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: AddSinks 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:
        AddSinks
    + Details:
        ()
* Step 4: 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)
          5. eval(A,B)  -> exitus616(A,B) True                   (?,1)
        Signature:
          {(eval,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{0,3,5},3->{0,3,5},4->{0,3,5},5->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3),(3,0)]
* Step 5: LooptreeTransformer 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)
          5. eval(A,B)  -> exitus616(A,B) True                   (?,1)
        Signature:
          {(eval,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{0,5},3->{3,5},4->{0,3,5},5->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,3,4,5]
          |
          +- p:[3] c: [3]
          |
          `- p:[0] c: [0]
* Step 6: SizeAbstraction 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)
          5. eval(A,B)  -> exitus616(A,B) True                   (?,1)
        Signature:
          {(eval,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{0,5},3->{3,5},4->{0,3,5},5->{}]
        
        ,We construct a looptree:
          P: [0,3,4,5]
          |
          +- p:[3] c: [3]
          |
          `- p:[0] c: [0])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 7: FlowAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0,0.1]
           eval   ~>  eval        [A <= A, B <= A + B]
           eval   ~>  eval        [A <= A + B, B <= B]
           start  ~>  eval        [A <= A, B <= B]
           eval   ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A + B]
               eval  ~>  eval   [A <= A + B, B <= B]
          + Loop: [0.1 <= A + B]
               eval  ~>  eval   [A <= A, B <= A + B]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 8: LareProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0,0.1]
           eval   ~>  eval        [A ~+> B,B ~+> B]
           eval   ~>  eval        [A ~+> A,B ~+> A]
           start  ~>  eval        []
           eval   ~>  exitus616   []
          + Loop: [A ~+> 0.0,B ~+> 0.0,K ~+> 0.0]
               eval  ~>  eval   [A ~+> A,B ~+> A]
          + Loop: [A ~+> 0.1,B ~+> 0.1]
               eval  ~>  eval   [A ~+> B,B ~+> B]
    + Applied Processor:
        LareProcessor
    + Details:
         start  ~>  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 ~+> 0.0
                                ,K ~+> tick
                                ,A ~*> A
                                ,A ~*> B
                                ,B ~*> A
                                ,B ~*> B
                                ,K ~*> A]
        + <eval  ~>  eval>  [A ~+> A
                            ,A ~+> 0.0
                            ,A ~+> tick
                            ,B ~+> A
                            ,B ~+> 0.0
                            ,B ~+> tick
                            ,tick ~+> tick
                            ,K ~+> 0.0
                            ,K ~+> tick
                            ,A ~*> A
                            ,B ~*> A
                            ,K ~*> A]
        + <eval  ~>  eval>  [A ~+> B
                            ,A ~+> 0.1
                            ,A ~+> tick
                            ,B ~+> B
                            ,B ~+> 0.1
                            ,B ~+> tick
                            ,tick ~+> tick
                            ,A ~*> B
                            ,B ~*> B]

YES(?,O(n^1))