YES(?,O(n^1))
* Step 1: TrivialSCCs WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (1,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
        Signature:
          {(end,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 3: LooptreeTransformer WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
          3. sumto(A,B) -> exitus616(A,B) True         (?,1)
        Signature:
          {(end,2);(exitus616,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1,3},2->{0,1,3},3->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]
* Step 4: SizeAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          0. sumto(A,B) -> end(A,B)       [A >= 1 + B] (?,1)
          1. sumto(A,B) -> sumto(1 + A,B) [B >= A]     (?,1)
          2. start(A,B) -> sumto(A,B)     True         (1,1)
          3. sumto(A,B) -> exitus616(A,B) True         (?,1)
        Signature:
          {(end,2);(exitus616,2);(start,2);(sumto,2)}
        Flow Graph:
          [0->{},1->{0,1,3},2->{0,1,3},3->{}]
        
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 5: FlowAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0]
           sumto  ~>  end         [A <= A, B <= B]
           sumto  ~>  sumto       [A <= K + A, B <= B]
           start  ~>  sumto       [A <= A, B <= B]
           sumto  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A + B]
               sumto  ~>  sumto   [A <= K + A, B <= B]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 6: LareProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0]
           sumto  ~>  end         []
           sumto  ~>  sumto       [A ~+> A,K ~+> A]
           start  ~>  sumto       []
           sumto  ~>  exitus616   []
          + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0]
               sumto  ~>  sumto   [A ~+> A,K ~+> A]
    + Applied Processor:
        LareProcessor
    + Details:
         start  ~>  exitus616   [A ~+> A
                                ,A ~+> 0.0
                                ,A ~+> tick
                                ,B ~+> 0.0
                                ,B ~+> tick
                                ,tick ~+> tick
                                ,K ~+> A
                                ,K ~+> 0.0
                                ,K ~+> tick
                                ,A ~*> A
                                ,B ~*> A
                                ,K ~*> A]
         start  ~>  end         [A ~+> A
                                ,A ~+> 0.0
                                ,A ~+> tick
                                ,B ~+> 0.0
                                ,B ~+> tick
                                ,tick ~+> tick
                                ,K ~+> A
                                ,K ~+> 0.0
                                ,K ~+> tick
                                ,A ~*> A
                                ,B ~*> A
                                ,K ~*> A]
        + <sumto  ~>  sumto>  [A ~+> A
                              ,A ~+> 0.0
                              ,A ~+> tick
                              ,B ~+> 0.0
                              ,B ~+> tick
                              ,tick ~+> tick
                              ,K ~+> A
                              ,K ~+> 0.0
                              ,K ~+> tick
                              ,A ~*> A
                              ,B ~*> A
                              ,K ~*> A]

YES(?,O(n^1))