YES(?,O(1))
* Step 1: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)     True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 0 && A >= 10] (?,1)
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + 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. f3(A,B,C,D) -> f0(0,B,C,D)     True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 0 && A >= 10] (1,1)
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 3: AddSinks WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)     True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 0 && A >= 10] (1,1)
        Signature:
          {(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)        True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 0 && A >= 10] (?,1)
          3. f0(A,B,C,D) -> exitus616(A,B,C,D) True                (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 5: LooptreeTransformer WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)        True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 0 && A >= 10] (?,1)
          3. f0(A,B,C,D) -> exitus616(A,B,C,D) True                (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]
* Step 6: SizeAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        (Rules:
          0. f3(A,B,C,D) -> f0(0,B,C,D)        True                (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [A >= 0 && 9 >= A]  (?,1)
          2. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 0 && A >= 10] (?,1)
          3. f0(A,B,C,D) -> exitus616(A,B,C,D) True                (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{1,3},1->{1,2,3},2->{},3->{}]
        
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 7: FlowAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [A,B,C,D,0.0]
           f3  ~>  f0          [A <= 0*K, B <= B, C <= C, D <= D]
           f0  ~>  f0          [A <= 10*K, B <= B, C <= A, D <= D]
           f0  ~>  f4          [A <= A, B <= unknown, C <= C, D <= D]
           f0  ~>  exitus616   [A <= A, B <= B, C <= C, D <= D]
          + Loop: [0.0 <= 10*K + A]
               f0  ~>  f0   [A <= 10*K, B <= B, C <= A, D <= D]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 8: LareProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,D,0.0]
           f3  ~>  f0          [K ~=> A]
           f0  ~>  f0          [A ~=> C,K ~=> A]
           f0  ~>  f4          [huge ~=> B]
           f0  ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~*> 0.0]
               f0  ~>  f0   [A ~=> C,K ~=> A]
    + Applied Processor:
        LareProcessor
    + Details:
         f3  ~>  exitus616   [K ~=> A,K ~=> C,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick]
         f3  ~>  f4          [K ~=> A,K ~=> C,huge ~=> B,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick]
        + <f0  ~>  f0>  [A ~=> C,K ~=> A,K ~=> C,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick]

YES(?,O(1))