YES(?,O(1))
* Step 1: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                                                               (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [A >= 0 && 1 >= A]                                                 (?,1)
          2. f10(A,B) -> f10(A,1 + B) [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && 1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 0 && A >= 2]                                                 (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1,5},1->{1,5},2->{2,3,4},3->{},4->{},5->{2,3,4}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,5),(5,3),(5,4)]
* Step 2: FromIts WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                                                               (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [A >= 0 && 1 >= A]                                                 (?,1)
          2. f10(A,B) -> f10(A,1 + B) [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && 1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 0 && A >= 2]                                                 (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2,3,4},3->{},4->{},5->{2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: AddSinks WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          f0(A,B)  -> f4(0,B)       True
          f4(A,B)  -> f4(1 + A,B)   [A >= 0 && 1 >= A]
          f10(A,B) -> f10(A,1 + B)  [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && 1 >= B]
          f10(A,B) -> f18(A,B)      [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2 && 0 >= 1 + C]
          f10(A,B) -> f18(A,B)      [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2]
          f4(A,B)  -> f10(A,0)      [A >= 0 && A >= 2]
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Rule Graph:
          [0->{1},1->{1,5},2->{2,3,4},3->{},4->{},5->{2}]
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: Decompose WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          f0(A,B)  -> f4(0,B)         True
          f4(A,B)  -> f4(1 + A,B)     [A >= 0 && 1 >= A]
          f10(A,B) -> f10(A,1 + B)    [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && 1 >= B]
          f10(A,B) -> f18(A,B)        [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2 && 0 >= 1 + C]
          f10(A,B) -> f18(A,B)        [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2]
          f4(A,B)  -> f10(A,0)        [A >= 0 && A >= 2]
          f18(A,B) -> exitus616(A,B)  True
          f18(A,B) -> exitus616(A,B)  True
        Signature:
          {(exitus616,2);(f0,2);(f10,2);(f18,2);(f4,2)}
        Rule Graph:
          [0->{1},1->{1,5},2->{2,3,4},3->{7},4->{6},5->{2}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7]
          |
          +- p:[1] c: [1]
          |
          `- p:[2] c: [2]
* Step 5: AbstractSize WORST_CASE(?,O(1))
    + Considered Problem:
        (Rules:
          f0(A,B)  -> f4(0,B)         True
          f4(A,B)  -> f4(1 + A,B)     [A >= 0 && 1 >= A]
          f10(A,B) -> f10(A,1 + B)    [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && 1 >= B]
          f10(A,B) -> f18(A,B)        [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2 && 0 >= 1 + C]
          f10(A,B) -> f18(A,B)        [B >= 0 && -2 + A + B >= 0 && -2 + A >= 0 && B >= 2]
          f4(A,B)  -> f10(A,0)        [A >= 0 && A >= 2]
          f18(A,B) -> exitus616(A,B)  True
          f18(A,B) -> exitus616(A,B)  True
        Signature:
          {(exitus616,2);(f0,2);(f10,2);(f18,2);(f4,2)}
        Rule Graph:
          [0->{1},1->{1,5},2->{2,3,4},3->{7},4->{6},5->{2}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7]
          |
          +- p:[1] c: [1]
          |
          `- p:[2] c: [2])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 6: AbstractFlow WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [A,B,0.0,0.1]
           f0   ~>  f4          [A <= 0*K, B <= B]
           f4   ~>  f4          [A <= 2*K, B <= B]
           f10  ~>  f10         [A <= A, B <= 2*K]
           f10  ~>  f18         [A <= A, B <= B]
           f10  ~>  f18         [A <= A, B <= B]
           f4   ~>  f10         [A <= A, B <= 0*K]
           f18  ~>  exitus616   [A <= A, B <= B]
           f18  ~>  exitus616   [A <= A, B <= B]
          + Loop: [0.0 <= K + A]
               f4  ~>  f4   [A <= 2*K, B <= B]
          + Loop: [0.1 <= K + B]
               f10  ~>  f10   [A <= A, B <= 2*K]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 7: Lare WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,0.0,0.1]
           f0   ~>  f4          [K ~=> A]
           f4   ~>  f4          [K ~=> A]
           f10  ~>  f10         [K ~=> B]
           f10  ~>  f18         []
           f10  ~>  f18         []
           f4   ~>  f10         [K ~=> B]
           f18  ~>  exitus616   []
           f18  ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~+> 0.0]
               f4  ~>  f4   [K ~=> A]
          + Loop: [B ~+> 0.1,K ~+> 0.1]
               f10  ~>  f10   [K ~=> B]
    + Applied Processor:
        Lare
    + Details:
         f0  ~>  exitus616   [K ~=> A
                             ,K ~=> B
                             ,tick ~+> tick
                             ,K ~+> 0.0
                             ,K ~+> 0.1
                             ,K ~+> tick
                             ,K ~*> 0.0
                             ,K ~*> 0.1
                             ,K ~*> tick]
        + <f4  ~>  f4>  [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~+> 0.0,K ~+> tick]
        + <f10  ~>  f10>  [K ~=> B,B ~+> 0.1,B ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick]

YES(?,O(1))