YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalNestedMultipleDepstart(A,B,C,D,E) -> evalNestedMultipleDepentryin(A,B,C,D,E) True (1,1) 1. evalNestedMultipleDepentryin(A,B,C,D,E) -> evalNestedMultipleDepbb3in(0,B,C,D,E) True (?,1) 2. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepbbin(A,B,C,D,E) [A >= 0 && B >= 1 + A] (?,1) 3. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepreturnin(A,B,C,D,E) [A >= 0 && A >= B] (?,1) 4. evalNestedMultipleDepbbin(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,1 + A,0,E) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb1in(A,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && E >= 1 + D] 6. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb3in(C,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && D >= E] 7. evalNestedMultipleDepbb1in(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,C,1 + D,E) [-1 + E >= 0 (?,1) && -1 + D + E >= 0 && -1 + -1*D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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. evalNestedMultipleDepreturnin(A,B,C,D,E) -> evalNestedMultipleDepstop(A,B,C,D,E) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalNestedMultipleDepbb1in,5) ;(evalNestedMultipleDepbb2in,5) ;(evalNestedMultipleDepbb3in,5) ;(evalNestedMultipleDepbbin,5) ;(evalNestedMultipleDepentryin,5) ;(evalNestedMultipleDepreturnin,5) ;(evalNestedMultipleDepstart,5) ;(evalNestedMultipleDepstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{5,6},5->{7},6->{2,3},7->{5,6},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. evalNestedMultipleDepstart(A,B,C,D,E) -> evalNestedMultipleDepentryin(A,B,C,D,E) True (1,1) 1. evalNestedMultipleDepentryin(A,B,C,D,E) -> evalNestedMultipleDepbb3in(0,B,C,D,E) True (1,1) 2. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepbbin(A,B,C,D,E) [A >= 0 && B >= 1 + A] (?,1) 3. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepreturnin(A,B,C,D,E) [A >= 0 && A >= B] (1,1) 4. evalNestedMultipleDepbbin(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,1 + A,0,E) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb1in(A,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && E >= 1 + D] 6. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb3in(C,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && D >= E] 7. evalNestedMultipleDepbb1in(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,C,1 + D,E) [-1 + E >= 0 (?,1) && -1 + D + E >= 0 && -1 + -1*D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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. evalNestedMultipleDepreturnin(A,B,C,D,E) -> evalNestedMultipleDepstop(A,B,C,D,E) [A + -1*B >= 0 && A >= 0] (1,1) Signature: {(evalNestedMultipleDepbb1in,5) ;(evalNestedMultipleDepbb2in,5) ;(evalNestedMultipleDepbb3in,5) ;(evalNestedMultipleDepbbin,5) ;(evalNestedMultipleDepentryin,5) ;(evalNestedMultipleDepreturnin,5) ;(evalNestedMultipleDepstart,5) ;(evalNestedMultipleDepstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{5,6},5->{7},6->{2,3},7->{5,6},8->{}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalNestedMultipleDepstart(A,B,C,D,E) -> evalNestedMultipleDepentryin(A,B,C,D,E) True (1,1) 1. evalNestedMultipleDepentryin(A,B,C,D,E) -> evalNestedMultipleDepbb3in(0,B,C,D,E) True (?,1) 2. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepbbin(A,B,C,D,E) [A >= 0 && B >= 1 + A] (?,1) 3. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepreturnin(A,B,C,D,E) [A >= 0 && A >= B] (?,1) 4. evalNestedMultipleDepbbin(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,1 + A,0,E) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb1in(A,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && E >= 1 + D] 6. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb3in(C,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && D >= E] 7. evalNestedMultipleDepbb1in(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,C,1 + D,E) [-1 + E >= 0 (?,1) && -1 + D + E >= 0 && -1 + -1*D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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. evalNestedMultipleDepreturnin(A,B,C,D,E) -> evalNestedMultipleDepstop(A,B,C,D,E) [A + -1*B >= 0 && A >= 0] (?,1) 9. evalNestedMultipleDepreturnin(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(evalNestedMultipleDepbb1in,5) ;(evalNestedMultipleDepbb2in,5) ;(evalNestedMultipleDepbb3in,5) ;(evalNestedMultipleDepbbin,5) ;(evalNestedMultipleDepentryin,5) ;(evalNestedMultipleDepreturnin,5) ;(evalNestedMultipleDepstart,5) ;(evalNestedMultipleDepstop,5) ;(exitus616,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8,9},4->{5,6},5->{7},6->{2,3},7->{5,6},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: [6] | `- p:[5,7] c: [7] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalNestedMultipleDepstart(A,B,C,D,E) -> evalNestedMultipleDepentryin(A,B,C,D,E) True (1,1) 1. evalNestedMultipleDepentryin(A,B,C,D,E) -> evalNestedMultipleDepbb3in(0,B,C,D,E) True (?,1) 2. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepbbin(A,B,C,D,E) [A >= 0 && B >= 1 + A] (?,1) 3. evalNestedMultipleDepbb3in(A,B,C,D,E) -> evalNestedMultipleDepreturnin(A,B,C,D,E) [A >= 0 && A >= B] (?,1) 4. evalNestedMultipleDepbbin(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,1 + A,0,E) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb1in(A,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && E >= 1 + D] 6. evalNestedMultipleDepbb2in(A,B,C,D,E) -> evalNestedMultipleDepbb3in(C,B,C,D,E) [D >= 0 (?,1) && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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 && D >= E] 7. evalNestedMultipleDepbb1in(A,B,C,D,E) -> evalNestedMultipleDepbb2in(A,B,C,1 + D,E) [-1 + E >= 0 (?,1) && -1 + D + E >= 0 && -1 + -1*D + E >= 0 && -2 + C + E >= 0 && -2 + B + E >= 0 && -1 + A + E >= 0 && D >= 0 && -1 + C + D >= 0 && -1 + B + D >= 0 && A + D >= 0 && B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -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. evalNestedMultipleDepreturnin(A,B,C,D,E) -> evalNestedMultipleDepstop(A,B,C,D,E) [A + -1*B >= 0 && A >= 0] (?,1) 9. evalNestedMultipleDepreturnin(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(evalNestedMultipleDepbb1in,5) ;(evalNestedMultipleDepbb2in,5) ;(evalNestedMultipleDepbb3in,5) ;(evalNestedMultipleDepbbin,5) ;(evalNestedMultipleDepentryin,5) ;(evalNestedMultipleDepreturnin,5) ;(evalNestedMultipleDepstart,5) ;(evalNestedMultipleDepstop,5) ;(exitus616,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8,9},4->{5,6},5->{7},6->{2,3},7->{5,6},8->{},9->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [6] | `- p:[5,7] c: [7]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.0.0] evalNestedMultipleDepstart ~> evalNestedMultipleDepentryin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepentryin ~> evalNestedMultipleDepbb3in [A <= 0*K, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepbbin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepreturnin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbbin ~> evalNestedMultipleDepbb2in [A <= A, B <= B, C <= B, D <= 0*K, E <= E] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb3in [A <= C, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [A <= A, B <= B, C <= C, D <= E, E <= E] evalNestedMultipleDepreturnin ~> evalNestedMultipleDepstop [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepreturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= K + A + B + C] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepbbin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb3in [A <= C, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbbin ~> evalNestedMultipleDepbb2in [A <= A, B <= B, C <= B, D <= 0*K, E <= E] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [A <= A, B <= B, C <= C, D <= E, E <= E] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0.0 <= D + E] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [A <= A, B <= B, C <= C, D <= E, E <= E] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0,0.0.0] evalNestedMultipleDepstart ~> evalNestedMultipleDepentryin [] evalNestedMultipleDepentryin ~> evalNestedMultipleDepbb3in [K ~=> A] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepbbin [] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepreturnin [] evalNestedMultipleDepbbin ~> evalNestedMultipleDepbb2in [B ~=> C,K ~=> D] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb3in [C ~=> A] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [E ~=> D] evalNestedMultipleDepreturnin ~> evalNestedMultipleDepstop [] evalNestedMultipleDepreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~+> 0.0] evalNestedMultipleDepbb3in ~> evalNestedMultipleDepbbin [] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb3in [C ~=> A] evalNestedMultipleDepbbin ~> evalNestedMultipleDepbb2in [B ~=> C,K ~=> D] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [E ~=> D] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [] + Loop: [D ~+> 0.0.0,E ~+> 0.0.0] evalNestedMultipleDepbb2in ~> evalNestedMultipleDepbb1in [] evalNestedMultipleDepbb1in ~> evalNestedMultipleDepbb2in [E ~=> D] + Applied Processor: LareProcessor + Details: evalNestedMultipleDepstart ~> exitus616 [B ~=> A ,B ~=> C ,E ~=> D ,K ~=> A ,K ~=> D ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> tick ,C ~*> tick ,E ~*> 0.0.0 ,E ~*> tick ,K ~*> 0.0 ,K ~*> tick] evalNestedMultipleDepstart ~> evalNestedMultipleDepstop [B ~=> A ,B ~=> C ,E ~=> D ,K ~=> A ,K ~=> D ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> tick ,C ~*> tick ,E ~*> 0.0.0 ,E ~*> tick ,K ~*> 0.0 ,K ~*> tick] + evalNestedMultipleDepbb3in> [B ~=> A ,B ~=> C ,E ~=> D ,K ~=> D ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0 ,C ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,C ~*> tick ,E ~*> 0.0.0 ,E ~*> tick ,K ~*> tick] + evalNestedMultipleDepbb2in> [E ~=> D ,D ~+> 0.0.0 ,D ~+> tick ,E ~+> 0.0.0 ,E ~+> tick ,tick ~+> tick] YES(?,POLY)