YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (1,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (1,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] (1,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] (?,1) 9. evalfreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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: [7] | `- p:[4,6] c: [6] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(B,A,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,1) [B >= 1] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [0 >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + B >= 0 && C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [A + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(A,-1 + B,C) [-1 + C >= 0 && -2 + B + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0] (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [-1*B >= 0] (?,1) 9. evalfreturnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,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: [7] | `- p:[4,6] c: [6]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C] evalfentryin ~> evalfbb4in [A <= B, B <= A, C <= C] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= K] evalfbb4in ~> evalfreturnin [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + C] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= B] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= K] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= K + A + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B + 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] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb4in [A ~=> B,B ~=> A] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb4in ~> evalfreturnin [] evalfbb2in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] evalfbb3in ~> evalfbb4in [] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [B ~=> 0.0] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb3in ~> evalfbb4in [] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] evalfbb2in ~> evalfbb1in [] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalfbb2in ~> evalfbb1in [] evalfbb1in ~> evalfbb2in [B ~+> C,C ~+> C] + Applied Processor: LareProcessor + Details: evalfstart ~> exitus616 [A ~=> B ,A ~=> 0.0 ,B ~=> A ,K ~=> C ,A ~+> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C] evalfstart ~> evalfstop [A ~=> B ,A ~=> 0.0 ,B ~=> A ,K ~=> C ,A ~+> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C] + evalfbb4in> [B ~=> 0.0 ,K ~=> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> C ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> C ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C] + evalfbb2in> [A ~+> 0.0.0 ,A ~+> tick ,B ~+> C ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,B ~*> C ,C ~*> C ,K ~*> C] YES(?,POLY)