YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [D >= 1 + A] (?,1) 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [A >= D] (?,1) 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) True (?,1) 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) True (?,1) 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) True (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (1,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= C] (1,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [D >= 1 + A] (?,1) 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [A >= D] (?,1) 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) True (?,1) 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) True (?,1) 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) True (1,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [D >= 1 + A] (?,1) 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [A >= D] (?,1) 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) True (?,1) 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) True (?,1) 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) True (?,1) 9. evalSimpleMultiplereturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2,3},7->{2,3},8->{},9->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [4] | `- p:[2,7,5] c: [2] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalSimpleMultiplestart(A,B,C,D) -> evalSimpleMultipleentryin(A,B,C,D) True (1,1) 1. evalSimpleMultipleentryin(A,B,C,D) -> evalSimpleMultiplebb3in(0,0,C,D) True (?,1) 2. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplebbin(A,B,C,D) [C >= 1 + B] (?,1) 3. evalSimpleMultiplebb3in(A,B,C,D) -> evalSimpleMultiplereturnin(A,B,C,D) [B >= C] (?,1) 4. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb1in(A,B,C,D) [D >= 1 + A] (?,1) 5. evalSimpleMultiplebbin(A,B,C,D) -> evalSimpleMultiplebb2in(A,B,C,D) [A >= D] (?,1) 6. evalSimpleMultiplebb1in(A,B,C,D) -> evalSimpleMultiplebb3in(1 + A,B,C,D) True (?,1) 7. evalSimpleMultiplebb2in(A,B,C,D) -> evalSimpleMultiplebb3in(A,1 + B,C,D) True (?,1) 8. evalSimpleMultiplereturnin(A,B,C,D) -> evalSimpleMultiplestop(A,B,C,D) True (?,1) 9. evalSimpleMultiplereturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalSimpleMultiplebb1in,4) ;(evalSimpleMultiplebb2in,4) ;(evalSimpleMultiplebb3in,4) ;(evalSimpleMultiplebbin,4) ;(evalSimpleMultipleentryin,4) ;(evalSimpleMultiplereturnin,4) ;(evalSimpleMultiplestart,4) ;(evalSimpleMultiplestop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{2,3},7->{2,3},8->{},9->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [4] | `- p:[2,7,5] c: [2]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] evalSimpleMultiplestart ~> evalSimpleMultipleentryin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultipleentryin ~> evalSimpleMultiplebb3in [A <= 0*K, B <= 0*K, C <= C, D <= D] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb3in ~> evalSimpleMultiplereturnin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A <= K + A, B <= B, C <= C, D <= D] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [A <= A, B <= K + B, C <= C, D <= D] evalSimpleMultiplereturnin ~> evalSimpleMultiplestop [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplereturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + D] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A <= K + A, B <= B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [A <= A, B <= K + B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= 2*K + B + C] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [A <= A, B <= B, C <= C, D <= D] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [A <= A, B <= K + B, C <= C, D <= D] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] evalSimpleMultiplestart ~> evalSimpleMultipleentryin [] evalSimpleMultipleentryin ~> evalSimpleMultiplebb3in [K ~=> A,K ~=> B] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [] evalSimpleMultiplebb3in ~> evalSimpleMultiplereturnin [] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A ~+> A,K ~+> A] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [B ~+> B,K ~+> B] evalSimpleMultiplereturnin ~> evalSimpleMultiplestop [] evalSimpleMultiplereturnin ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,K ~+> 0.0] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [] evalSimpleMultiplebb1in ~> evalSimpleMultiplebb3in [A ~+> A,K ~+> A] evalSimpleMultiplebbin ~> evalSimpleMultiplebb1in [] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [B ~+> B,K ~+> B] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~*> 0.0.0] evalSimpleMultiplebb3in ~> evalSimpleMultiplebbin [] evalSimpleMultiplebb2in ~> evalSimpleMultiplebb3in [B ~+> B,K ~+> B] evalSimpleMultiplebbin ~> evalSimpleMultiplebb2in [] + Applied Processor: LareProcessor + Details: evalSimpleMultiplestart ~> exitus616 [K ~=> A ,K ~=> B ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> B ,C ~*> 0.0.0 ,C ~*> tick ,D ~*> A ,D ~*> B ,D ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,D ~^> B ,K ~^> B] evalSimpleMultiplestart ~> evalSimpleMultiplestop [K ~=> A ,K ~=> B ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,C ~*> B ,C ~*> 0.0.0 ,C ~*> tick ,D ~*> A ,D ~*> B ,D ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,D ~^> B ,K ~^> B] + evalSimpleMultiplebb3in> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> tick ,B ~*> B ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> B ,C ~*> 0.0.0 ,C ~*> tick ,D ~*> A ,D ~*> B ,D ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,D ~^> B ,K ~^> B] + evalSimpleMultiplebbin> [B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,C ~*> B ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] evalSimpleMultiplebb3in> [B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,B ~*> B ,C ~*> B ,K ~*> B ,K ~*> 0.0.0 ,K ~*> tick] YES(?,POLY)