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