YES(?,O(n^1))
* Step 1: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval1(A,B) -> eval2(A,B)           [A >= 1 && B = A] (?,1)
          1. eval2(A,B) -> eval2(-1 + A,-1 + B) [A >= 1]          (?,1)
          2. eval2(A,B) -> eval1(A,B)           [0 >= A]          (?,1)
          3. start(A,B) -> eval1(A,B)           True              (1,1)
        Signature:
          {(eval1,2);(eval2,2);(start,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{0},3->{0}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(2,0)]
* Step 2: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval1(A,B) -> eval2(A,B)           [A >= 1 && B = A] (?,1)
          1. eval2(A,B) -> eval2(-1 + A,-1 + B) [A >= 1]          (?,1)
          2. eval2(A,B) -> eval1(A,B)           [0 >= A]          (?,1)
          3. start(A,B) -> eval1(A,B)           True              (1,1)
        Signature:
          {(eval1,2);(eval2,2);(start,2)}
        Flow Graph:
          [0->{1},1->{1,2},2->{},3->{0}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 3: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval1(A,B) -> eval2(A,B)           [A >= 1 && B = A] (?,1)
          1. eval2(A,B) -> eval2(-1 + A,-1 + B) [A >= 1]          (?,1)
          2. eval2(A,B) -> eval1(A,B)           [0 >= A]          (?,1)
          3. start(A,B) -> eval1(A,B)           True              (1,1)
          4. eval2(A,B) -> exitus616(A,B)       True              (?,1)
        Signature:
          {(eval1,2);(eval2,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{1,2,4},1->{1,2,4},2->{0},3->{0},4->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(2,0)]
* Step 4: LooptreeTransformer WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. eval1(A,B) -> eval2(A,B)           [A >= 1 && B = A] (?,1)
          1. eval2(A,B) -> eval2(-1 + A,-1 + B) [A >= 1]          (?,1)
          2. eval2(A,B) -> eval1(A,B)           [0 >= A]          (?,1)
          3. start(A,B) -> eval1(A,B)           True              (1,1)
          4. eval2(A,B) -> exitus616(A,B)       True              (?,1)
        Signature:
          {(eval1,2);(eval2,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{1,4},1->{1,2,4},2->{},3->{0},4->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1] c: [1]
* Step 5: SizeAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          0. eval1(A,B) -> eval2(A,B)           [A >= 1 && B = A] (?,1)
          1. eval2(A,B) -> eval2(-1 + A,-1 + B) [A >= 1]          (?,1)
          2. eval2(A,B) -> eval1(A,B)           [0 >= A]          (?,1)
          3. start(A,B) -> eval1(A,B)           True              (1,1)
          4. eval2(A,B) -> exitus616(A,B)       True              (?,1)
        Signature:
          {(eval1,2);(eval2,2);(exitus616,2);(start,2)}
        Flow Graph:
          [0->{1,4},1->{1,2,4},2->{},3->{0},4->{}]
        
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 6: FlowAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0]
           eval1  ~>  eval2       [A <= A, B <= B]
           eval2  ~>  eval2       [A <= A, B <= K + B]
           eval2  ~>  eval1       [A <= A, B <= B]
           start  ~>  eval1       [A <= A, B <= B]
           eval2  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= A]
               eval2  ~>  eval2   [A <= A, B <= K + B]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 7: LareProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0]
           eval1  ~>  eval2       []
           eval2  ~>  eval2       [B ~+> B,K ~+> B]
           eval2  ~>  eval1       []
           start  ~>  eval1       []
           eval2  ~>  exitus616   []
          + Loop: [A ~=> 0.0]
               eval2  ~>  eval2   [B ~+> B,K ~+> B]
    + Applied Processor:
        LareProcessor
    + Details:
         start  ~>  exitus616   [A ~=> 0.0,A ~+> tick,B ~+> B,tick ~+> tick,K ~+> B,A ~*> B,K ~*> B]
        + <eval2  ~>  eval2>  [A ~=> 0.0,A ~+> tick,B ~+> B,tick ~+> tick,K ~+> B,A ~*> B,K ~*> B]

YES(?,O(n^1))