YES(?,O(n^1))
* Step 1: UnsatRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A,1 + B) [A >= 1 + B]               (?,1)
          1. eval(A,B)  -> eval(A,1 + B) [B >= 1 + A && A >= 1 + B] (?,1)
          2. eval(A,B)  -> eval(1 + A,B) [A >= 1 + B && B >= A]     (?,1)
          3. eval(A,B)  -> eval(1 + A,B) [B >= 1 + A && B >= A]     (?,1)
          4. start(A,B) -> eval(A,B)     True                       (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,1,2,3},1->{0,1,2,3},2->{0,1,2,3},3->{0,1,2,3},4->{0,1,2,3}]
        
    + Applied Processor:
        UnsatRules
    + Details:
        Following transitions have unsatisfiable constraints and are removed:  [1,2]
* Step 2: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A,1 + B) [A >= 1 + B]           (?,1)
          3. eval(A,B)  -> eval(1 + A,B) [B >= 1 + A && B >= A] (?,1)
          4. start(A,B) -> eval(A,B)     True                   (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0,3},3->{0,3},4->{0,3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3),(3,0)]
* Step 3: FromIts WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval(A,B)  -> eval(A,1 + B) [A >= 1 + B]           (?,1)
          3. eval(A,B)  -> eval(1 + A,B) [B >= 1 + A && B >= A] (?,1)
          4. start(A,B) -> eval(A,B)     True                   (1,1)
        Signature:
          {(eval,2);(start,2)}
        Flow Graph:
          [0->{0},3->{3},4->{0,3}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 4: Unfold WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          eval(A,B)  -> eval(A,1 + B)  [A >= 1 + B]
          eval(A,B)  -> eval(1 + A,B)  [B >= 1 + A && B >= A]
          start(A,B) -> eval(A,B)      True
        Signature:
          {(eval,2);(start,2)}
        Rule Graph:
          [0->{0},3->{3},4->{0,3}]
    + Applied Processor:
        Unfold
    + Details:
        ()
* Step 5: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          eval.0(A,B)  -> eval.0(A,1 + B)  [A >= 1 + B]
          eval.3(A,B)  -> eval.3(1 + A,B)  [B >= 1 + A && B >= A]
          start.4(A,B) -> eval.0(A,B)      True
          start.4(A,B) -> eval.3(A,B)      True
        Signature:
          {(eval.0,2);(eval.3,2);(start.4,2)}
        Rule Graph:
          [0->{0},1->{1},2->{0},3->{1}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 6: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          eval.0(A,B)  -> eval.0(A,1 + B)  [A >= 1 + B]
          eval.3(A,B)  -> eval.3(1 + A,B)  [B >= 1 + A && B >= A]
          start.4(A,B) -> eval.0(A,B)      True
          start.4(A,B) -> eval.3(A,B)      True
          eval.3(A,B)  -> exitus616(A,B)   True
          eval.0(A,B)  -> exitus616(A,B)   True
        Signature:
          {(eval.0,2);(eval.3,2);(exitus616,2);(start.4,2)}
        Rule Graph:
          [0->{0,5},1->{1,4},2->{0},3->{1}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[0] c: [0]
* Step 7: AbstractSize WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          eval.0(A,B)  -> eval.0(A,1 + B)  [A >= 1 + B]
          eval.3(A,B)  -> eval.3(1 + A,B)  [B >= 1 + A && B >= A]
          start.4(A,B) -> eval.0(A,B)      True
          start.4(A,B) -> eval.3(A,B)      True
          eval.3(A,B)  -> exitus616(A,B)   True
          eval.0(A,B)  -> exitus616(A,B)   True
        Signature:
          {(eval.0,2);(eval.3,2);(exitus616,2);(start.4,2)}
        Rule Graph:
          [0->{0,5},1->{1,4},2->{0},3->{1}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[0] c: [0])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 8: AbstractFlow WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0,0.1]
           eval.0   ~>  eval.0      [A <= A, B <= A + B]
           eval.3   ~>  eval.3      [A <= A + B, B <= B]
           start.4  ~>  eval.0      [A <= A, B <= B]
           start.4  ~>  eval.3      [A <= A, B <= B]
           eval.3   ~>  exitus616   [A <= A, B <= B]
           eval.0   ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= A + B]
               eval.3  ~>  eval.3   [A <= A + B, B <= B]
          + Loop: [0.1 <= K + A + B]
               eval.0  ~>  eval.0   [A <= A, B <= A + B]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 9: Lare WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0,0.1]
           eval.0   ~>  eval.0      [A ~+> B,B ~+> B]
           eval.3   ~>  eval.3      [A ~+> A,B ~+> A]
           start.4  ~>  eval.0      []
           start.4  ~>  eval.3      []
           eval.3   ~>  exitus616   []
           eval.0   ~>  exitus616   []
          + Loop: [A ~+> 0.0,B ~+> 0.0]
               eval.3  ~>  eval.3   [A ~+> A,B ~+> A]
          + Loop: [A ~+> 0.1,B ~+> 0.1,K ~+> 0.1]
               eval.0  ~>  eval.0   [A ~+> B,B ~+> B]
    + Applied Processor:
        Lare
    + Details:
         start.4  ~>  exitus616   [A ~+> A
                                  ,A ~+> B
                                  ,A ~+> 0.0
                                  ,A ~+> 0.1
                                  ,A ~+> tick
                                  ,B ~+> A
                                  ,B ~+> B
                                  ,B ~+> 0.0
                                  ,B ~+> 0.1
                                  ,B ~+> tick
                                  ,tick ~+> tick
                                  ,K ~+> 0.1
                                  ,K ~+> tick
                                  ,A ~*> A
                                  ,A ~*> B
                                  ,B ~*> A
                                  ,B ~*> B
                                  ,K ~*> B]
        + <eval.3  ~>  eval.3>  [A ~+> A
                                ,A ~+> 0.0
                                ,A ~+> tick
                                ,B ~+> A
                                ,B ~+> 0.0
                                ,B ~+> tick
                                ,tick ~+> tick
                                ,A ~*> A
                                ,B ~*> A]
        + <eval.0  ~>  eval.0>  [A ~+> B
                                ,A ~+> 0.1
                                ,A ~+> tick
                                ,B ~+> B
                                ,B ~+> 0.1
                                ,B ~+> tick
                                ,tick ~+> tick
                                ,K ~+> 0.1
                                ,K ~+> tick
                                ,A ~*> B
                                ,B ~*> B
                                ,K ~*> B]

YES(?,O(n^1))