YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C) -> f300(A,B,C) True (1,1) 1. f300(A,B,C) -> f1(A,B,D) [0 >= B] (?,1) 2. f300(A,B,C) -> f1(A,B,D) [B >= 1 && 0 >= A] (?,1) 3. f300(A,B,C) -> f300(-1 + A,-2 + A,C) [A >= 1 && A + B >= 1 && B >= 1] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,2,3}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f1(A,B) [0 >= B] (?,1) 2. f300(A,B) -> f1(A,B) [B >= 1 && 0 >= A] (?,1) 3. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,2,3}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,2)] * Step 3: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f300(A,B) True (1,1) 1. f300(A,B) -> f1(A,B) [0 >= B] (?,1) 2. f300(A,B) -> f1(A,B) [B >= 1 && 0 >= A] (?,1) 3. f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3},1->{},2->{},3->{1,3}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B) -> f300(A,B) True f300(A,B) -> f1(A,B) [0 >= B] f300(A,B) -> f1(A,B) [B >= 1 && 0 >= A] f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3},1->{},2->{},3->{1,3}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B) -> f300(A,B) True f300(A,B) -> f1(A,B) [0 >= B] f300(A,B) -> f1(A,B) [B >= 1 && 0 >= A] f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] f1(A,B) -> exitus616(A,B) True f1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3},1->{4},2->{5},3->{1,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[3] c: [3] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f2(A,B) -> f300(A,B) True f300(A,B) -> f1(A,B) [0 >= B] f300(A,B) -> f1(A,B) [B >= 1 && 0 >= A] f300(A,B) -> f300(-1 + A,-2 + A) [A >= 1 && A + B >= 1 && B >= 1] f1(A,B) -> exitus616(A,B) True f1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3},1->{4},2->{5},3->{1,3}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] f2 ~> f300 [A <= A, B <= B] f300 ~> f1 [A <= A, B <= B] f300 ~> f1 [A <= A, B <= B] f300 ~> f300 [A <= A, B <= A] f1 ~> exitus616 [A <= A, B <= B] f1 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A] f300 ~> f300 [A <= A, B <= A] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f2 ~> f300 [] f300 ~> f1 [] f300 ~> f1 [] f300 ~> f300 [A ~=> B] f1 ~> exitus616 [] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f300 ~> f300 [A ~=> B] + Applied Processor: Lare + Details: f2 ~> exitus616 [A ~=> B,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] + f300> [A ~=> B,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick] YES(?,O(n^1))