YES
* Step 1: Looptree YES
    + Considered Problem:
        Rules:
          0. f3(A) -> f1(A)      [A >= 0]           (1,1)
          1. f1(A) -> f1(-1 + A) [A >= 0 && A >= 1] (?,1)
        Signature:
          {(f1,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1]
          |
          `- p:[1] c: [1]

YES