YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalSimpleSinglestart(A,B) -> evalSimpleSingleentryin(A,B) True (1,1) 1. evalSimpleSingleentryin(A,B) -> evalSimpleSinglebb3in(0,B) True (?,1) 2. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglebbin(A,B) [B >= 1 + A] (?,1) 3. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglereturnin(A,B) [A >= B] (?,1) 4. evalSimpleSinglebbin(A,B) -> evalSimpleSinglebb3in(1 + A,B) True (?,1) 5. evalSimpleSinglereturnin(A,B) -> evalSimpleSinglestop(A,B) True (?,1) Signature: {(evalSimpleSinglebb3in,2) ;(evalSimpleSinglebbin,2) ;(evalSimpleSingleentryin,2) ;(evalSimpleSinglereturnin,2) ;(evalSimpleSinglestart,2) ;(evalSimpleSinglestop,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + 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. evalSimpleSinglestart(A,B) -> evalSimpleSingleentryin(A,B) True (1,1) 1. evalSimpleSingleentryin(A,B) -> evalSimpleSinglebb3in(0,B) True (1,1) 2. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglebbin(A,B) [B >= 1 + A] (?,1) 3. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglereturnin(A,B) [A >= B] (1,1) 4. evalSimpleSinglebbin(A,B) -> evalSimpleSinglebb3in(1 + A,B) True (?,1) 5. evalSimpleSinglereturnin(A,B) -> evalSimpleSinglestop(A,B) True (1,1) Signature: {(evalSimpleSinglebb3in,2) ;(evalSimpleSinglebbin,2) ;(evalSimpleSingleentryin,2) ;(evalSimpleSinglereturnin,2) ;(evalSimpleSinglestart,2) ;(evalSimpleSinglestop,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalSimpleSinglestart(A,B) -> evalSimpleSingleentryin(A,B) True (1,1) 1. evalSimpleSingleentryin(A,B) -> evalSimpleSinglebb3in(0,B) True (?,1) 2. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglebbin(A,B) [B >= 1 + A] (?,1) 3. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglereturnin(A,B) [A >= B] (?,1) 4. evalSimpleSinglebbin(A,B) -> evalSimpleSinglebb3in(1 + A,B) True (?,1) 5. evalSimpleSinglereturnin(A,B) -> evalSimpleSinglestop(A,B) True (?,1) 6. evalSimpleSinglereturnin(A,B) -> exitus616(A,B) True (?,1) Signature: {(evalSimpleSinglebb3in,2) ;(evalSimpleSinglebbin,2) ;(evalSimpleSingleentryin,2) ;(evalSimpleSinglereturnin,2) ;(evalSimpleSinglestart,2) ;(evalSimpleSinglestop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [2] * Step 4: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. evalSimpleSinglestart(A,B) -> evalSimpleSingleentryin(A,B) True (1,1) 1. evalSimpleSingleentryin(A,B) -> evalSimpleSinglebb3in(0,B) True (?,1) 2. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglebbin(A,B) [B >= 1 + A] (?,1) 3. evalSimpleSinglebb3in(A,B) -> evalSimpleSinglereturnin(A,B) [A >= B] (?,1) 4. evalSimpleSinglebbin(A,B) -> evalSimpleSinglebb3in(1 + A,B) True (?,1) 5. evalSimpleSinglereturnin(A,B) -> evalSimpleSinglestop(A,B) True (?,1) 6. evalSimpleSinglereturnin(A,B) -> exitus616(A,B) True (?,1) Signature: {(evalSimpleSinglebb3in,2) ;(evalSimpleSinglebbin,2) ;(evalSimpleSingleentryin,2) ;(evalSimpleSinglereturnin,2) ;(evalSimpleSinglestart,2) ;(evalSimpleSinglestop,2) ;(exitus616,2)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{2,3},5->{},6->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[2,4] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] evalSimpleSinglestart ~> evalSimpleSingleentryin [A <= A, B <= B] evalSimpleSingleentryin ~> evalSimpleSinglebb3in [A <= 0*K, B <= B] evalSimpleSinglebb3in ~> evalSimpleSinglebbin [A <= A, B <= B] evalSimpleSinglebb3in ~> evalSimpleSinglereturnin [A <= A, B <= B] evalSimpleSinglebbin ~> evalSimpleSinglebb3in [A <= K + A, B <= B] evalSimpleSinglereturnin ~> evalSimpleSinglestop [A <= A, B <= B] evalSimpleSinglereturnin ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 2*K + A + B] evalSimpleSinglebb3in ~> evalSimpleSinglebbin [A <= A, B <= B] evalSimpleSinglebbin ~> evalSimpleSinglebb3in [A <= K + A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] evalSimpleSinglestart ~> evalSimpleSingleentryin [] evalSimpleSingleentryin ~> evalSimpleSinglebb3in [K ~=> A] evalSimpleSinglebb3in ~> evalSimpleSinglebbin [] evalSimpleSinglebb3in ~> evalSimpleSinglereturnin [] evalSimpleSinglebbin ~> evalSimpleSinglebb3in [A ~+> A,K ~+> A] evalSimpleSinglereturnin ~> evalSimpleSinglestop [] evalSimpleSinglereturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~*> 0.0] evalSimpleSinglebb3in ~> evalSimpleSinglebbin [] evalSimpleSinglebbin ~> evalSimpleSinglebb3in [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: evalSimpleSinglestart ~> exitus616 [K ~=> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,B ~*> A ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] evalSimpleSinglestart ~> evalSimpleSinglestop [K ~=> A ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,B ~*> A ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] + evalSimpleSinglebb3in> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,A ~*> A ,B ~*> A ,K ~*> A ,K ~*> 0.0 ,K ~*> tick] YES(?,O(n^1))