YES(?,O(1))
* Step 1: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C,D) -> f2(1 + A,1 + B,-1 + C,D) True                                     (?,1)
          1. f1(A,B,C,D) -> f2(A,B,C,D)              [A >= C && B >= 1 + A && C >= 1 + B]     (1,1)
          2. f1(A,B,C,D) -> f300(A,B,C,E)            [C >= 1 + B && B >= 1 + A && C >= 1 + A] (1,1)
          3. f1(A,B,C,D) -> f300(A,B,C,E)            [B >= 1 + A && B >= C]                   (1,1)
          4. f1(A,B,C,D) -> f300(A,B,C,E)            [A >= B]                                 (1,1)
        Signature:
          {(f1,4);(f2,4);(f300,4)}
        Flow Graph:
          [0->{0},1->{0},2->{},3->{},4->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,0)]
* Step 2: UnreachableRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C,D) -> f2(1 + A,1 + B,-1 + C,D) True                                     (?,1)
          1. f1(A,B,C,D) -> f2(A,B,C,D)              [A >= C && B >= 1 + A && C >= 1 + B]     (1,1)
          2. f1(A,B,C,D) -> f300(A,B,C,E)            [C >= 1 + B && B >= 1 + A && C >= 1 + A] (1,1)
          3. f1(A,B,C,D) -> f300(A,B,C,E)            [B >= 1 + A && B >= C]                   (1,1)
          4. f1(A,B,C,D) -> f300(A,B,C,E)            [A >= B]                                 (1,1)
        Signature:
          {(f1,4);(f2,4);(f300,4)}
        Flow Graph:
          [0->{0},1->{},2->{},3->{},4->{}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [0]
* Step 3: TrivialSCCs WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          1. f1(A,B,C,D) -> f2(A,B,C,D)   [A >= C && B >= 1 + A && C >= 1 + B]     (1,1)
          2. f1(A,B,C,D) -> f300(A,B,C,E) [C >= 1 + B && B >= 1 + A && C >= 1 + A] (1,1)
          3. f1(A,B,C,D) -> f300(A,B,C,E) [B >= 1 + A && B >= C]                   (1,1)
          4. f1(A,B,C,D) -> f300(A,B,C,E) [A >= B]                                 (1,1)
        Signature:
          {(f1,4);(f2,4);(f300,4)}
        Flow Graph:
          [1->{},2->{},3->{},4->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        The problem is already solved.

YES(?,O(1))