YES(?,O(1))
* Step 1: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10]         (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (?,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1},3->{0,1},4->{0,1}]
        
    + 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,D) -> f4(A,E,C,D)     [A >= 10]         (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (1,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (1,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{0,1},3->{0,1},4->{0,1}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0),(3,0),(4,0)]
* Step 3: UnreachableRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10]         (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]          (?,1)
          2. f1(A,B,C,D) -> f0(1,B,C,D)     [9 >= E && A = 0] (1,1)
          3. f2(A,B,C,D) -> f0(2,B,C,2)     [9 >= A]          (1,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True              (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},2->{1},3->{1},4->{1}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [2,3]
* Step 4: AddSinks WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)     [A >= 10] (1,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D) [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)     True      (1,1)
        Signature:
          {(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1},4->{1}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 5: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)        True      (1,1)
          5. f0(A,B,C,D) -> exitus616(A,B,C,D) True      (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1,5},4->{0,1,5},5->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(4,0)]
* Step 6: LooptreeTransformer WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)        True      (1,1)
          5. f0(A,B,C,D) -> exitus616(A,B,C,D) True      (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1,5},4->{1,5},5->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,4,5]
          |
          `- p:[1] c: [1]
* Step 7: SizeAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        (Rules:
          0. f0(A,B,C,D) -> f4(A,E,C,D)        [A >= 10] (?,1)
          1. f0(A,B,C,D) -> f0(1 + A,B,A,D)    [9 >= A]  (?,1)
          4. f3(A,B,C,D) -> f0(0,B,C,D)        True      (1,1)
          5. f0(A,B,C,D) -> exitus616(A,B,C,D) True      (?,1)
        Signature:
          {(exitus616,4);(f0,4);(f1,4);(f2,4);(f3,4);(f4,4)}
        Flow Graph:
          [0->{},1->{0,1,5},4->{1,5},5->{}]
        
        ,We construct a looptree:
          P: [0,1,4,5]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 8: FlowAbstraction WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [A,B,C,D,0.0]
           f0  ~>  f4          [A <= A, B <= unknown, C <= C, D <= D]
           f0  ~>  f0          [A <= K + A, B <= B, C <= A, D <= D]
           f3  ~>  f0          [A <= 0*K, B <= B, C <= C, D <= D]
           f0  ~>  exitus616   [A <= A, B <= B, C <= C, D <= D]
          + Loop: [0.0 <= 10*K + A]
               f0  ~>  f0   [A <= K + A, B <= B, C <= A, D <= D]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 9: LareProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,D,0.0]
           f0  ~>  f4          [huge ~=> B]
           f0  ~>  f0          [A ~=> C,A ~+> A,K ~+> A]
           f3  ~>  f0          [K ~=> A]
           f0  ~>  exitus616   []
          + Loop: [A ~+> 0.0,K ~*> 0.0]
               f0  ~>  f0   [A ~=> C,A ~+> A,K ~+> A]
    + Applied Processor:
        LareProcessor
    + Details:
         f3  ~>  exitus616   [K ~=> A
                             ,K ~=> C
                             ,tick ~+> tick
                             ,K ~+> A
                             ,K ~+> C
                             ,K ~+> 0.0
                             ,K ~+> tick
                             ,K ~*> A
                             ,K ~*> C
                             ,K ~*> 0.0
                             ,K ~*> tick]
         f3  ~>  f4          [K ~=> A
                             ,K ~=> C
                             ,huge ~=> B
                             ,tick ~+> tick
                             ,K ~+> A
                             ,K ~+> C
                             ,K ~+> 0.0
                             ,K ~+> tick
                             ,K ~*> A
                             ,K ~*> C
                             ,K ~*> 0.0
                             ,K ~*> tick]
        + <f0  ~>  f0>  [A ~=> C
                        ,A ~+> A
                        ,A ~+> C
                        ,A ~+> 0.0
                        ,A ~+> tick
                        ,tick ~+> tick
                        ,K ~+> A
                        ,K ~+> C
                        ,A ~*> A
                        ,K ~*> A
                        ,K ~*> C
                        ,K ~*> 0.0
                        ,K ~*> tick]

YES(?,O(1))