YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. f2(A,B,C) -> f2(A + -1*B,1 + B,C) [-1 + B >= 0 && A >= 1] (?,1)
          1. f3(A,B,C) -> f2(A,B,C)            [B >= 1]                (1,1)
          2. f2(A,B,C) -> f4(A,B,D)            [-1 + B >= 0 && 0 >= A] (?,1)
          3. f3(A,B,C) -> f4(A,B,D)            [0 >= B]                (1,1)
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          f2(A,B,C) -> f2(A + -1*B,1 + B,C)  [-1 + B >= 0 && A >= 1]
          f3(A,B,C) -> f2(A,B,C)             [B >= 1]
          f2(A,B,C) -> f4(A,B,D)             [-1 + B >= 0 && 0 >= A]
          f3(A,B,C) -> f4(A,B,D)             [0 >= B]
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0] c: [0]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          f2(A,B,C) -> f2(A + -1*B,1 + B,C)  [-1 + B >= 0 && A >= 1]
          f3(A,B,C) -> f2(A,B,C)             [B >= 1]
          f2(A,B,C) -> f4(A,B,D)             [-1 + B >= 0 && 0 >= A]
          f3(A,B,C) -> f4(A,B,D)             [0 >= B]
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0] c: [0])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES