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