] f3 ~> f13 [A <= A] f3 ~> exitus616 [A <= A] + Loop: [0.0 <= 42*K + A] f3 ~> f3 [A <= K + A] f3 ~> f3 [A <= K + A] + Loop: [0.0.0 <= 42*K + A] f3 ~> f3 [A <= K + A] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0,0.0.0] f0 ~> f3 [K ~=> A] f3 ~> f3 [A ~+> A,K ~+> A] f3 ~> f3 [A ~+> A,K ~+> A] f3 ~> f13 [] f3 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f3 ~> f3 [A ~+> A,K ~+> A] f3 ~> f3 [A ~+> A,K ~+> A] + Loop: [A ~+> 0.0.0,K ~*> 0.0.0] f3 ~> f3 [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,K ~^> A] f0 ~> f13 [K ~=> A ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,K ~^> A] + f3> [A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> A ,K ~^> A] + f3> [A ~+> A ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,A ~*> A ,K ~*> A ,K ~*> 0.0.0 ,K ~*> tick] YES(?,O(1))