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