YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f8(0,B,C,D)         True                             (1,1)
          1. f8(A,B,C,D) -> f8(1 + A,B,C,D)     [A >= 0 && 3 >= A]               (?,1)
          2. f8(A,B,C,D) -> f8(1 + A,A,1 + A,E) [A >= 0 && 3 >= A]               (?,1)
          3. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4 && 0 >= 1 + E] (?,1)
          4. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4]               (?,1)
        Signature:
          {(f0,4);(f23,4);(f8,4)}
        Flow Graph:
          [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f8(0,B,C,D)         True                             (1,1)
          1. f8(A,B,C,D) -> f8(1 + A,B,C,D)     [A >= 0 && 3 >= A]               (?,1)
          2. f8(A,B,C,D) -> f8(1 + A,A,1 + A,E) [A >= 0 && 3 >= A]               (?,1)
          3. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4 && 0 >= 1 + E] (1,1)
          4. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4]               (1,1)
        Signature:
          {(f0,4);(f23,4);(f8,4)}
        Flow Graph:
          [0->{1,2,3,4},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3),(0,4)]
* Step 3: Looptree YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f8(0,B,C,D)         True                             (1,1)
          1. f8(A,B,C,D) -> f8(1 + A,B,C,D)     [A >= 0 && 3 >= A]               (?,1)
          2. f8(A,B,C,D) -> f8(1 + A,A,1 + A,E) [A >= 0 && 3 >= A]               (?,1)
          3. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4 && 0 >= 1 + E] (1,1)
          4. f8(A,B,C,D) -> f23(A,B,C,D)        [A >= 0 && A >= 4]               (1,1)
        Signature:
          {(f0,4);(f23,4);(f8,4)}
        Flow Graph:
          [0->{1,2},1->{1,2,3,4},2->{1,2,3,4},3->{},4->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          `- p:[1,2] c: [2]
             |
             `- p:[1] c: [1]

YES