YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (?,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [A >= 0 && B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [A >= 0 && 1 + A >= B] (?,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) [-2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [-1 + C >= 0 (?,1) && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [-1 + C >= 0 (?,1) && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && C >= B] 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && D >= 1 + E] 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= D] 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) [-2 + C >= 0 (?,1) && -4 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && -2 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) [1 + A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5,6},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,6)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True (1,1) 1. evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True (?,1) 2. evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [A >= 0 && B >= 2 + A] (?,1) 3. evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [A >= 0 && 1 + A >= B] (?,1) 4. evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) [-2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [-1 + C >= 0 (?,1) && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] 6. evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [-1 + C >= 0 (?,1) && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && C >= B] 7. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && D >= 1 + E] 8. evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 (?,1) && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= D] 9. evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) [-2 + C >= 0 (?,1) && -4 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && -2 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) [1 + A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [A >= 0 && B >= 2 + A] evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [A >= 0 && 1 + A >= B] evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) [-2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && C >= B] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && D >= 1 + E] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= D] evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) [-2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && -2 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) [1 + A + -1*B >= 0 && A >= 0] Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [A >= 0 && B >= 2 + A] evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [A >= 0 && 1 + A >= B] evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) [-2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && C >= B] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && D >= 1 + E] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= D] evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) [-2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && -2 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) [1 + A + -1*B >= 0 && A >= 0] evalrealselectstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{11}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,9,6,7,5,4,8] c: [2,4,6,9] | `- p:[5,7,8] c: [5,7,8] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalrealselectstart(A,B,C) -> evalrealselectentryin(A,B,C) True evalrealselectentryin(A,B,C) -> evalrealselectbb6in(0,B,C) True evalrealselectbb6in(A,B,C) -> evalrealselectbbin(A,B,C) [A >= 0 && B >= 2 + A] evalrealselectbb6in(A,B,C) -> evalrealselectreturnin(A,B,C) [A >= 0 && 1 + A >= B] evalrealselectbbin(A,B,C) -> evalrealselectbb4in(A,B,1 + A) [-2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectbb4in(A,B,C) -> evalrealselectbb1in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && B >= 1 + C] evalrealselectbb4in(A,B,C) -> evalrealselectbb5in(A,B,C) [-1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && C >= B] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && D >= 1 + E] evalrealselectbb1in(A,B,C) -> evalrealselectbb4in(A,B,1 + C) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -1 + A + C >= 0 && -1 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= D] evalrealselectbb5in(A,B,C) -> evalrealselectbb6in(1 + A,B,C) [-2 + C >= 0 && -4 + B + C >= 0 && -1*B + C >= 0 && -2 + A + C >= 0 && -2 + -1*A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] evalrealselectreturnin(A,B,C) -> evalrealselectstop(A,B,C) [1 + A + -1*B >= 0 && A >= 0] evalrealselectstop(A,B,C) -> exitus616(A,B,C) True Signature: {(evalrealselectbb1in,3) ;(evalrealselectbb4in,3) ;(evalrealselectbb5in,3) ;(evalrealselectbb6in,3) ;(evalrealselectbbin,3) ;(evalrealselectentryin,3) ;(evalrealselectreturnin,3) ;(evalrealselectstart,3) ;(evalrealselectstop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{10},4->{5},5->{7,8},6->{9},7->{5,6},8->{5,6},9->{2,3},10->{11}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[2,9,6,7,5,4,8] c: [2,4,6,9] | `- p:[5,7,8] c: [5,7,8]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalrealselectstart ~> evalrealselectentryin [A <= A, B <= B, C <= C] evalrealselectentryin ~> evalrealselectbb6in [A <= 0*K, B <= B, C <= C] evalrealselectbb6in ~> evalrealselectbbin [A <= A, B <= B, C <= C] evalrealselectbb6in ~> evalrealselectreturnin [A <= A, B <= B, C <= C] evalrealselectbbin ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbb4in ~> evalrealselectbb5in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb5in ~> evalrealselectbb6in [A <= C, B <= B, C <= C] evalrealselectreturnin ~> evalrealselectstop [A <= A, B <= B, C <= C] evalrealselectstop ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A + B] evalrealselectbb6in ~> evalrealselectbbin [A <= A, B <= B, C <= C] evalrealselectbb5in ~> evalrealselectbb6in [A <= C, B <= B, C <= C] evalrealselectbb4in ~> evalrealselectbb5in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbbin ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] + Loop: [0.0.0 <= K + B + C] evalrealselectbb4in ~> evalrealselectbb1in [A <= A, B <= B, C <= C] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] evalrealselectbb1in ~> evalrealselectbb4in [A <= A, B <= B, C <= B] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalrealselectstart ~> evalrealselectentryin [] evalrealselectentryin ~> evalrealselectbb6in [K ~=> A] evalrealselectbb6in ~> evalrealselectbbin [] evalrealselectbb6in ~> evalrealselectreturnin [] evalrealselectbbin ~> evalrealselectbb4in [B ~=> C] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbb4in ~> evalrealselectbb5in [] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] evalrealselectbb5in ~> evalrealselectbb6in [C ~=> A] evalrealselectreturnin ~> evalrealselectstop [] evalrealselectstop ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalrealselectbb6in ~> evalrealselectbbin [] evalrealselectbb5in ~> evalrealselectbb6in [C ~=> A] evalrealselectbb4in ~> evalrealselectbb5in [] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbbin ~> evalrealselectbb4in [B ~=> C] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalrealselectbb4in ~> evalrealselectbb1in [] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] evalrealselectbb1in ~> evalrealselectbb4in [B ~=> C] + Applied Processor: Lare + Details: evalrealselectstart ~> exitus616 [B ~=> A ,B ~=> C ,K ~=> A ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] + evalrealselectbb6in> [B ~=> A ,B ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> tick] + evalrealselectbb4in> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)