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(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True (1,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (1,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 3: 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(0,B,C) True (1,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (1,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C) -> evalfentryin(A,B,C) True (1,1) 1. evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 5: 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(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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},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 6: 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(0,B,C) True (?,1) 2. evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= 0 && A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && A >= C] 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 0 (?,1) && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1 + A] 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && A + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) [-1 + C >= 0 (?,1) && -2 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) [A + -1*B >= 0 && A >= 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},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 7: 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 <= 0*K, B <= B, C <= C] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= 0*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] evalfbb3in ~> evalfbb4in [A <= C, B <= B, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= 0*K] evalfbb3in ~> evalfbb4in [A <= C, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= B + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= B] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb4in [K ~=> A] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb4in ~> evalfreturnin [] evalfbb2in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~=> C] evalfbb3in ~> evalfbb4in [C ~=> A] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb3in ~> evalfbb4in [C ~=> A] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~=> C] evalfbb2in ~> evalfbb1in [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0] evalfbb2in ~> evalfbb1in [] evalfbb1in ~> evalfbb2in [B ~=> C] + Applied Processor: LareProcessor + Details: evalfstart ~> exitus616 [B ~=> A ,B ~=> C ,K ~=> A ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] evalfstart ~> evalfstop [B ~=> A ,B ~=> C ,K ~=> A ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] + evalfbb4in> [B ~=> A ,B ~=> C ,K ~=> A ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] + evalfbb2in> [B ~=> C,B ~+> 0.0.0,B ~+> tick,C ~+> 0.0.0,C ~+> tick,tick ~+> tick] YES(?,POLY)