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*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1)
          2. eval2(A,B) -> eval1(A,B)           [A + -1*B >= 0 && -1*A + B >= 0 && 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: FromIts 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*B >= 0 && -1*A + B >= 0 && A >= 1] (?,1)
          2. eval2(A,B) -> eval1(A,B)           [A + -1*B >= 0 && -1*A + B >= 0 && 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:
        FromIts
    + Details:
        ()
* Step 3: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          eval1(A,B) -> eval2(A,B)            [A >= 1 && B = A]
          eval2(A,B) -> eval2(-1 + A,-1 + B)  [A + -1*B >= 0 && -1*A + B >= 0 && A >= 1]
          eval2(A,B) -> eval1(A,B)            [A + -1*B >= 0 && -1*A + B >= 0 && 0 >= A]
          start(A,B) -> eval1(A,B)            True
        Signature:
          {(eval1,2);(eval2,2);(start,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{},3->{0}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          eval1(A,B) -> eval2(A,B)            [A >= 1 && B = A]
          eval2(A,B) -> eval2(-1 + A,-1 + B)  [A + -1*B >= 0 && -1*A + B >= 0 && A >= 1]
          eval2(A,B) -> eval1(A,B)            [A + -1*B >= 0 && -1*A + B >= 0 && 0 >= A]
          start(A,B) -> eval1(A,B)            True
          eval1(A,B) -> exitus616(A,B)        True
        Signature:
          {(eval1,2);(eval2,2);(exitus616,2);(start,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{4},3->{0}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1] c: [1]
* Step 5: AbstractSize WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          eval1(A,B) -> eval2(A,B)            [A >= 1 && B = A]
          eval2(A,B) -> eval2(-1 + A,-1 + B)  [A + -1*B >= 0 && -1*A + B >= 0 && A >= 1]
          eval2(A,B) -> eval1(A,B)            [A + -1*B >= 0 && -1*A + B >= 0 && 0 >= A]
          start(A,B) -> eval1(A,B)            True
          eval1(A,B) -> exitus616(A,B)        True
        Signature:
          {(eval1,2);(eval2,2);(exitus616,2);(start,2)}
        Rule Graph:
          [0->{1},1->{1,2},2->{4},3->{0}]
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- 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]
           eval1  ~>  eval2       [A <= A, B <= B]
           eval2  ~>  eval2       [A <= B, B <= B]
           eval2  ~>  eval1       [A <= A, B <= B]
           start  ~>  eval1       [A <= A, B <= B]
           eval1  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A]
               eval2  ~>  eval2   [A <= B, 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]
           eval1  ~>  eval2       []
           eval2  ~>  eval2       [B ~=> A]
           eval2  ~>  eval1       []
           start  ~>  eval1       []
           eval1  ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~+> 0.0]
               eval2  ~>  eval2   [B ~=> A]
    + Applied Processor:
        Lare
    + Details:
         start  ~>  exitus616   [B ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick]
        + <eval2  ~>  eval2>  [B ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick]

YES(?,O(n^1))