YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,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: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (1,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (1,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (1,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,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: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (1,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (1,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (1,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8},4->{6},5->{7},6->{4,5},7->{2,3},8->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) 9. evalwhile2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{8,9},4->{6},5->{7},6->{4,5},7->{2,3},8->{},9->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) 9. evalwhile2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8,9},4->{6},5->{7},6->{4,5},7->{2,3},8->{},9->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9] | `- p:[2,7,5,6,4] c: [7] | `- p:[4,6] c: [6] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalwhile2start(A,B,C) -> evalwhile2entryin(A,B,C) True (1,1) 1. evalwhile2entryin(A,B,C) -> evalwhile2bb4in(B,B,C) True (?,1) 2. evalwhile2bb4in(A,B,C) -> evalwhile2bb2in(A,B,B) [-1*A + B >= 0 && A >= 1] (?,1) 3. evalwhile2bb4in(A,B,C) -> evalwhile2returnin(A,B,C) [-1*A + B >= 0 && 0 >= A] (?,1) 4. evalwhile2bb2in(A,B,C) -> evalwhile2bb1in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1] (?,1) 5. evalwhile2bb2in(A,B,C) -> evalwhile2bb3in(A,B,C) [B + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && 0 >= C] (?,1) 6. evalwhile2bb1in(A,B,C) -> evalwhile2bb2in(A,B,-1 + C) [B + -1*C >= 0 (?,1) && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 7. evalwhile2bb3in(A,B,C) -> evalwhile2bb4in(-1 + A,B,C) [-1*C >= 0 (?,1) && -1 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 8. evalwhile2returnin(A,B,C) -> evalwhile2stop(A,B,C) [-1*A + B >= 0 && -1*A >= 0] (?,1) 9. evalwhile2returnin(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(evalwhile2bb1in,3) ;(evalwhile2bb2in,3) ;(evalwhile2bb3in,3) ;(evalwhile2bb4in,3) ;(evalwhile2entryin,3) ;(evalwhile2returnin,3) ;(evalwhile2start,3) ;(evalwhile2stop,3) ;(exitus616,3)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{8,9},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: [7] | `- p:[4,6] c: [6]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,0.0,0.0.0] evalwhile2start ~> evalwhile2entryin [A <= A, B <= B, C <= C] evalwhile2entryin ~> evalwhile2bb4in [A <= B, B <= B, C <= C] evalwhile2bb4in ~> evalwhile2bb2in [A <= A, B <= B, C <= B] evalwhile2bb4in ~> evalwhile2returnin [A <= A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb3in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [A <= A, B <= B, C <= C] evalwhile2bb3in ~> evalwhile2bb4in [A <= B, B <= B, C <= C] evalwhile2returnin ~> evalwhile2stop [A <= A, B <= B, C <= C] evalwhile2returnin ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= A] evalwhile2bb4in ~> evalwhile2bb2in [A <= A, B <= B, C <= B] evalwhile2bb3in ~> evalwhile2bb4in [A <= B, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb3in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [A <= A, B <= B, C <= C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] + Loop: [0.0.0 <= C] evalwhile2bb2in ~> evalwhile2bb1in [A <= A, B <= B, C <= C] evalwhile2bb1in ~> evalwhile2bb2in [A <= A, B <= B, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.0.0] evalwhile2start ~> evalwhile2entryin [] evalwhile2entryin ~> evalwhile2bb4in [B ~=> A] evalwhile2bb4in ~> evalwhile2bb2in [B ~=> C] evalwhile2bb4in ~> evalwhile2returnin [] evalwhile2bb2in ~> evalwhile2bb1in [] evalwhile2bb2in ~> evalwhile2bb3in [] evalwhile2bb1in ~> evalwhile2bb2in [] evalwhile2bb3in ~> evalwhile2bb4in [B ~=> A] evalwhile2returnin ~> evalwhile2stop [] evalwhile2returnin ~> exitus616 [] + Loop: [A ~=> 0.0] evalwhile2bb4in ~> evalwhile2bb2in [B ~=> C] evalwhile2bb3in ~> evalwhile2bb4in [B ~=> A] evalwhile2bb2in ~> evalwhile2bb3in [] evalwhile2bb1in ~> evalwhile2bb2in [] evalwhile2bb2in ~> evalwhile2bb1in [] + Loop: [C ~=> 0.0.0] evalwhile2bb2in ~> evalwhile2bb1in [] evalwhile2bb1in ~> evalwhile2bb2in [] + Applied Processor: LareProcessor + Details: evalwhile2start ~> exitus616 [B ~=> A ,B ~=> C ,B ~=> 0.0 ,B ~=> 0.0.0 ,B ~+> tick ,tick ~+> tick ,B ~*> tick] evalwhile2start ~> evalwhile2stop [B ~=> A ,B ~=> C ,B ~=> 0.0 ,B ~=> 0.0.0 ,B ~+> tick ,tick ~+> tick ,B ~*> tick] + evalwhile2bb4in> [A ~=> 0.0 ,B ~=> A ,B ~=> C ,B ~=> 0.0.0 ,A ~+> tick ,B ~+> tick ,tick ~+> tick ,A ~*> tick ,B ~*> tick] + evalwhile2bb2in> [C ~=> 0.0.0,C ~+> tick,tick ~+> tick] YES(?,POLY)