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: FromIts 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: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B) -> eval2(1 + A,1) [A >= 0] eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start(A,B) -> eval1(A,B) True Signature: {(eval1,2);(eval2,2);(start,2)} Rule Graph: [0->{1},1->{1,2},2->{0},3->{0}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: eval1(A,B) -> eval2(1 + A,1) [A >= 0] eval2(A,B) -> eval2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2(A,B) -> eval1(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start(A,B) -> eval1(A,B) True eval2(A,B) -> exitus616(A,B) True eval1(A,B) -> exitus616(A,B) True eval2(A,B) -> exitus616(A,B) True Signature: {(eval1,2);(eval2,2);(exitus616,2);(start,2)} Rule Graph: [0->{1,4},1->{1,2,6},2->{0,5},3->{0}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval1.0(A,B) -> eval2.1(1 + A,1) [A >= 0] eval1.0(A,B) -> eval2.4(1 + A,1) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.6(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.2(A,B) -> eval1.0(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] eval2.2(A,B) -> eval1.5(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start.3(A,B) -> eval1.0(A,B) True eval2.4(A,B) -> exitus616.7(A,B) True eval1.5(A,B) -> exitus616.7(A,B) True eval2.6(A,B) -> exitus616.7(A,B) True Signature: {(eval1.0,2);(eval1.5,2);(eval2.1,2);(eval2.2,2);(eval2.4,2);(eval2.6,2);(exitus616.7,2);(start.3,2)} Rule Graph: [0->{2,3,4},1->{8},2->{2,3,4},3->{5,6},4->{10},5->{0,1},6->{9},7->{0,1},8->{},9->{},10->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[0,5,3,2] c: [0,3,5] | `- p:[2] c: [2] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval1.0(A,B) -> eval2.1(1 + A,1) [A >= 0] eval1.0(A,B) -> eval2.4(1 + A,1) [A >= 0] eval2.1(A,B) -> eval2.1(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.2(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.1(A,B) -> eval2.6(A,1 + B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && A >= B] eval2.2(A,B) -> eval1.0(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] eval2.2(A,B) -> eval1.5(-2 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 0 && B >= 1 && B >= 1 + A] start.3(A,B) -> eval1.0(A,B) True eval2.4(A,B) -> exitus616.7(A,B) True eval1.5(A,B) -> exitus616.7(A,B) True eval2.6(A,B) -> exitus616.7(A,B) True Signature: {(eval1.0,2);(eval1.5,2);(eval2.1,2);(eval2.2,2);(eval2.4,2);(eval2.6,2);(exitus616.7,2);(start.3,2)} Rule Graph: [0->{2,3,4},1->{8},2->{2,3,4},3->{5,6},4->{10},5->{0,1},6->{9},7->{0,1},8->{},9->{},10->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10] | `- p:[0,5,3,2] c: [0,3,5] | `- p:[2] c: [2]) + Applied Processor: AbstractSize NoMinimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [A <= K + A, B <= K] eval1.0 ~> eval2.4 [A <= K + A, B <= K] eval2.1 ~> eval2.1 [A <= A, B <= 2*K + B] eval2.1 ~> eval2.2 [A <= A, B <= 2*K + B] eval2.1 ~> eval2.6 [A <= A, B <= 2*K + B] eval2.2 ~> eval1.0 [A <= 2*K + A, B <= B] eval2.2 ~> eval1.5 [A <= 2*K + A, B <= B] start.3 ~> eval1.0 [A <= A, B <= B] eval2.4 ~> exitus616.7 [A <= A, B <= B] eval1.5 ~> exitus616.7 [A <= A, B <= B] eval2.6 ~> exitus616.7 [A <= A, B <= B] + Loop: [0.0 <= A] eval1.0 ~> eval2.1 [A <= K + A, B <= K] eval2.2 ~> eval1.0 [A <= 2*K + A, B <= B] eval2.1 ~> eval2.2 [A <= A, B <= 2*K + B] eval2.1 ~> eval2.1 [A <= A, B <= 2*K + B] + Loop: [0.0.0 <= A + B] eval2.1 ~> eval2.1 [A <= A, B <= 2*K + B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] eval1.0 ~> eval2.1 [K ~=> B,A ~+> A,K ~+> A] eval1.0 ~> eval2.4 [K ~=> B,A ~+> A,K ~+> A] eval2.1 ~> eval2.1 [B ~+> B,K ~*> B] eval2.1 ~> eval2.2 [B ~+> B,K ~*> B] eval2.1 ~> eval2.6 [B ~+> B,K ~*> B] eval2.2 ~> eval1.0 [A ~+> A,K ~*> A] eval2.2 ~> eval1.5 [A ~+> A,K ~*> A] start.3 ~> eval1.0 [] eval2.4 ~> exitus616.7 [] eval1.5 ~> exitus616.7 [] eval2.6 ~> exitus616.7 [] + Loop: [A ~=> 0.0] eval1.0 ~> eval2.1 [K ~=> B,A ~+> A,K ~+> A] eval2.2 ~> eval1.0 [A ~+> A,K ~*> A] eval2.1 ~> eval2.2 [B ~+> B,K ~*> B] eval2.1 ~> eval2.1 [B ~+> B,K ~*> B] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0] eval2.1 ~> eval2.1 [B ~+> B,K ~*> B] + Applied Processor: Lare + Details: start.3 ~> exitus616.7 [A ~=> 0.0 ,K ~=> B ,A ~+> A ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,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] + eval2.2> [A ~=> 0.0 ,A ~+> A ,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 ~*> 0.0.0 ,K ~*> tick ,A ~^> B] eval2.1> [A ~=> 0.0 ,K ~=> B ,A ~+> A ,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 ~*> 0.0.0 ,K ~*> tick ,A ~^> B] eval1.0> [A ~=> 0.0 ,A ~+> A ,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 ~*> 0.0.0 ,K ~*> tick ,A ~^> B] + eval2.1> [A ~+> 0.0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] YES(?,POLY)