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