YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (?,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [1 + A >= B] (?,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) True (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [B >= 1 + C] (?,1) 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [C >= B] (?,1) 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [D >= 1 + E] (?,1) 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [E >= D] (?,1) 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) True (?,1) 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) True (?,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5,6},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (1,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [1 + A >= B] (1,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) True (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [B >= 1 + C] (?,1) 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [C >= B] (?,1) 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [D >= 1 + E] (?,1) 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [E >= D] (?,1) 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) True (?,1) 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) True (1,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5,6},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (?,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [1 + A >= B] (?,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) True (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [B >= 1 + C] (?,1) 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [C >= B] (?,1) 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [D >= 1 + E] (?,1) 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [E >= D] (?,1) 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) True (?,1) 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) True (?,1) 11. evalrealselectreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10,11},4->{5,6},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{},11->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,9,6,4,7,5,8] c: [2] | `- p:[5,7,8] c: [5] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (?,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [1 + A >= B] (?,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) True (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [B >= 1 + C] (?,1) 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [C >= B] (?,1) 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [D >= 1 + E] (?,1) 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [E >= D] (?,1) 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) True (?,1) 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) True (?,1) 11. evalrealselectreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10,11},4->{5,6},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,9,6,4,7,5,8] c: [2] | `- p:[5,7,8] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalrealselectstart ~> evalrealselectentryin [A <= A, B <= B, C <= C] evalrealselectentryin ~> evalrealselectbb6in [A <= 0*K, B <= B, C <= C] evalrealselectbb6in ~> evalrealselectbbin [A <= A, B <= B, C <= C] evalrealselectbb6in ~> evalrealselectreturnin [A <= A, B <= B, C <= C] evalrealselectbbin ~> evalrealselectbb4in [A <= A, B <= B, C <= K + A] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbb4in ~> evalrealselectbb5in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] evalrealselectbb5in ~> evalrealselectbb6in [A <= K + A, B <= B, C <= C] evalrealselectreturnin ~> evalrealselectstop [A <= A, B <= B, C <= C] evalrealselectreturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B] evalrealselectbb6in ~> evalrealselectbbin [A <= A, B <= B, C <= C] evalrealselectbb5in ~> evalrealselectbb6in [A <= K + A, B <= B, C <= C] evalrealselectbb4in ~> evalrealselectbb5in [A <= A, B <= B, C <= C] evalrealselectbbin ~> evalrealselectbb4in [A <= A, B <= B, C <= K + A] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] + Loop: [0.0.0 <= 2*K + B + C] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= K + C] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalrealselectstart ~> evalrealselectentryin [] evalrealselectentryin ~> evalrealselectbb6in [K ~=> A] evalrealselectbb6in ~> evalrealselectbbin [] evalrealselectbb6in ~> evalrealselectreturnin [] evalrealselectbbin ~> evalrealselectbb4in [A ~+> C,K ~+> C] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbb4in ~> evalrealselectbb5in [] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] evalrealselectbb5in ~> evalrealselectbb6in [A ~+> A,K ~+> A] evalrealselectreturnin ~> evalrealselectstop [] evalrealselectreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] evalrealselectbb6in ~> evalrealselectbbin [] evalrealselectbb5in ~> evalrealselectbb6in [A ~+> A,K ~+> A] evalrealselectbb4in ~> evalrealselectbb5in [] evalrealselectbbin ~> evalrealselectbb4in [A ~+> C,K ~+> C] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~*> 0.0.0] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] evalrealselectbb1in ~> evalrealselectbb4in [C ~+> C,K ~+> C] + Applied Processor: LareProcessor + Details: evalrealselectstart ~> exitus616 [K ~=> A ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,K ~^> C] evalrealselectstart ~> evalrealselectstop [K ~=> A ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,K ~^> C] + evalrealselectbb6in> [A ~+> A ,A ~+> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C ,B ~^> C ,K ~^> C] + evalrealselectbb4in> [B ~+> 0.0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,B ~*> C ,C ~*> C ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick] YES(?,POLY)