YES(?,O(n^1)) * Step 1: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(A,B + C,C) [A >= B && C >= 1] (?,1) Signature: {(eval,3);(start,3)} Flow Graph: [0->{1},1->{1}] + Applied Processor: AddSinks + Details: () * Step 2: LooptreeTransformer WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(A,B + C,C) [A >= B && C >= 1] (?,1) 2. eval(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(eval,3);(exitus616,3);(start,3)} 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. start(A,B,C) -> eval(A,B,C) True (1,1) 1. eval(A,B,C) -> eval(A,B + C,C) [A >= B && C >= 1] (?,1) 2. eval(A,B,C) -> exitus616(A,B,C) True (?,1) Signature: {(eval,3);(exitus616,3);(start,3)} 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,C,0.0] start ~> eval [A <= A, B <= B, C <= C] eval ~> eval [A <= A, B <= B + C, C <= C] eval ~> exitus616 [A <= A, B <= B, C <= C] + Loop: [0.0 <= K + A + B] eval ~> eval [A <= A, B <= B + C, C <= C] + Applied Processor: FlowAbstraction + Details: () * Step 5: LareProcessor WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0] start ~> eval [] eval ~> eval [B ~+> B,C ~+> B] eval ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0] eval ~> eval [B ~+> B,C ~+> B] + Applied Processor: LareProcessor + Details: start ~> exitus616 [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,C ~*> B ,K ~*> B] + eval> [A ~+> 0.0 ,A ~+> tick ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,C ~+> B ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,A ~*> B ,B ~*> B ,C ~*> B ,K ~*> B] YES(?,O(n^1))