YES(?,O(n^1))
* Step 1: TrivialSCCs WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f1(0,B,C,D)          True                                                       (1,1)
          1. f1(A,B,C,D) -> f2(A,B,C,E)          [-1*A >= 0 && A >= 0 && B >= C]                            (?,1)
          2. f1(A,B,C,D) -> f2(1,1 + B,C,E)      [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0]                (?,1)
          3. f1(A,B,C,D) -> f1(0,1 + B,-1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1)
        Signature:
          {(f1,4);(f2,4);(f3,4)}
        Flow Graph:
          [0->{1,2,3},1->{},2->{},3->{1,2,3}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: AddSinks WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f1(0,B,C,D)          True                                                       (1,1)
          1. f1(A,B,C,D) -> f2(A,B,C,E)          [-1*A >= 0 && A >= 0 && B >= C]                            (1,1)
          2. f1(A,B,C,D) -> f2(1,1 + B,C,E)      [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0]                (1,1)
          3. f1(A,B,C,D) -> f1(0,1 + B,-1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1)
        Signature:
          {(f1,4);(f2,4);(f3,4)}
        Flow Graph:
          [0->{1,2,3},1->{},2->{},3->{1,2,3}]
        
    + Applied Processor:
        AddSinks
    + Details:
        ()
* Step 3: LooptreeTransformer WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A,B,C,D) -> f1(0,B,C,D)          True                                                       (1,1)
          1. f1(A,B,C,D) -> f2(A,B,C,E)          [-1*A >= 0 && A >= 0 && B >= C]                            (?,1)
          2. f1(A,B,C,D) -> f2(1,1 + B,C,E)      [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0]                (?,1)
          3. f1(A,B,C,D) -> f1(0,1 + B,-1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1)
          4. f1(A,B,C,D) -> exitus616(A,B,C,D)   True                                                       (?,1)
        Signature:
          {(exitus616,4);(f1,4);(f2,4);(f3,4)}
        Flow Graph:
          [0->{1,2,3,4},1->{},2->{},3->{1,2,3,4},4->{}]
        
    + Applied Processor:
        LooptreeTransformer
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[3] c: [3]
* Step 4: SizeAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        (Rules:
          0. f3(A,B,C,D) -> f1(0,B,C,D)          True                                                       (1,1)
          1. f1(A,B,C,D) -> f2(A,B,C,E)          [-1*A >= 0 && A >= 0 && B >= C]                            (?,1)
          2. f1(A,B,C,D) -> f2(1,1 + B,C,E)      [-1*A >= 0 && A >= 0 && 1 + B = C && A = 0]                (?,1)
          3. f1(A,B,C,D) -> f1(0,1 + B,-1 + C,D) [-1*A >= 0 && A >= 0 && C >= 2 + B && C >= 1 + B && A = 0] (?,1)
          4. f1(A,B,C,D) -> exitus616(A,B,C,D)   True                                                       (?,1)
        Signature:
          {(exitus616,4);(f1,4);(f2,4);(f3,4)}
        Flow Graph:
          [0->{1,2,3,4},1->{},2->{},3->{1,2,3,4},4->{}]
        
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[3] c: [3])
    + Applied Processor:
        SizeAbstraction UseCFG Minimize
    + Details:
        ()
* Step 5: FlowAbstraction WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,C,D,0.0]
           f3  ~>  f1          [A <= 0*K, B <= B, C <= C, D <= D]
           f1  ~>  f2          [A <= A, B <= B, C <= C, D <= unknown]
           f1  ~>  f2          [A <= K, B <= C, C <= C, D <= unknown]
           f1  ~>  f1          [A <= 0*K, B <= B + C, C <= B + C, D <= D]
           f1  ~>  exitus616   [A <= A, B <= B, C <= C, D <= D]
          + Loop: [0.0 <= B + C]
               f1  ~>  f1   [A <= 0*K, B <= B + C, C <= B + C, D <= D]
    + Applied Processor:
        FlowAbstraction
    + Details:
        ()
* Step 6: LareProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,D,0.0]
           f3  ~>  f1          [K ~=> A]
           f1  ~>  f2          [huge ~=> D]
           f1  ~>  f2          [C ~=> B,K ~=> A,huge ~=> D]
           f1  ~>  f1          [K ~=> A,B ~+> B,B ~+> C,C ~+> B,C ~+> C]
           f1  ~>  exitus616   []
          + Loop: [B ~+> 0.0,C ~+> 0.0]
               f1  ~>  f1   [K ~=> A,B ~+> B,B ~+> C,C ~+> B,C ~+> C]
    + Applied Processor:
        LareProcessor
    + Details:
         f3  ~>  exitus616   [K ~=> A
                             ,B ~+> B
                             ,B ~+> C
                             ,B ~+> 0.0
                             ,B ~+> tick
                             ,C ~+> B
                             ,C ~+> C
                             ,C ~+> 0.0
                             ,C ~+> tick
                             ,tick ~+> tick
                             ,B ~*> B
                             ,B ~*> C
                             ,C ~*> B
                             ,C ~*> C
                             ,B ~^> B
                             ,B ~^> C
                             ,C ~^> B
                             ,C ~^> C]
         f3  ~>  f2          [C ~=> B
                             ,K ~=> A
                             ,huge ~=> D
                             ,B ~+> B
                             ,B ~+> C
                             ,B ~+> 0.0
                             ,B ~+> tick
                             ,C ~+> B
                             ,C ~+> C
                             ,C ~+> 0.0
                             ,C ~+> tick
                             ,tick ~+> tick
                             ,B ~*> B
                             ,B ~*> C
                             ,C ~*> B
                             ,C ~*> C
                             ,B ~^> B
                             ,B ~^> C
                             ,C ~^> B
                             ,C ~^> C]
        + <f1  ~>  f1>  [K ~=> A
                        ,B ~+> B
                        ,B ~+> C
                        ,B ~+> 0.0
                        ,B ~+> tick
                        ,C ~+> B
                        ,C ~+> C
                        ,C ~+> 0.0
                        ,C ~+> tick
                        ,tick ~+> tick
                        ,B ~*> B
                        ,B ~*> C
                        ,C ~*> B
                        ,C ~*> C
                        ,B ~^> B
                        ,B ~^> C
                        ,C ~^> B
                        ,C ~^> C]

YES(?,O(n^1))