YES(?,O(n^1)) * Step 1: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f1(A) -> f1(-1000 + A) [A >= 1001] (?,1) 1. f0(A) -> f1(A) True (1,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{0},1->{0}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f1(A) -> f1(-1000 + A) [A >= 1001] f0(A) -> f1(A) True Signature: {(f0,1);(f1,1)} Rule Graph: [0->{0},1->{0}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f1(A) -> f1(-1000 + A) [A >= 1001] f0(A) -> f1(A) True f1(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,1);(f1,1)} Rule Graph: [0->{0,2},1->{0}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2] | `- p:[0] c: [0] * Step 4: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f1(A) -> f1(-1000 + A) [A >= 1001] f0(A) -> f1(A) True f1(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,1);(f1,1)} Rule Graph: [0->{0,2},1->{0}] ,We construct a looptree: P: [0,1,2] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,0.0] f1 ~> f1 [A <= A] f0 ~> f1 [A <= A] f1 ~> exitus616 [A <= A] + Loop: [0.0 <= 1001*K + A] f1 ~> f1 [A <= A] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f1 ~> f1 [] f0 ~> f1 [] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f1 ~> f1 [] + Applied Processor: Lare + Details: f0 ~> exitus616 [A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f1> [A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(n^1))