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: Decompose 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: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | +- p:[2] c: [2] | `- 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) [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}] ,We construct a looptree: P: [0,1,2,3,4,5] | +- p:[2] c: [2] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0,0.1] f2 ~> f300 [A <= A, B <= B] f300 ~> f1 [A <= A, B <= B] f300 ~> f300 [A <= A, B <= B] f300 ~> f300 [A <= A, B <= K + B] f300 ~> f300 [A <= 99*K + A, B <= 0*K] f1 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 2*K + B] f300 ~> f300 [A <= A, B <= B] + Loop: [0.1 <= K + A] f300 ~> f300 [A <= A, B <= K + B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.1] f2 ~> f300 [] f300 ~> f1 [] f300 ~> f300 [] f300 ~> f300 [B ~+> B,K ~+> B] f300 ~> f300 [K ~=> B,A ~+> A,K ~*> A] f1 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f300 ~> f300 [] + Loop: [A ~+> 0.1,K ~+> 0.1] f300 ~> f300 [B ~+> B,K ~+> B] + Applied Processor: Lare + Details: f2 ~> exitus616 [K ~=> B ,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 ~*> tick] + f300> [B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f300> [A ~+> 0.1 ,A ~+> tick ,B ~+> B ,tick ~+> tick ,K ~+> B ,K ~+> 0.1 ,K ~+> tick ,A ~*> B ,K ~*> B] YES(?,O(n^1))