YES(?,O(n^1)) * Step 1: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f3(A) -> f1(A) [A >= 0] (1,1) 1. f1(A) -> f1(-1 + A) [A >= 1] (?,1) Signature: {(f1,1);(f3,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: AddSinks + Details: () * Step 2: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f3(A) -> f1(A) [A >= 0] (1,1) 1. f1(A) -> f1(-1 + A) [A >= 1] (?,1) 2. f1(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f1,1);(f3,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2] | `- p:[1] c: [1] * Step 3: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f3(A) -> f1(A) [A >= 0] (1,1) 1. f1(A) -> f1(-1 + A) [A >= 1] (?,1) 2. f1(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f1,1);(f3,1)} Flow Graph: [0->{1,2},1->{1,2},2->{}] ,We construct a looptree: P: [0,1,2] | `- p:[1] c: [1]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 4: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] f3 ~> f1 [A <= A] f1 ~> f1 [A <= A] f1 ~> exitus616 [A <= A] + Loop: [0.0 <= A] f1 ~> f1 [A <= A] + Applied Processor: FlowAbstraction + Details: () * Step 5: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f3 ~> f1 [] f1 ~> f1 [] f1 ~> exitus616 [] + Loop: [A ~=> 0.0] f1 ~> f1 [] + Applied Processor: LareProcessor + Details: f3 ~> exitus616 [A ~=> 0.0,A ~+> tick,tick ~+> tick] + f1> [A ~=> 0.0,A ~+> tick,tick ~+> tick] YES(?,O(n^1))