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

YES(?,O(n^1))