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) [A >= 0] (?,1) 2. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B,C) -> f300(1 + A,1 + B,C) [0 >= 1 + A && B >= 0] (?,1) 4. f300(A,B,C) -> f300(-99 + A,0,C) [0 >= 1 + A && 1 + B = 0] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3,4},1->{},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + 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) [A >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 4. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3,4},1->{},2->{1,2,3,4},3->{1,2,3,4},4->{1,2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,3),(3,2),(3,4),(4,1),(4,2),(4,4)] * 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) [A >= 0] (?,1) 2. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] (?,1) 3. f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] (?,1) 4. f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] (?,1) Signature: {(f1,3);(f2,3);(f300,3)} Flow Graph: [0->{1,2,3,4},1->{},2->{1,2,4},3->{1,3},4->{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) [A >= 0] f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] Signature: {(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3,4},1->{},2->{1,2,4},3->{1,3},4->{3}] + Applied Processor: AddSinks + Details: () * Step 5: Unfold WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B) -> f300(A,B) True f300(A,B) -> f1(A,B) [A >= 0] f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300(A,B) -> f300(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300(A,B) -> f300(-99 + A,0) [0 >= 1 + A && 1 + B = 0] f1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1,3);(f2,3);(f300,3)} Rule Graph: [0->{1,2,3,4},1->{5},2->{1,2,4},3->{1,3},4->{3}] + Applied Processor: Unfold + Details: () * Step 6: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2.0(A,B) -> f300.1(A,B) True f2.0(A,B) -> f300.2(A,B) True f2.0(A,B) -> f300.3(A,B) True f2.0(A,B) -> f300.4(A,B) True f300.1(A,B) -> f1.5(A,B) [A >= 0] f300.2(A,B) -> f300.1(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B) -> f300.2(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B) -> f300.4(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.3(A,B) -> f300.1(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300.3(A,B) -> f300.3(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300.4(A,B) -> f300.3(-99 + A,0) [0 >= 1 + A && 1 + B = 0] f1.5(A,B) -> exitus616.6(A,B) True Signature: {(exitus616.6,2);(f1.5,2);(f2.0,2);(f300.1,2);(f300.2,2);(f300.3,2);(f300.4,2)} Rule Graph: [0->{4},1->{5,6,7},2->{8,9},3->{10},4->{11},5->{4},6->{5,6,7},7->{10},8->{4},9->{8,9},10->{8,9},11->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | +- p:[6] c: [6] | `- p:[9] c: [9] * Step 7: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f2.0(A,B) -> f300.1(A,B) True f2.0(A,B) -> f300.2(A,B) True f2.0(A,B) -> f300.3(A,B) True f2.0(A,B) -> f300.4(A,B) True f300.1(A,B) -> f1.5(A,B) [A >= 0] f300.2(A,B) -> f300.1(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B) -> f300.2(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.2(A,B) -> f300.4(1 + A,1 + B) [0 >= 1 + A && 0 >= 2 + B] f300.3(A,B) -> f300.1(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300.3(A,B) -> f300.3(1 + A,1 + B) [0 >= 1 + A && B >= 0] f300.4(A,B) -> f300.3(-99 + A,0) [0 >= 1 + A && 1 + B = 0] f1.5(A,B) -> exitus616.6(A,B) True Signature: {(exitus616.6,2);(f1.5,2);(f2.0,2);(f300.1,2);(f300.2,2);(f300.3,2);(f300.4,2)} Rule Graph: [0->{4},1->{5,6,7},2->{8,9},3->{10},4->{11},5->{4},6->{5,6,7},7->{10},8->{4},9->{8,9},10->{8,9},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | +- p:[6] c: [6] | `- p:[9] c: [9]) + Applied Processor: AbstractSize Minimize + Details: () * Step 8: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0,0.1] f2.0 ~> f300.1 [A <= A, B <= B] f2.0 ~> f300.2 [A <= A, B <= B] f2.0 ~> f300.3 [A <= A, B <= B] f2.0 ~> f300.4 [A <= A, B <= B] f300.1 ~> f1.5 [A <= A, B <= B] f300.2 ~> f300.1 [A <= A, B <= B] f300.2 ~> f300.2 [A <= A, B <= B] f300.2 ~> f300.4 [A <= A, B <= B] f300.3 ~> f300.1 [A <= A, B <= K + B] f300.3 ~> f300.3 [A <= A, B <= K + B] f300.4 ~> f300.3 [A <= 99*K + A, B <= 0*K] f1.5 ~> exitus616.6 [A <= A, B <= B] + Loop: [0.0 <= 2*K + B] f300.2 ~> f300.2 [A <= A, B <= B] + Loop: [0.1 <= K + A] f300.3 ~> f300.3 [A <= A, B <= K + B] + Applied Processor: AbstractFlow + Details: () * Step 9: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] f2.0 ~> f300.1 [] f2.0 ~> f300.2 [] f2.0 ~> f300.3 [] f2.0 ~> f300.4 [] f300.1 ~> f1.5 [] f300.2 ~> f300.1 [] f300.2 ~> f300.2 [] f300.2 ~> f300.4 [] f300.3 ~> f300.1 [B ~+> B,K ~+> B] f300.3 ~> f300.3 [B ~+> B,K ~+> B] f300.4 ~> f300.3 [K ~=> B,A ~+> A,K ~*> A] f1.5 ~> exitus616.6 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f300.2 ~> f300.2 [] + Loop: [A ~+> 0.1,K ~+> 0.1] f300.3 ~> f300.3 [B ~+> B,K ~+> B] + Applied Processor: Lare + Details: f2.0 ~> exitus616.6 [A ~+> A ,A ~+> 0.1 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,K ~*> A ,K ~*> B ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f300.2> [B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f300.3> [A ~+> 0.1 ,A ~+> tick ,B ~+> B ,tick ~+> tick ,K ~+> B ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,K ~*> B] YES(?,O(n^1))