YES(?,O(n^1)) * Step 1: FromIts 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: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0(A) -> f0(-1 + A) [A >= 0] f1(A) -> f0(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: f0(A) -> f0(-1 + A) [A >= 0] f1(A) -> f0(A) True f0(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: f0(A) -> f0(-1 + A) [A >= 0] f1(A) -> f0(A) True f0(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] f0 ~> f0 [A <= K + A] f1 ~> f0 [A <= A] f0 ~> exitus616 [A <= A] + Loop: [0.0 <= A] f0 ~> f0 [A <= K + A] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare 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] f0 ~> f0 [A ~+> A,K ~+> A] + Applied Processor: Lare + Details: f1 ~> exitus616 [A ~=> 0.0,A ~+> A,A ~+> tick,tick ~+> tick,K ~+> A,A ~*> A,K ~*> A] + f0> [A ~=> 0.0,A ~+> A,A ~+> tick,tick ~+> tick,K ~+> A,A ~*> A,K ~*> A] YES(?,O(n^1))