YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f3(A,1)      [-1*B >= 0 && B >= 0 && 0 >= A] (?,1)
          1. f0(A,B) -> f2(A,0)      True                            (1,1)
          2. f2(A,B) -> f2(-1 + A,B) [-1*B >= 0 && B >= 0 && A >= 1] (?,1)
        Signature:
          {(f0,2);(f2,2);(f3,2)}
        Flow Graph:
          [0->{},1->{0,2},2->{0,2}]
        
    + Applied Processor:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: Looptree YES
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f3(A,1)      [-1*B >= 0 && B >= 0 && 0 >= A] (1,1)
          1. f0(A,B) -> f2(A,0)      True                            (1,1)
          2. f2(A,B) -> f2(-1 + A,B) [-1*B >= 0 && B >= 0 && A >= 1] (?,1)
        Signature:
          {(f0,2);(f2,2);(f3,2)}
        Flow Graph:
          [0->{},1->{0,2},2->{0,2}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          `- p:[2] c: [2]

YES