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