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