YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalcomplexstart(A,B,C,D,E) -> evalcomplexentryin(A,B,C,D,E) True (1,1) 1. evalcomplexentryin(A,B,C,D,E) -> evalcomplexbb10in(B,A,C,D,E) True (?,1) 2. evalcomplexbb10in(A,B,C,D,E) -> evalcomplexreturnin(A,B,C,D,E) [B >= 30] (?,1) 3. evalcomplexbb10in(A,B,C,D,E) -> evalcomplexbb8in(A,B,A,B,E) [29 >= B] (?,1) 4. evalcomplexreturnin(A,B,C,D,E) -> evalcomplexstop(A,B,C,D,E) [-30 + B >= 0] (?,1) 5. evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb9in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= D] (?,1) 6. evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb1in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && D >= 1 + C] (?,1) 7. evalcomplexbb9in(A,B,C,D,E) -> evalcomplexbb10in(-10 + C,2 + D,C,D,E) [C + -1*D >= 0 && -1*B + D >= 0 && -1*B + C >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] (?,1) 8. evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,2 + C) [-1 + -1*C + D >= 0 (?,1) && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && 5 >= C && 7 >= C] 9. evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,7 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= 6] (?,1) 10. evalcomplexbb7in(A,B,C,D,E) -> evalcomplexbb8in(A,B,E,1 + D,E) [6 + D + -1*E >= 0 (?,1) && 7 + C + -1*E >= 0 && -2 + -1*C + E >= 0 && -2 + -1*A + E >= 0 && -1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] Signature: {(evalcomplexbb10in,5) ;(evalcomplexbb1in,5) ;(evalcomplexbb7in,5) ;(evalcomplexbb8in,5) ;(evalcomplexbb9in,5) ;(evalcomplexentryin,5) ;(evalcomplexreturnin,5) ;(evalcomplexstart,5) ;(evalcomplexstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{},5->{7},6->{8,9},7->{2,3},8->{10},9->{10},10->{5,6}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalcomplexstart(A,B,C,D,E) -> evalcomplexentryin(A,B,C,D,E) True evalcomplexentryin(A,B,C,D,E) -> evalcomplexbb10in(B,A,C,D,E) True evalcomplexbb10in(A,B,C,D,E) -> evalcomplexreturnin(A,B,C,D,E) [B >= 30] evalcomplexbb10in(A,B,C,D,E) -> evalcomplexbb8in(A,B,A,B,E) [29 >= B] evalcomplexreturnin(A,B,C,D,E) -> evalcomplexstop(A,B,C,D,E) [-30 + B >= 0] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb9in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= D] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb1in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && D >= 1 + C] evalcomplexbb9in(A,B,C,D,E) -> evalcomplexbb10in(-10 + C,2 + D,C,D,E) [C + -1*D >= 0 && -1*B + D >= 0 && -1*B + C >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,2 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && 5 >= C && 7 >= C] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,7 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= 6] evalcomplexbb7in(A,B,C,D,E) -> evalcomplexbb8in(A,B,E,1 + D,E) [6 + D + -1*E >= 0 && 7 + C + -1*E >= 0 && -2 + -1*C + E >= 0 && -2 + -1*A + E >= 0 && -1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] Signature: {(evalcomplexbb10in,5) ;(evalcomplexbb1in,5) ;(evalcomplexbb7in,5) ;(evalcomplexbb8in,5) ;(evalcomplexbb9in,5) ;(evalcomplexentryin,5) ;(evalcomplexreturnin,5) ;(evalcomplexstart,5) ;(evalcomplexstop,5)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{},5->{7},6->{8,9},7->{2,3},8->{10},9->{10},10->{5,6}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalcomplexstart(A,B,C,D,E) -> evalcomplexentryin(A,B,C,D,E) True evalcomplexentryin(A,B,C,D,E) -> evalcomplexbb10in(B,A,C,D,E) True evalcomplexbb10in(A,B,C,D,E) -> evalcomplexreturnin(A,B,C,D,E) [B >= 30] evalcomplexbb10in(A,B,C,D,E) -> evalcomplexbb8in(A,B,A,B,E) [29 >= B] evalcomplexreturnin(A,B,C,D,E) -> evalcomplexstop(A,B,C,D,E) [-30 + B >= 0] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb9in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= D] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb1in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && D >= 1 + C] evalcomplexbb9in(A,B,C,D,E) -> evalcomplexbb10in(-10 + C,2 + D,C,D,E) [C + -1*D >= 0 && -1*B + D >= 0 && -1*B + C >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,2 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && 5 >= C && 7 >= C] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,7 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= 6] evalcomplexbb7in(A,B,C,D,E) -> evalcomplexbb8in(A,B,E,1 + D,E) [6 + D + -1*E >= 0 && 7 + C + -1*E >= 0 && -2 + -1*C + E >= 0 && -2 + -1*A + E >= 0 && -1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] evalcomplexstop(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(evalcomplexbb10in,5) ;(evalcomplexbb1in,5) ;(evalcomplexbb7in,5) ;(evalcomplexbb8in,5) ;(evalcomplexbb9in,5) ;(evalcomplexentryin,5) ;(evalcomplexreturnin,5) ;(evalcomplexstart,5) ;(evalcomplexstop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{11},5->{7},6->{8,9},7->{2,3},8->{10},9->{10},10->{5,6}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[3,7,5,10,8,6,9] c: [3,5,6,7,8,9,10] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalcomplexstart(A,B,C,D,E) -> evalcomplexentryin(A,B,C,D,E) True evalcomplexentryin(A,B,C,D,E) -> evalcomplexbb10in(B,A,C,D,E) True evalcomplexbb10in(A,B,C,D,E) -> evalcomplexreturnin(A,B,C,D,E) [B >= 30] evalcomplexbb10in(A,B,C,D,E) -> evalcomplexbb8in(A,B,A,B,E) [29 >= B] evalcomplexreturnin(A,B,C,D,E) -> evalcomplexstop(A,B,C,D,E) [-30 + B >= 0] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb9in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= D] evalcomplexbb8in(A,B,C,D,E) -> evalcomplexbb1in(A,B,C,D,E) [-1*B + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && D >= 1 + C] evalcomplexbb9in(A,B,C,D,E) -> evalcomplexbb10in(-10 + C,2 + D,C,D,E) [C + -1*D >= 0 && -1*B + D >= 0 && -1*B + C >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,2 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && 5 >= C && 7 >= C] evalcomplexbb1in(A,B,C,D,E) -> evalcomplexbb7in(A,B,C,D,7 + C) [-1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0 && C >= 6] evalcomplexbb7in(A,B,C,D,E) -> evalcomplexbb8in(A,B,E,1 + D,E) [6 + D + -1*E >= 0 && 7 + C + -1*E >= 0 && -2 + -1*C + E >= 0 && -2 + -1*A + E >= 0 && -1 + -1*C + D >= 0 && -1*B + D >= 0 && -1 + -1*A + D >= 0 && -1*A + C >= 0 && 29 + -1*B >= 0] evalcomplexstop(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(evalcomplexbb10in,5) ;(evalcomplexbb1in,5) ;(evalcomplexbb7in,5) ;(evalcomplexbb8in,5) ;(evalcomplexbb9in,5) ;(evalcomplexentryin,5) ;(evalcomplexreturnin,5) ;(evalcomplexstart,5) ;(evalcomplexstop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{5,6},4->{11},5->{7},6->{8,9},7->{2,3},8->{10},9->{10},10->{5,6}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[3,7,5,10,8,6,9] c: [3,5,6,7,8,9,10]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0] evalcomplexstart ~> evalcomplexentryin [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexentryin ~> evalcomplexbb10in [A <= B, B <= A, C <= C, D <= D, E <= E] evalcomplexbb10in ~> evalcomplexreturnin [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb10in ~> evalcomplexbb8in [A <= A, B <= B, C <= A, D <= B, E <= E] evalcomplexreturnin ~> evalcomplexstop [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb8in ~> evalcomplexbb9in [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb8in ~> evalcomplexbb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb9in ~> evalcomplexbb10in [A <= 10*K + C, B <= 2*K + D, C <= C, D <= D, E <= E] evalcomplexbb1in ~> evalcomplexbb7in [A <= A, B <= B, C <= C, D <= D, E <= 2*K + C] evalcomplexbb1in ~> evalcomplexbb7in [A <= A, B <= B, C <= C, D <= D, E <= C + D] evalcomplexbb7in ~> evalcomplexbb8in [A <= A, B <= B, C <= E, D <= K + D, E <= E] evalcomplexstop ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= 178*K + A + 5*B] evalcomplexbb10in ~> evalcomplexbb8in [A <= A, B <= B, C <= A, D <= B, E <= E] evalcomplexbb9in ~> evalcomplexbb10in [A <= 10*K + C, B <= 2*K + D, C <= C, D <= D, E <= E] evalcomplexbb8in ~> evalcomplexbb9in [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb7in ~> evalcomplexbb8in [A <= A, B <= B, C <= E, D <= K + D, E <= E] evalcomplexbb1in ~> evalcomplexbb7in [A <= A, B <= B, C <= C, D <= D, E <= 2*K + C] evalcomplexbb8in ~> evalcomplexbb1in [A <= A, B <= B, C <= C, D <= D, E <= E] evalcomplexbb1in ~> evalcomplexbb7in [A <= A, B <= B, C <= C, D <= D, E <= C + D] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0] evalcomplexstart ~> evalcomplexentryin [] evalcomplexentryin ~> evalcomplexbb10in [A ~=> B,B ~=> A] evalcomplexbb10in ~> evalcomplexreturnin [] evalcomplexbb10in ~> evalcomplexbb8in [A ~=> C,B ~=> D] evalcomplexreturnin ~> evalcomplexstop [] evalcomplexbb8in ~> evalcomplexbb9in [] evalcomplexbb8in ~> evalcomplexbb1in [] evalcomplexbb9in ~> evalcomplexbb10in [C ~+> A,D ~+> B,K ~*> A,K ~*> B] evalcomplexbb1in ~> evalcomplexbb7in [C ~+> E,K ~*> E] evalcomplexbb1in ~> evalcomplexbb7in [C ~+> E,D ~+> E] evalcomplexbb7in ~> evalcomplexbb8in [E ~=> C,D ~+> D,K ~+> D] evalcomplexstop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~*> 0.0,K ~*> 0.0] evalcomplexbb10in ~> evalcomplexbb8in [A ~=> C,B ~=> D] evalcomplexbb9in ~> evalcomplexbb10in [C ~+> A,D ~+> B,K ~*> A,K ~*> B] evalcomplexbb8in ~> evalcomplexbb9in [] evalcomplexbb7in ~> evalcomplexbb8in [E ~=> C,D ~+> D,K ~+> D] evalcomplexbb1in ~> evalcomplexbb7in [C ~+> E,K ~*> E] evalcomplexbb8in ~> evalcomplexbb1in [] evalcomplexbb1in ~> evalcomplexbb7in [C ~+> E,D ~+> E] + Applied Processor: Lare + Details: evalcomplexstart ~> exitus616 [A ~=> B ,A ~=> D ,B ~=> A ,B ~=> C ,A ~+> A ,A ~+> B ,A ~+> C ,A ~+> D ,A ~+> E ,B ~+> A ,B ~+> C ,B ~+> E ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> C ,C ~+> E ,D ~+> A ,D ~+> B ,D ~+> C ,D ~+> D ,D ~+> E ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> E ,A ~*> A ,A ~*> B ,A ~*> C ,A ~*> D ,A ~*> E ,A ~*> 0.0 ,A ~*> tick ,B ~*> A ,B ~*> B ,B ~*> C ,B ~*> D ,B ~*> E ,D ~*> A ,D ~*> C ,D ~*> E ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> E ,K ~*> 0.0 ,K ~*> tick] + evalcomplexbb10in> [A ~=> C ,B ~=> D ,A ~+> A ,A ~+> C ,A ~+> E ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> B ,B ~+> C ,B ~+> D ,B ~+> E ,C ~+> A ,C ~+> C ,C ~+> E ,D ~+> A ,D ~+> B ,D ~+> C ,D ~+> D ,D ~+> E ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> E ,A ~*> A ,A ~*> B ,A ~*> C ,A ~*> D ,A ~*> E ,B ~*> A ,B ~*> B ,B ~*> C ,B ~*> D ,B ~*> E ,B ~*> 0.0 ,B ~*> tick ,D ~*> A ,D ~*> C ,D ~*> E ,K ~*> A ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> E ,K ~*> 0.0 ,K ~*> tick] YES(?,POLY)