YES(?,O(1))
* Step 1: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C)  -> f8(D,0,C)      True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)  [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C) [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)     [C >= 10] (?,1)
          4. f8(A,B,C)  -> f19(A,B,0)     [B >= 10] (?,1)
        Signature:
          {(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C)  -> f8(D,0,C)      True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)  [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C) [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)     [C >= 10] (1,1)
          4. f8(A,B,C)  -> f19(A,B,0)     [B >= 10] (1,1)
        Signature:
          {(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1,4},1->{1,4},2->{2,3},3->{},4->{2,3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,4),(4,3)]
* Step 3: AddSinks WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C)  -> f8(D,0,C)      True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)  [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C) [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)     [C >= 10] (1,1)
          4. f8(A,B,C)  -> f19(A,B,0)     [B >= 10] (1,1)
        Signature:
          {(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,4},2->{2,3},3->{},4->{2}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C)  -> f8(D,0,C)        True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)    [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C)   [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)       [C >= 10] (?,1)
          4. f8(A,B,C)  -> f19(A,B,0)       [B >= 10] (?,1)
          5. f19(A,B,C) -> exitus616(A,B,C) True      (?,1)
        Signature:
          {(exitus616,3);(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1,4},1->{1,4},2->{2,3,5},3->{},4->{2,3,5},5->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,4),(4,3)]
* Step 5: LooptreeTransformer WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C)  -> f8(D,0,C)        True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)    [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C)   [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)       [C >= 10] (?,1)
          4. f8(A,B,C)  -> f19(A,B,0)       [B >= 10] (?,1)
          5. f19(A,B,C) -> exitus616(A,B,C) True      (?,1)
        Signature:
          {(exitus616,3);(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[2] c: [2]
* Step 6: SizeAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        (Rules:
          0. f0(A,B,C)  -> f8(D,0,C)        True      (1,1)
          1. f8(A,B,C)  -> f8(A,1 + B,C)    [9 >= B]  (?,1)
          2. f19(A,B,C) -> f19(A,B,1 + C)   [9 >= C]  (?,1)
          3. f19(A,B,C) -> f29(A,B,C)       [C >= 10] (?,1)
          4. f8(A,B,C)  -> f19(A,B,0)       [B >= 10] (?,1)
          5. f19(A,B,C) -> exitus616(A,B,C) True      (?,1)
        Signature:
          {(exitus616,3);(f0,3);(f19,3);(f29,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,4},2->{2,3,5},3->{},4->{2,5},5->{}]
        
        ,We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[2] c: [2])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 7: FlowAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [A,B,C,0.0,0.1]
           f0   ~>  f8          [A <= unknown, B <= 0*K, C <= C]
           f8   ~>  f8          [A <= A, B <= K + B, C <= C]
           f19  ~>  f19         [A <= A, B <= B, C <= K + C]
           f19  ~>  f29         [A <= A, B <= B, C <= C]
           f8   ~>  f19         [A <= A, B <= B, C <= 0*K]
           f19  ~>  exitus616   [A <= A, B <= B, C <= C]
          + Loop: [0.0 <= 10*K + B]
               f8  ~>  f8   [A <= A, B <= K + B, C <= C]
          + Loop: [0.1 <= 10*K + C]
               f19  ~>  f19   [A <= A, B <= B, C <= K + C]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 8: LareProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,0.0,0.1]
           f0   ~>  f8          [K ~=> B,huge ~=> A]
           f8   ~>  f8          [B ~+> B,K ~+> B]
           f19  ~>  f19         [C ~+> C,K ~+> C]
           f19  ~>  f29         []
           f8   ~>  f19         [K ~=> C]
           f19  ~>  exitus616   []
          + Loop: [B ~+> 0.0,K ~*> 0.0]
               f8  ~>  f8   [B ~+> B,K ~+> B]
          + Loop: [C ~+> 0.1,K ~*> 0.1]
               f19  ~>  f19   [C ~+> C,K ~+> C]
    + Applied Processor:
        LareProcessor
    + Details:
         f0  ~>  f29         [K ~=> B
                             ,K ~=> C
                             ,huge ~=> A
                             ,tick ~+> tick
                             ,K ~+> B
                             ,K ~+> C
                             ,K ~+> 0.0
                             ,K ~+> 0.1
                             ,K ~+> tick
                             ,K ~*> B
                             ,K ~*> C
                             ,K ~*> 0.0
                             ,K ~*> 0.1
                             ,K ~*> tick]
         f0  ~>  exitus616   [K ~=> B
                             ,K ~=> C
                             ,huge ~=> A
                             ,tick ~+> tick
                             ,K ~+> B
                             ,K ~+> C
                             ,K ~+> 0.0
                             ,K ~+> 0.1
                             ,K ~+> tick
                             ,K ~*> B
                             ,K ~*> C
                             ,K ~*> 0.0
                             ,K ~*> 0.1
                             ,K ~*> tick]
        + <f8  ~>  f8>  [B ~+> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~+> B,B ~*> B,K ~*> B,K ~*> 0.0,K ~*> tick]
        + <f19  ~>  f19>  [C ~+> C,C ~+> 0.1,C ~+> tick,tick ~+> tick,K ~+> C,C ~*> C,K ~*> C,K ~*> 0.1,K ~*> tick]

YES(?,O(1))