YES(?,POLY) * Step 1: FromIts 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) [B >= 1 + A] (?,1) 3. evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= B] (?,1) 4. evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] (?,1) 5. evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] (?,1) 6. evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True (?,1) 7. evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True (?,1) 8. evalfreturnin(A,B,C) -> evalfstop(A,B,C) True (?,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: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [B >= 1 + A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True evalfreturnin(A,B,C) -> evalfstop(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3)} Rule 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: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [B >= 1 + A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True evalfreturnin(A,B,C) -> evalfstop(A,B,C) True evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,6,4] c: [2,5,7] | `- p:[4,6] c: [4,6] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalfstart(A,B,C) -> evalfentryin(A,B,C) True evalfentryin(A,B,C) -> evalfbb4in(0,B,C) True evalfbb4in(A,B,C) -> evalfbb2in(A,B,0) [B >= 1 + A] evalfbb4in(A,B,C) -> evalfreturnin(A,B,C) [A >= B] evalfbb2in(A,B,C) -> evalfbb1in(A,B,C) [A >= C] evalfbb2in(A,B,C) -> evalfbb3in(A,B,C) [C >= 1 + A] evalfbb1in(A,B,C) -> evalfbb2in(A,B,1 + C) True evalfbb3in(A,B,C) -> evalfbb4in(1 + A,B,C) True evalfreturnin(A,B,C) -> evalfstop(A,B,C) True evalfstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalfbb1in,3) ;(evalfbb2in,3) ;(evalfbb3in,3) ;(evalfbb4in,3) ;(evalfentryin,3) ;(evalfreturnin,3) ;(evalfstart,3) ;(evalfstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},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: [2,5,7] | `- p:[4,6] c: [4,6]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow 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 <= K + C] evalfbb3in ~> evalfbb4in [A <= K + A, B <= B, C <= C] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C] evalfstop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B] evalfbb4in ~> evalfbb2in [A <= A, B <= B, C <= 0*K] evalfbb3in ~> evalfbb4in [A <= K + A, B <= B, C <= C] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= K + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= K + A + C] evalfbb2in ~> evalfbb1in [A <= A, B <= B, C <= C] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= K + C] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare 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 [C ~+> C,K ~+> C] evalfbb3in ~> evalfbb4in [A ~+> A,K ~+> A] evalfreturnin ~> evalfstop [] evalfstop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] evalfbb4in ~> evalfbb2in [K ~=> C] evalfbb3in ~> evalfbb4in [A ~+> A,K ~+> A] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [C ~+> C,K ~+> C] evalfbb2in ~> evalfbb1in [] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalfbb2in ~> evalfbb1in [] evalfbb1in ~> evalfbb2in [C ~+> C,K ~+> C] + Applied Processor: Lare + Details: evalfstart ~> exitus616 [K ~=> A ,K ~=> C ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,B ~^> C ,K ~^> C] + evalfbb4in> [K ~=> C ,A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> 0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> C ,B ~^> C ,K ~^> C] + evalfbb2in> [A ~+> 0.0.0 ,A ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> C ,C ~*> C ,K ~*> C] YES(?,POLY)