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