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

YES