YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,C) True (1,1) 1. f300(A,B,C) -> f1(A,B,D) [A >= B] (?,1) 2. f300(A,B,C) -> f300(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2},1->{},2->{1,2}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,C) True (1,1) 1. f300(A,B,C) -> f1(A,B,D) [A >= B] (1,1) 2. f300(A,B,C) -> f300(1 + A,B,C) [B >= 1 + A] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2},1->{},2->{1,2}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,C) True (1,1) 1. f300(A,B,C) -> f1(A,B,D) [A >= B] (?,1) 2. f300(A,B,C) -> f300(1 + A,B,C) [B >= 1 + A] (?,1) 3. f300(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{1,2,3},3->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f2(A,B,C) -> f300(A,B,C) True (1,1) 1. f300(A,B,C) -> f1(A,B,D) [A >= B] (?,1) 2. f300(A,B,C) -> f300(1 + A,B,C) [B >= 1 + A] (?,1) 3. f300(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(exitus616,3);(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{1,2,3},3->{}] ,We construct a looptree: P: [0,1,2,3] | `- p:[2] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] f2 ~> f300 [A <= A, B <= B, C <= C] f300 ~> f1 [A <= A, B <= B, C <= unknown] f300 ~> f300 [A <= A + B, B <= B, C <= C] f300 ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] f300 ~> f300 [A <= A + B, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] f2 ~> f300 [] f300 ~> f1 [huge ~=> C] f300 ~> f300 [A ~+> A,B ~+> A] f300 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f300 ~> f300 [A ~+> A,B ~+> A] + Applied Processor: LareProcessor + Details: f2 ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,B ~*> A] f2 ~> f1 [huge ~=> C ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,B ~*> A] + f300> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,B ~*> A] YES(?,O(n^1))