YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. f1(A,B,C) -> f3(A,D,C)     [A >= 500] (?,1)
          1. f1(A,B,C) -> f1(1 + A,B,C) [499 >= A] (?,1)
          2. f2(A,B,C) -> f3(E,D,E)     [E >= 500] (1,1)
          3. f2(A,B,C) -> f1(1 + D,B,D) [499 >= D] (1,1)
        Signature:
          {(f1,3);(f2,3);(f3,3)}
        Flow Graph:
          [0->{},1->{0,1},2->{},3->{0,1}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          f1(A,B,C) -> f3(A,D,C)      [A >= 500]
          f1(A,B,C) -> f1(1 + A,B,C)  [499 >= A]
          f2(A,B,C) -> f3(E,D,E)      [E >= 500]
          f2(A,B,C) -> f1(1 + D,B,D)  [499 >= D]
        Signature:
          {(f1,3);(f2,3);(f3,3)}
        Rule Graph:
          [0->{},1->{0,1},2->{},3->{0,1}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          f1(A,B,C) -> f3(A,D,C)      [A >= 500]
          f1(A,B,C) -> f1(1 + A,B,C)  [499 >= A]
          f2(A,B,C) -> f3(E,D,E)      [E >= 500]
          f2(A,B,C) -> f1(1 + D,B,D)  [499 >= D]
        Signature:
          {(f1,3);(f2,3);(f3,3)}
        Rule Graph:
          [0->{},1->{0,1},2->{},3->{0,1}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES