YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) True (?,1) 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) True (?,1) 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},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. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (1,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [0 >= A] (1,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) True (?,1) 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) True (?,1) 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) True (1,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) True (?,1) 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) True (?,1) 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) True (?,1) 9. evalwhile2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{4,5},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:[2,7,5,6,4] c: [2] | `- p:[4,6] c: [4] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) True (?,1) 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) True (?,1) 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) True (?,1) 9. evalwhile2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{4,5},7->{2,3},8->{},9->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,6,4] c: [2] | `- p:[4,6] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalwhile2start ~> evalwhile2entryin [A <= A, B <= B, C <= C] evalwhile2entryin ~> evalwhile2bb4in [A <= B, B <= B, C <= C] evalwhile2bb4in ~> evalwhile2bb2in [A <= A, B <= B, C <= B] evalwhile2bb4in ~> evalwhile2returnin [A <= A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb3in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [A <= A, B <= B, C <= K + C] evalwhile2bb3in ~> evalwhile2bb4in [A <= K + A, B <= B, C <= C] evalwhile2returnin ~> evalwhile2stop [A <= A, B <= B, C <= C] evalwhile2returnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A] evalwhile2bb4in ~> evalwhile2bb2in [A <= A, B <= B, C <= B] evalwhile2bb3in ~> evalwhile2bb4in [A <= K + A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb3in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [A <= A, B <= B, C <= K + C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= 2*K + C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [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] evalwhile2start ~> evalwhile2entryin [] evalwhile2entryin ~> evalwhile2bb4in [B ~=> A] evalwhile2bb4in ~> evalwhile2bb2in [B ~=> C] evalwhile2bb4in ~> evalwhile2returnin [] evalwhile2bb2in ~> evalwhile2bb1in [] evalwhile2bb2in ~> evalwhile2bb3in [] evalwhile2bb1in ~> evalwhile2bb2in [C ~+> C,K ~+> C] evalwhile2bb3in ~> evalwhile2bb4in [A ~+> A,K ~+> A] evalwhile2returnin ~> evalwhile2stop [] evalwhile2returnin ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] evalwhile2bb4in ~> evalwhile2bb2in [B ~=> C] evalwhile2bb3in ~> evalwhile2bb4in [A ~+> A,K ~+> A] evalwhile2bb2in ~> evalwhile2bb3in [] evalwhile2bb1in ~> evalwhile2bb2in [C ~+> C,K ~+> C] evalwhile2bb2in ~> evalwhile2bb1in [] + Loop: [C ~+> 0.0.0,K ~*> 0.0.0] evalwhile2bb2in ~> evalwhile2bb1in [] evalwhile2bb1in ~> evalwhile2bb2in [C ~+> C,K ~+> C] + Applied Processor: LareProcessor + Details: evalwhile2start ~> exitus616 [B ~=> A ,B ~=> C ,B ~+> A ,B ~+> C ,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 ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,K ~^> C] evalwhile2start ~> evalwhile2stop [B ~=> A ,B ~=> C ,B ~+> A ,B ~+> C ,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 ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,K ~^> C] + evalwhile2bb4in> [B ~=> C ,A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> C ,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 ~*> tick ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C ,K ~^> C] + evalwhile2bb2in> [C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,C ~*> C ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick] YES(?,POLY)