YES(?,O(n^1))
* Step 1: ArgumentFilter WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C) -> f2(A + -1*B,1 + B,C) [-1 + B >= 0 && A >= 1] (?,1)
          1. f3(A,B,C) -> f2(A,B,C)            [B >= 1]                (1,1)
          2. f2(A,B,C) -> f4(A,B,D)            [-1 + B >= 0 && 0 >= A] (?,1)
          3. f3(A,B,C) -> f4(A,B,D)            [0 >= B]                (1,1)
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        
    + Applied Processor:
        ArgumentFilter [2]
    + Details:
        We remove following argument positions: [2].
* Step 2: FromIts WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [-1 + B >= 0 && A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1]                (1,1)
          2. f2(A,B) -> f4(A,B)            [-1 + B >= 0 && 0 >= A] (?,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B]                (1,1)
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          f2(A,B) -> f2(A + -1*B,1 + B)  [-1 + B >= 0 && A >= 1]
          f3(A,B) -> f2(A,B)             [B >= 1]
          f2(A,B) -> f4(A,B)             [-1 + B >= 0 && 0 >= A]
          f3(A,B) -> f4(A,B)             [0 >= B]
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: Decompose WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          f2(A,B) -> f2(A + -1*B,1 + B)  [-1 + B >= 0 && A >= 1]
          f3(A,B) -> f2(A,B)             [B >= 1]
          f2(A,B) -> f4(A,B)             [-1 + B >= 0 && 0 >= A]
          f3(A,B) -> f4(A,B)             [0 >= B]
          f4(A,B) -> exitus616(A,B)      True
          f4(A,B) -> exitus616(A,B)      True
        Signature:
          {(exitus616,2);(f2,3);(f3,3);(f4,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{5},3->{4}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          `- p:[0] c: [0]
* Step 5: AbstractSize WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          f2(A,B) -> f2(A + -1*B,1 + B)  [-1 + B >= 0 && A >= 1]
          f3(A,B) -> f2(A,B)             [B >= 1]
          f2(A,B) -> f4(A,B)             [-1 + B >= 0 && 0 >= A]
          f3(A,B) -> f4(A,B)             [0 >= B]
          f4(A,B) -> exitus616(A,B)      True
          f4(A,B) -> exitus616(A,B)      True
        Signature:
          {(exitus616,2);(f2,3);(f3,3);(f4,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{5},3->{4}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          `- p:[0] c: [0])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 6: AbstractFlow WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0]
           f2  ~>  f2          [A <= A + B, B <= K + B]
           f3  ~>  f2          [A <= A, B <= B]
           f2  ~>  f4          [A <= A, B <= B]
           f3  ~>  f4          [A <= A, B <= B]
           f4  ~>  exitus616   [A <= A, B <= B]
           f4  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A]
               f2  ~>  f2   [A <= A + B, B <= K + B]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 7: Lare WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0]
           f2  ~>  f2          [A ~+> A,B ~+> A,B ~+> B,K ~+> B]
           f3  ~>  f2          []
           f2  ~>  f4          []
           f3  ~>  f4          []
           f4  ~>  exitus616   []
           f4  ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~+> 0.0]
               f2  ~>  f2   [A ~+> A,B ~+> A,B ~+> B,K ~+> B]
    + Applied Processor:
        Lare
    + Details:
         f3  ~>  exitus616   [A ~+> A
                             ,A ~+> 0.0
                             ,A ~+> tick
                             ,B ~+> A
                             ,B ~+> B
                             ,tick ~+> tick
                             ,K ~+> A
                             ,K ~+> B
                             ,K ~+> 0.0
                             ,K ~+> tick
                             ,A ~*> A
                             ,A ~*> B
                             ,B ~*> A
                             ,K ~*> A
                             ,K ~*> B]
        + <f2  ~>  f2>  [A ~+> A
                        ,A ~+> 0.0
                        ,A ~+> tick
                        ,B ~+> A
                        ,B ~+> B
                        ,tick ~+> tick
                        ,K ~+> A
                        ,K ~+> B
                        ,K ~+> 0.0
                        ,K ~+> tick
                        ,A ~*> A
                        ,A ~*> B
                        ,B ~*> A
                        ,K ~*> A
                        ,K ~*> B]

YES(?,O(n^1))