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