YES(?,O(1)) * Step 1: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A) -> f1(300) True (1,1) 1. f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] (?,1) Signature: {(f0,1);(f1,1)} Flow Graph: [0->{1},1->{1}] + Applied Processor: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A) -> f1(300) True f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] Signature: {(f0,1);(f1,1)} Rule Graph: [0->{1},1->{1}] + Applied Processor: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f0(A) -> f1(300) True f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] f1(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,1);(f1,1)} 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(1)) + Considered Problem: (Rules: f0(A) -> f1(300) True f1(A) -> f1(-1 + A) [300 + -1*A >= 0 && A >= 102] f1(A) -> exitus616(A) True Signature: {(exitus616,1);(f0,1);(f1,1)} 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(1)) + Considered Problem: Program: Domain: [A,0.0] f0 ~> f1 [A <= 300*K] f1 ~> f1 [A <= 299*K] f1 ~> exitus616 [A <= A] + Loop: [0.0 <= 102*K + A] f1 ~> f1 [A <= 299*K] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,0.0] f0 ~> f1 [K ~=> A] f1 ~> f1 [K ~=> A] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f1 ~> f1 [K ~=> A] + Applied Processor: Lare + Details: f0 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f1> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))