YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B) -> eval(A,B) True (1,1) 1. eval(A,B) -> eval(1 + A,B) [B >= 1 + A && B >= A] (?,1) 2. eval(A,B) -> eval(A,1 + B) [A >= 1 + B] (?,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(2,1)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B) -> eval(A,B) True (1,1) 1. eval(A,B) -> eval(1 + A,B) [B >= 1 + A && B >= A] (?,1) 2. eval(A,B) -> eval(A,1 + B) [A >= 1 + B] (?,1) Signature: {(eval,2);(start,2)} Flow Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start(A,B) -> eval(A,B) True eval(A,B) -> eval(1 + A,B) [B >= 1 + A && B >= A] eval(A,B) -> eval(A,1 + B) [A >= 1 + B] Signature: {(eval,2);(start,2)} Rule Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start.0(A,B) -> eval.1(A,B) True start.0(A,B) -> eval.2(A,B) True eval.1(A,B) -> eval.1(1 + A,B) [B >= 1 + A && B >= A] eval.2(A,B) -> eval.2(A,1 + B) [A >= 1 + B] Signature: {(eval.1,2);(eval.2,2);(start.0,2)} Rule Graph: [0->{2},1->{3},2->{2},3->{3}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: start.0(A,B) -> eval.1(A,B) True start.0(A,B) -> eval.2(A,B) True eval.1(A,B) -> eval.1(1 + A,B) [B >= 1 + A && B >= A] eval.2(A,B) -> eval.2(A,1 + B) [A >= 1 + B] eval.2(A,B) -> exitus616(A,B) True eval.1(A,B) -> exitus616(A,B) True Signature: {(eval.1,2);(eval.2,2);(exitus616,2);(start.0,2)} Rule Graph: [0->{2},1->{3},2->{2,5},3->{3,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3] c: [3] | `- p:[2] c: [2] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: start.0(A,B) -> eval.1(A,B) True start.0(A,B) -> eval.2(A,B) True eval.1(A,B) -> eval.1(1 + A,B) [B >= 1 + A && B >= A] eval.2(A,B) -> eval.2(A,1 + B) [A >= 1 + B] eval.2(A,B) -> exitus616(A,B) True eval.1(A,B) -> exitus616(A,B) True Signature: {(eval.1,2);(eval.2,2);(exitus616,2);(start.0,2)} Rule Graph: [0->{2},1->{3},2->{2,5},3->{3,4}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[3] c: [3] | `- p:[2] c: [2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0,0.1] start.0 ~> eval.1 [A <= A, B <= B] start.0 ~> eval.2 [A <= A, B <= B] eval.1 ~> eval.1 [A <= A + B, B <= B] eval.2 ~> eval.2 [A <= A, B <= A + B] eval.2 ~> exitus616 [A <= A, B <= B] eval.1 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A + B] eval.2 ~> eval.2 [A <= A, B <= A + B] + Loop: [0.1 <= A + B] eval.1 ~> eval.1 [A <= A + B, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] start.0 ~> eval.1 [] start.0 ~> eval.2 [] eval.1 ~> eval.1 [A ~+> A,B ~+> A] eval.2 ~> eval.2 [A ~+> B,B ~+> B] eval.2 ~> exitus616 [] eval.1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] eval.2 ~> eval.2 [A ~+> B,B ~+> B] + Loop: [A ~+> 0.1,B ~+> 0.1] eval.1 ~> eval.1 [A ~+> A,B ~+> A] + Applied Processor: Lare + Details: start.0 ~> exitus616 [A ~+> A ,A ~+> B ,A ~+> 0.0 ,A ~+> 0.1 ,A ~+> tick ,B ~+> A ,B ~+> B ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,A ~*> B ,B ~*> A ,B ~*> B ,K ~*> B] + eval.2> [A ~+> B ,A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,K ~*> B] + eval.1> [A ~+> A ,A ~+> 0.1 ,A ~+> tick ,B ~+> A ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,A ~*> A ,B ~*> A] YES(?,O(n^1))