YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A) -> f4(B)     True               (1,1)
          1. f4(A) -> f4(1 + A) [3 >= A && A >= 1] (?,1)
          2. f4(A) -> f4(1)     [0 >= A && 3 >= A] (?,1)
          3. f4(A) -> f12(A)    [A >= 4]           (?,1)
        Signature:
          {(f0,1);(f12,1);(f4,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,2),(2,2),(2,3)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A) -> f4(B)     True               (1,1)
          1. f4(A) -> f4(1 + A) [3 >= A && A >= 1] (?,1)
          2. f4(A) -> f4(1)     [0 >= A && 3 >= A] (?,1)
          3. f4(A) -> f12(A)    [A >= 4]           (?,1)
        Signature:
          {(f0,1);(f12,1);(f4,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,3},2->{1},3->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A) -> f4(B)      True
          f4(A) -> f4(1 + A)  [3 >= A && A >= 1]
          f4(A) -> f4(1)      [0 >= A && 3 >= A]
          f4(A) -> f12(A)     [A >= 4]
        Signature:
          {(f0,1);(f12,1);(f4,1)}
        Rule Graph:
          [0->{1,2,3},1->{1,3},2->{1},3->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A) -> f4(B)      True
          f4(A) -> f4(1 + A)  [3 >= A && A >= 1]
          f4(A) -> f4(1)      [0 >= A && 3 >= A]
          f4(A) -> f12(A)     [A >= 4]
        Signature:
          {(f0,1);(f12,1);(f4,1)}
        Rule Graph:
          [0->{1,2,3},1->{1,3},2->{1},3->{}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES