YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1,2},1->{1,2},2->{0},3->{0}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) Signature: {(eval1,2);(eval2,2);(start,2)} Flow Graph: [0->{1},1->{1,2},2->{0},3->{0}] + Applied Processor: AddSinks + Details: () * Step 3: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) 4. eval1(A,B) -> exitus616(A,B) True (?,1) 5. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Flow Graph: [0->{1,2,5},1->{1,2,5},2->{0,4},3->{0,4},4->{},5->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2)] * Step 4: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) 4. eval1(A,B) -> exitus616(A,B) True (?,1) 5. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Flow Graph: [0->{1,5},1->{1,2,5},2->{0,4},3->{0,4},4->{},5->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [2] | `- p:[1] c: [1] * Step 5: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. eval1(A,B) -> eval2(1 + A,1) [A >= 0] (?,1) 1. eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] (?,1) 2. eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] (?,1) 3. start(A,B) -> eval1(A,B) True (1,1) 4. eval1(A,B) -> exitus616(A,B) True (?,1) 5. eval2(A,B) -> exitus616(A,B) True (?,1) Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Flow Graph: [0->{1,5},1->{1,2,5},2->{0,4},3->{0,4},4->{},5->{}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG NoMinimize + Details: () * Step 6: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1 ~> eval2 [A <= K + A, B <= K] eval2 ~> eval2 [A <= A, B <= 2*K + B] eval2 ~> eval1 [A <= 2*K + A, B <= B] start ~> eval1 [A <= A, B <= B] eval1 ~> exitus616 [A <= A, B <= B] eval2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 2*K + A] eval1 ~> eval2 [A <= K + A, B <= K] eval2 ~> eval1 [A <= 2*K + A, B <= B] eval2 ~> eval2 [A <= A, B <= 2*K + B] + Loop: [0.0.0 <= K + A + B] eval2 ~> eval2 [A <= A, B <= 2*K + B] + Applied Processor: FlowAbstraction + Details: () * Step 7: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1 ~> eval2 [K ~=> B,A ~+> A,K ~+> A] eval2 ~> eval2 [B ~+> B,K ~*> B] eval2 ~> eval1 [A ~+> A,K ~*> A] start ~> eval1 [] eval1 ~> exitus616 [] eval2 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] eval1 ~> eval2 [K ~=> B,A ~+> A,K ~+> A] eval2 ~> eval1 [A ~+> A,K ~*> A] eval2 ~> eval2 [B ~+> B,K ~*> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,K ~+> 0.0.0] eval2 ~> eval2 [B ~+> B,K ~*> B] + Applied Processor: LareProcessor + Details: start ~> exitus616 [K ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0 ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,K ~^> B] + eval2> [K ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,K ~^> B] eval1> [K ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> B ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,A ~*> 0.0.0 ,A ~*> tick ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick ,A ~^> B ,K ~^> B] + eval2> [A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,POLY)