YES(?,O(n^1)) * Step 1: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A) -> f0(-1 + A) [A >= 0] (?,1) 1. f1(A) -> f0(A) True (1,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{0},1->{0}] + Applied Processor: AddSinks + Details: () * Step 2: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A) -> f0(-1 + A) [A >= 0] (?,1) 1. f1(A) -> f0(A) True (1,1) 2. f0(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f1,1)} Flow Graph: [0->{0,2},1->{0,2},2->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2] | `- p:[0] c: [0] * Step 3: SizeAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: 0. f0(A) -> f0(-1 + A) [A >= 0] (?,1) 1. f1(A) -> f0(A) True (1,1) 2. f0(A) -> exitus616(A) True (?,1) Signature: {(exitus616,1);(f0,1);(f1,1)} Flow Graph: [0->{0,2},1->{0,2},2->{}] ,We construct a looptree: P: [0,1,2] | `- p:[0] c: [0]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 4: FlowAbstraction WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] f0 ~> f0 [A <= K + A] f1 ~> f0 [A <= A] f0 ~> exitus616 [A <= A] + Loop: [0.0 <= K + A] f0 ~> f0 [A <= K + A] + Applied Processor: FlowAbstraction + Details: () * Step 5: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f0 ~> f0 [A ~+> A,K ~+> A] f1 ~> f0 [] f0 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f0 ~> f0 [A ~+> A,K ~+> A] + Applied Processor: LareProcessor + Details: f1 ~> exitus616 [A ~+> A ,A ~+> 0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> 0.0 ,K ~+> tick ,A ~*> A ,K ~*> A] + f0> [A ~+> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> A,K ~+> 0.0,K ~+> tick,A ~*> A,K ~*> A] YES(?,O(n^1))