YES(?,O(n^1))
* Step 1: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B)      True                   (1,1)
          1. eval(A,B)  -> eval(B,B)      [A >= 1 && A >= 1 + B] (?,1)
          2. eval(A,B)  -> eval(-1 + A,B) [A >= 1 && B >= A]     (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,1),(2,1)]
* Step 2: FromIts WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. start(A,B) -> eval(A,B)      True                   (1,1)
          1. eval(A,B)  -> eval(B,B)      [A >= 1 && A >= 1 + B] (?,1)
          2. eval(A,B)  -> eval(-1 + A,B) [A >= 1 && B >= A]     (?,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{1,2},1->{2},2->{2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          start(A,B) -> eval(A,B)       True
          eval(A,B)  -> eval(B,B)       [A >= 1 && A >= 1 + B]
          eval(A,B)  -> eval(-1 + A,B)  [A >= 1 && B >= A]
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{1,2},1->{2},2->{2}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          start(A,B) -> eval(A,B)       True
          eval(A,B)  -> eval(B,B)       [A >= 1 && A >= 1 + B]
          eval(A,B)  -> eval(-1 + A,B)  [A >= 1 && B >= A]
          eval(A,B)  -> exitus616(A,B)  True
        Signature:
          {(eval,2);(exitus616,2);(start,2)}
        Rule Graph:
          [0->{1,2},1->{2},2->{2,3}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[2] c: [2]
* Step 5: AbstractSize WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          start(A,B) -> eval(A,B)       True
          eval(A,B)  -> eval(B,B)       [A >= 1 && A >= 1 + B]
          eval(A,B)  -> eval(-1 + A,B)  [A >= 1 && B >= A]
          eval(A,B)  -> exitus616(A,B)  True
        Signature:
          {(eval,2);(exitus616,2);(start,2)}
        Rule Graph:
          [0->{1,2},1->{2},2->{2,3}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[2] c: [2])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 6: AbstractFlow WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0]
           start  ~>  eval        [A <= A, B <= B]
           eval   ~>  eval        [A <= B, B <= B]
           eval   ~>  eval        [A <= A, B <= B]
           eval   ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A]
               eval  ~>  eval   [A <= A, B <= B]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 7: Lare WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0]
           start  ~>  eval        []
           eval   ~>  eval        [B ~=> A]
           eval   ~>  eval        []
           eval   ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~+> 0.0]
               eval  ~>  eval   []
    + Applied Processor:
        Lare
    + Details:
         start  ~>  exitus616   [B ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick]
        + <eval  ~>  eval>  [A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick]

YES(?,O(n^1))