YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalEx6start(A,B,C) -> evalEx6entryin(A,B,C) True (1,1) 1. evalEx6entryin(A,B,C) -> evalEx6bb3in(B,A,C) True (?,1) 2. evalEx6bb3in(A,B,C) -> evalEx6bbin(A,B,C) [C >= 1 + B] (?,1) 3. evalEx6bb3in(A,B,C) -> evalEx6returnin(A,B,C) [B >= C] (?,1) 4. evalEx6bbin(A,B,C) -> evalEx6bb1in(A,B,C) [-1 + -1*B + C >= 0 && A >= 1 + B] (?,1) 5. evalEx6bbin(A,B,C) -> evalEx6bb2in(A,B,C) [-1 + -1*B + C >= 0 && B >= A] (?,1) 6. evalEx6bb1in(A,B,C) -> evalEx6bb3in(A,1 + B,C) [-1 + -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 7. evalEx6bb2in(A,B,C) -> evalEx6bb3in(1 + A,B,C) [-1 + -1*B + C >= 0 && -1 + -1*A + C >= 0 && -1*A + B >= 0] (?,1) 8. evalEx6returnin(A,B,C) -> evalEx6stop(A,B,C) [B + -1*C >= 0] (?,1) Signature: {(evalEx6bb1in,3) ;(evalEx6bb2in,3) ;(evalEx6bb3in,3) ;(evalEx6bbin,3) ;(evalEx6entryin,3) ;(evalEx6returnin,3) ;(evalEx6start,3) ;(evalEx6stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2,3},8->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,3)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalEx6start(A,B,C) -> evalEx6entryin(A,B,C) True (1,1) 1. evalEx6entryin(A,B,C) -> evalEx6bb3in(B,A,C) True (?,1) 2. evalEx6bb3in(A,B,C) -> evalEx6bbin(A,B,C) [C >= 1 + B] (?,1) 3. evalEx6bb3in(A,B,C) -> evalEx6returnin(A,B,C) [B >= C] (?,1) 4. evalEx6bbin(A,B,C) -> evalEx6bb1in(A,B,C) [-1 + -1*B + C >= 0 && A >= 1 + B] (?,1) 5. evalEx6bbin(A,B,C) -> evalEx6bb2in(A,B,C) [-1 + -1*B + C >= 0 && B >= A] (?,1) 6. evalEx6bb1in(A,B,C) -> evalEx6bb3in(A,1 + B,C) [-1 + -1*B + C >= 0 && -1 + A + -1*B >= 0] (?,1) 7. evalEx6bb2in(A,B,C) -> evalEx6bb3in(1 + A,B,C) [-1 + -1*B + C >= 0 && -1 + -1*A + C >= 0 && -1*A + B >= 0] (?,1) 8. evalEx6returnin(A,B,C) -> evalEx6stop(A,B,C) [B + -1*C >= 0] (?,1) Signature: {(evalEx6bb1in,3) ;(evalEx6bb2in,3) ;(evalEx6bb3in,3) ;(evalEx6bbin,3) ;(evalEx6entryin,3) ;(evalEx6returnin,3) ;(evalEx6start,3) ;(evalEx6stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2},8->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalEx6start(A,B,C) -> evalEx6entryin(A,B,C) True evalEx6entryin(A,B,C) -> evalEx6bb3in(B,A,C) True evalEx6bb3in(A,B,C) -> evalEx6bbin(A,B,C) [C >= 1 + B] evalEx6bb3in(A,B,C) -> evalEx6returnin(A,B,C) [B >= C] evalEx6bbin(A,B,C) -> evalEx6bb1in(A,B,C) [-1 + -1*B + C >= 0 && A >= 1 + B] evalEx6bbin(A,B,C) -> evalEx6bb2in(A,B,C) [-1 + -1*B + C >= 0 && B >= A] evalEx6bb1in(A,B,C) -> evalEx6bb3in(A,1 + B,C) [-1 + -1*B + C >= 0 && -1 + A + -1*B >= 0] evalEx6bb2in(A,B,C) -> evalEx6bb3in(1 + A,B,C) [-1 + -1*B + C >= 0 && -1 + -1*A + C >= 0 && -1*A + B >= 0] evalEx6returnin(A,B,C) -> evalEx6stop(A,B,C) [B + -1*C >= 0] Signature: {(evalEx6bb1in,3) ;(evalEx6bb2in,3) ;(evalEx6bb3in,3) ;(evalEx6bbin,3) ;(evalEx6entryin,3) ;(evalEx6returnin,3) ;(evalEx6start,3) ;(evalEx6stop,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: evalEx6start(A,B,C) -> evalEx6entryin(A,B,C) True evalEx6entryin(A,B,C) -> evalEx6bb3in(B,A,C) True evalEx6bb3in(A,B,C) -> evalEx6bbin(A,B,C) [C >= 1 + B] evalEx6bb3in(A,B,C) -> evalEx6returnin(A,B,C) [B >= C] evalEx6bbin(A,B,C) -> evalEx6bb1in(A,B,C) [-1 + -1*B + C >= 0 && A >= 1 + B] evalEx6bbin(A,B,C) -> evalEx6bb2in(A,B,C) [-1 + -1*B + C >= 0 && B >= A] evalEx6bb1in(A,B,C) -> evalEx6bb3in(A,1 + B,C) [-1 + -1*B + C >= 0 && -1 + A + -1*B >= 0] evalEx6bb2in(A,B,C) -> evalEx6bb3in(1 + A,B,C) [-1 + -1*B + C >= 0 && -1 + -1*A + C >= 0 && -1*A + B >= 0] evalEx6returnin(A,B,C) -> evalEx6stop(A,B,C) [B + -1*C >= 0] evalEx6stop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalEx6bb1in,3) ;(evalEx6bb2in,3) ;(evalEx6bb3in,3) ;(evalEx6bbin,3) ;(evalEx6entryin,3) ;(evalEx6returnin,3) ;(evalEx6start,3) ;(evalEx6stop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2},8->{9}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: evalEx6start(A,B,C) -> evalEx6entryin(A,B,C) True evalEx6entryin(A,B,C) -> evalEx6bb3in(B,A,C) True evalEx6bb3in(A,B,C) -> evalEx6bbin(A,B,C) [C >= 1 + B] evalEx6bb3in(A,B,C) -> evalEx6returnin(A,B,C) [B >= C] evalEx6bbin(A,B,C) -> evalEx6bb1in(A,B,C) [-1 + -1*B + C >= 0 && A >= 1 + B] evalEx6bbin(A,B,C) -> evalEx6bb2in(A,B,C) [-1 + -1*B + C >= 0 && B >= A] evalEx6bb1in(A,B,C) -> evalEx6bb3in(A,1 + B,C) [-1 + -1*B + C >= 0 && -1 + A + -1*B >= 0] evalEx6bb2in(A,B,C) -> evalEx6bb3in(1 + A,B,C) [-1 + -1*B + C >= 0 && -1 + -1*A + C >= 0 && -1*A + B >= 0] evalEx6returnin(A,B,C) -> evalEx6stop(A,B,C) [B + -1*C >= 0] evalEx6stop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalEx6bb1in,3) ;(evalEx6bb2in,3) ;(evalEx6bb3in,3) ;(evalEx6bbin,3) ;(evalEx6entryin,3) ;(evalEx6returnin,3) ;(evalEx6start,3) ;(evalEx6stop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4,5},3->{8},4->{6},5->{7},6->{2,3},7->{2},8->{9}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,6,4,7,5] c: [2,4,5,6,7]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0] evalEx6start ~> evalEx6entryin [A <= A, B <= B, C <= C] evalEx6entryin ~> evalEx6bb3in [A <= B, B <= A, C <= C] evalEx6bb3in ~> evalEx6bbin [A <= A, B <= B, C <= C] evalEx6bb3in ~> evalEx6returnin [A <= A, B <= B, C <= C] evalEx6bbin ~> evalEx6bb1in [A <= A, B <= B, C <= C] evalEx6bbin ~> evalEx6bb2in [A <= A, B <= B, C <= C] evalEx6bb1in ~> evalEx6bb3in [A <= A, B <= K + B, C <= C] evalEx6bb2in ~> evalEx6bb3in [A <= A + C, B <= B, C <= C] evalEx6returnin ~> evalEx6stop [A <= A, B <= B, C <= C] evalEx6stop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B + C] evalEx6bb3in ~> evalEx6bbin [A <= A, B <= B, C <= C] evalEx6bb1in ~> evalEx6bb3in [A <= A, B <= K + B, C <= C] evalEx6bbin ~> evalEx6bb1in [A <= A, B <= B, C <= C] evalEx6bb2in ~> evalEx6bb3in [A <= A + C, B <= B, C <= C] evalEx6bbin ~> evalEx6bb2in [A <= A, B <= B, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] evalEx6start ~> evalEx6entryin [] evalEx6entryin ~> evalEx6bb3in [A ~=> B,B ~=> A] evalEx6bb3in ~> evalEx6bbin [] evalEx6bb3in ~> evalEx6returnin [] evalEx6bbin ~> evalEx6bb1in [] evalEx6bbin ~> evalEx6bb2in [] evalEx6bb1in ~> evalEx6bb3in [B ~+> B,K ~+> B] evalEx6bb2in ~> evalEx6bb3in [A ~+> A,C ~+> A] evalEx6returnin ~> evalEx6stop [] evalEx6stop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,K ~+> 0.0] evalEx6bb3in ~> evalEx6bbin [] evalEx6bb1in ~> evalEx6bb3in [B ~+> B,K ~+> B] evalEx6bbin ~> evalEx6bb1in [] evalEx6bb2in ~> evalEx6bb3in [A ~+> A,C ~+> A] evalEx6bbin ~> evalEx6bb2in [] + Applied Processor: Lare + Details: evalEx6start ~> exitus616 [A ~=> B ,B ~=> A ,A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> A ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B] + evalEx6bb3in> [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> A ,C ~+> 0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,C ~*> A ,C ~*> B ,K ~*> A ,K ~*> B] YES(?,O(n^1))