YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (?,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (?,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (?,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (?,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4,5},4->{6,7},5->{10},6->{8},7->{9},8->{4,5},9->{4,5},10->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (1,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (1,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (1,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (1,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (1,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4,5},4->{6,7},5->{10},6->{8},7->{9},8->{4,5},9->{4,5},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (1,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (1,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (1,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (1,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (1,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4},4->{6,7},5->{10},6->{8},7->{9},8->{4,5},9->{4,5},10->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (?,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (?,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (?,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (?,1) 11. evalspeedpldi4returnin(A,B) -> exitus616(A,B) True (?,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2) ;(exitus616,2)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4,5},4->{6,7},5->{10,11},6->{8},7->{9},8->{4,5},9->{4,5},10->{} ,11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (?,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (?,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (?,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (?,1) 11. evalspeedpldi4returnin(A,B) -> exitus616(A,B) True (?,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2) ;(exitus616,2)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4},4->{6,7},5->{10,11},6->{8},7->{9},8->{4,5},9->{4,5},10->{} ,11->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[4,8,6,9,7] c: [9] | `- p:[4,8,6] c: [8] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalspeedpldi4start(A,B) -> evalspeedpldi4entryin(A,B) True (1,1) 1. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [0 >= A] (?,1) 2. evalspeedpldi4entryin(A,B) -> evalspeedpldi4returnin(A,B) [A >= B] (?,1) 3. evalspeedpldi4entryin(A,B) -> evalspeedpldi4bb5in(A,B) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4bb2in(A,B) [-1 + A >= 0 && B >= 1] (?,1) 5. evalspeedpldi4bb5in(A,B) -> evalspeedpldi4returnin(A,B) [-1 + A >= 0 && 0 >= B] (?,1) 6. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb3in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 1 + B] (?,1) 7. evalspeedpldi4bb2in(A,B) -> evalspeedpldi4bb4in(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && B >= A] (?,1) 8. evalspeedpldi4bb3in(A,B) -> evalspeedpldi4bb5in(A,-1 + B) [-1 + A + -1*B >= 0 && -1 + B >= 0 && -3 + A + B >= 0 && -2 + A >= 0] (?,1) 9. evalspeedpldi4bb4in(A,B) -> evalspeedpldi4bb5in(A,-1*A + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] (?,1) 10. evalspeedpldi4returnin(A,B) -> evalspeedpldi4stop(A,B) True (?,1) 11. evalspeedpldi4returnin(A,B) -> exitus616(A,B) True (?,1) Signature: {(evalspeedpldi4bb2in,2) ;(evalspeedpldi4bb3in,2) ;(evalspeedpldi4bb4in,2) ;(evalspeedpldi4bb5in,2) ;(evalspeedpldi4entryin,2) ;(evalspeedpldi4returnin,2) ;(evalspeedpldi4start,2) ;(evalspeedpldi4stop,2) ;(exitus616,2)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4},4->{6,7},5->{10,11},6->{8},7->{9},8->{4,5},9->{4,5},10->{} ,11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[4,8,6,9,7] c: [9] | `- p:[4,8,6] c: [8]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] evalspeedpldi4start ~> evalspeedpldi4entryin [A <= A, B <= B] evalspeedpldi4entryin ~> evalspeedpldi4returnin [A <= A, B <= B] evalspeedpldi4entryin ~> evalspeedpldi4returnin [A <= A, B <= B] evalspeedpldi4entryin ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [A <= A, B <= B] evalspeedpldi4bb5in ~> evalspeedpldi4returnin [A <= A, B <= B] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [A <= A, B <= B] evalspeedpldi4bb2in ~> evalspeedpldi4bb4in [A <= A, B <= B] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4bb4in ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4returnin ~> evalspeedpldi4stop [A <= A, B <= B] evalspeedpldi4returnin ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + B] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [A <= A, B <= B] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [A <= A, B <= B] evalspeedpldi4bb4in ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4bb2in ~> evalspeedpldi4bb4in [A <= A, B <= B] + Loop: [0.0.0 <= B] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [A <= A, B <= B] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [A <= A, B <= B] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [A <= A, B <= B] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] evalspeedpldi4start ~> evalspeedpldi4entryin [] evalspeedpldi4entryin ~> evalspeedpldi4returnin [] evalspeedpldi4entryin ~> evalspeedpldi4returnin [] evalspeedpldi4entryin ~> evalspeedpldi4bb5in [] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [] evalspeedpldi4bb5in ~> evalspeedpldi4returnin [] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [] evalspeedpldi4bb2in ~> evalspeedpldi4bb4in [] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [] evalspeedpldi4bb4in ~> evalspeedpldi4bb5in [] evalspeedpldi4returnin ~> evalspeedpldi4stop [] evalspeedpldi4returnin ~> exitus616 [] + Loop: [B ~+> 0.0,K ~+> 0.0] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [] evalspeedpldi4bb4in ~> evalspeedpldi4bb5in [] evalspeedpldi4bb2in ~> evalspeedpldi4bb4in [] + Loop: [B ~=> 0.0.0] evalspeedpldi4bb5in ~> evalspeedpldi4bb2in [] evalspeedpldi4bb3in ~> evalspeedpldi4bb5in [] evalspeedpldi4bb2in ~> evalspeedpldi4bb3in [] + Applied Processor: LareProcessor + Details: evalspeedpldi4start ~> exitus616 [B ~=> 0.0.0 ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> tick ,K ~*> tick] evalspeedpldi4start ~> evalspeedpldi4stop [B ~=> 0.0.0 ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> tick ,K ~*> tick] + evalspeedpldi4bb5in> [B ~=> 0.0.0 ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> tick ,K ~*> tick] + evalspeedpldi4bb2in> [B ~=> 0.0.0,B ~+> tick,tick ~+> tick] evalspeedpldi4bb5in> [B ~=> 0.0.0,B ~+> tick,tick ~+> tick] YES(?,POLY)