YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalNestedMultiplestart(A,B,C,D,E) -> evalNestedMultipleentryin(A,B,C,D,E) True (1,1) 1. evalNestedMultipleentryin(A,B,C,D,E) -> evalNestedMultiplebb5in(B,A,D,C,E) True (?,1) 2. evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,D) [A >= 1 + B] (?,1) 3. evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplereturnin(A,B,C,D,E) [B >= A] (?,1) 4. evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && E >= C] (?,1) 5. evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb3in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && C >= 1 + E] (?,1) 6. evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + F] (?,1) 7. evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && F >= 1] (?,1) 8. evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] (?,1) 9. evalNestedMultiplebb1in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,1 + E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] (?,1) 10. evalNestedMultiplebb4in(A,B,C,D,E) -> evalNestedMultiplebb5in(A,1 + B,C,E,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0] (?,1) 11. evalNestedMultiplereturnin(A,B,C,D,E) -> evalNestedMultiplestop(A,B,C,D,E) [-1*A + B >= 0] (?,1) Signature: {(evalNestedMultiplebb1in,5) ;(evalNestedMultiplebb2in,5) ;(evalNestedMultiplebb3in,5) ;(evalNestedMultiplebb4in,5) ;(evalNestedMultiplebb5in,5) ;(evalNestedMultipleentryin,5) ;(evalNestedMultiplereturnin,5) ;(evalNestedMultiplestart,5) ;(evalNestedMultiplestop,5)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalNestedMultiplestart(A,B,C,D,E) -> evalNestedMultipleentryin(A,B,C,D,E) True evalNestedMultipleentryin(A,B,C,D,E) -> evalNestedMultiplebb5in(B,A,D,C,E) True evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,D) [A >= 1 + B] evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplereturnin(A,B,C,D,E) [B >= A] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && E >= C] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb3in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && C >= 1 + E] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + F] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && F >= 1] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb1in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,1 + E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb4in(A,B,C,D,E) -> evalNestedMultiplebb5in(A,1 + B,C,E,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplereturnin(A,B,C,D,E) -> evalNestedMultiplestop(A,B,C,D,E) [-1*A + B >= 0] Signature: {(evalNestedMultiplebb1in,5) ;(evalNestedMultiplebb2in,5) ;(evalNestedMultiplebb3in,5) ;(evalNestedMultiplebb4in,5) ;(evalNestedMultiplebb5in,5) ;(evalNestedMultipleentryin,5) ;(evalNestedMultiplereturnin,5) ;(evalNestedMultiplestart,5) ;(evalNestedMultiplestop,5)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalNestedMultiplestart(A,B,C,D,E) -> evalNestedMultipleentryin(A,B,C,D,E) True evalNestedMultipleentryin(A,B,C,D,E) -> evalNestedMultiplebb5in(B,A,D,C,E) True evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,D) [A >= 1 + B] evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplereturnin(A,B,C,D,E) [B >= A] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && E >= C] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb3in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && C >= 1 + E] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + F] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && F >= 1] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb1in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,1 + E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb4in(A,B,C,D,E) -> evalNestedMultiplebb5in(A,1 + B,C,E,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplereturnin(A,B,C,D,E) -> evalNestedMultiplestop(A,B,C,D,E) [-1*A + B >= 0] evalNestedMultiplestop(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(evalNestedMultiplebb1in,5) ;(evalNestedMultiplebb2in,5) ;(evalNestedMultiplebb3in,5) ;(evalNestedMultiplebb4in,5) ;(evalNestedMultiplebb5in,5) ;(evalNestedMultipleentryin,5) ;(evalNestedMultiplereturnin,5) ;(evalNestedMultiplestart,5) ;(evalNestedMultiplestop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{12}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,10,4,9,6,5,7,8] c: [2,4,5,6,7,8,9,10] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalNestedMultiplestart(A,B,C,D,E) -> evalNestedMultipleentryin(A,B,C,D,E) True evalNestedMultipleentryin(A,B,C,D,E) -> evalNestedMultiplebb5in(B,A,D,C,E) True evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,D) [A >= 1 + B] evalNestedMultiplebb5in(A,B,C,D,E) -> evalNestedMultiplereturnin(A,B,C,D,E) [B >= A] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && E >= C] evalNestedMultiplebb2in(A,B,C,D,E) -> evalNestedMultiplebb3in(A,B,C,D,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0 && C >= 1 + E] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && 0 >= 1 + F] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb1in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0 && F >= 1] evalNestedMultiplebb3in(A,B,C,D,E) -> evalNestedMultiplebb4in(A,B,C,D,E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb1in(A,B,C,D,E) -> evalNestedMultiplebb2in(A,B,C,D,1 + E) [-1 + C + -1*E >= 0 && -1*D + E >= 0 && -1 + C + -1*D >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplebb4in(A,B,C,D,E) -> evalNestedMultiplebb5in(A,1 + B,C,E,E) [-1*D + E >= 0 && -1 + A + -1*B >= 0] evalNestedMultiplereturnin(A,B,C,D,E) -> evalNestedMultiplestop(A,B,C,D,E) [-1*A + B >= 0] evalNestedMultiplestop(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(evalNestedMultiplebb1in,5) ;(evalNestedMultiplebb2in,5) ;(evalNestedMultiplebb3in,5) ;(evalNestedMultiplebb4in,5) ;(evalNestedMultiplebb5in,5) ;(evalNestedMultipleentryin,5) ;(evalNestedMultiplereturnin,5) ;(evalNestedMultiplestart,5) ;(evalNestedMultiplestop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{11},4->{10},5->{6,7,8},6->{9},7->{9},8->{10},9->{4,5},10->{2,3},11->{12}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,10,4,9,6,5,7,8] c: [2,4,5,6,7,8,9,10]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0] evalNestedMultiplestart ~> evalNestedMultipleentryin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultipleentryin ~> evalNestedMultiplebb5in [A <= B, B <= A, C <= D, D <= C, E <= E] evalNestedMultiplebb5in ~> evalNestedMultiplebb2in [A <= A, B <= B, C <= C, D <= D, E <= D] evalNestedMultiplebb5in ~> evalNestedMultiplereturnin [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb2in ~> evalNestedMultiplebb4in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb2in ~> evalNestedMultiplebb3in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb3in ~> evalNestedMultiplebb4in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb1in ~> evalNestedMultiplebb2in [A <= A, B <= B, C <= C, D <= D, E <= C + E] evalNestedMultiplebb4in ~> evalNestedMultiplebb5in [A <= A, B <= A + B, C <= C, D <= E, E <= E] evalNestedMultiplereturnin ~> evalNestedMultiplestop [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplestop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= A + B + C + D] evalNestedMultiplebb5in ~> evalNestedMultiplebb2in [A <= A, B <= B, C <= C, D <= D, E <= D] evalNestedMultiplebb4in ~> evalNestedMultiplebb5in [A <= A, B <= A + B, C <= C, D <= E, E <= E] evalNestedMultiplebb2in ~> evalNestedMultiplebb4in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb1in ~> evalNestedMultiplebb2in [A <= A, B <= B, C <= C, D <= D, E <= C + E] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb2in ~> evalNestedMultiplebb3in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalNestedMultiplebb3in ~> evalNestedMultiplebb4in [A <= A, B <= B, C <= C, D <= D, E <= E] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0] evalNestedMultiplestart ~> evalNestedMultipleentryin [] evalNestedMultipleentryin ~> evalNestedMultiplebb5in [A ~=> B,B ~=> A,C ~=> D,D ~=> C] evalNestedMultiplebb5in ~> evalNestedMultiplebb2in [D ~=> E] evalNestedMultiplebb5in ~> evalNestedMultiplereturnin [] evalNestedMultiplebb2in ~> evalNestedMultiplebb4in [] evalNestedMultiplebb2in ~> evalNestedMultiplebb3in [] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [] evalNestedMultiplebb3in ~> evalNestedMultiplebb4in [] evalNestedMultiplebb1in ~> evalNestedMultiplebb2in [C ~+> E,E ~+> E] evalNestedMultiplebb4in ~> evalNestedMultiplebb5in [E ~=> D,A ~+> B,B ~+> B] evalNestedMultiplereturnin ~> evalNestedMultiplestop [] evalNestedMultiplestop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,D ~+> 0.0] evalNestedMultiplebb5in ~> evalNestedMultiplebb2in [D ~=> E] evalNestedMultiplebb4in ~> evalNestedMultiplebb5in [E ~=> D,A ~+> B,B ~+> B] evalNestedMultiplebb2in ~> evalNestedMultiplebb4in [] evalNestedMultiplebb1in ~> evalNestedMultiplebb2in [C ~+> E,E ~+> E] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [] evalNestedMultiplebb2in ~> evalNestedMultiplebb3in [] evalNestedMultiplebb3in ~> evalNestedMultiplebb1in [] evalNestedMultiplebb3in ~> evalNestedMultiplebb4in [] + Applied Processor: Lare + Details: evalNestedMultiplestart ~> exitus616 [A ~=> B ,B ~=> A ,C ~=> D ,C ~=> E ,D ~=> C ,E ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> D ,C ~+> E ,C ~+> 0.0 ,C ~+> tick ,D ~+> D ,D ~+> E ,D ~+> 0.0 ,D ~+> tick ,E ~+> D ,E ~+> E ,tick ~+> tick ,A ~*> B ,A ~*> D ,A ~*> E ,B ~*> B ,B ~*> D ,B ~*> E ,C ~*> B ,C ~*> D ,C ~*> E ,D ~*> B ,D ~*> D ,D ~*> E] + evalNestedMultiplebb5in> [D ~=> E ,E ~=> D ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> D ,C ~+> E ,C ~+> 0.0 ,C ~+> tick ,D ~+> D ,D ~+> E ,D ~+> 0.0 ,D ~+> tick ,E ~+> D ,E ~+> E ,tick ~+> tick ,A ~*> B ,A ~*> D ,A ~*> E ,B ~*> B ,B ~*> D ,B ~*> E ,C ~*> B ,C ~*> D ,C ~*> E ,D ~*> B ,D ~*> D ,D ~*> E] YES(?,O(n^1))