YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f1(A,B,C) -> f1(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f3(A,B,C) -> f1(A,B,C)     [B >= 1 + C]           (1,1)
          2. f1(A,B,C) -> f1(A,B,1 + C) [B >= 2 + C && B >= A] (?,1)
        Signature:
          {(f1,3);(f3,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{0,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f1(A,B,C) -> f1(A,1 + B,C) [A >= 1 + B]           (?,1)
          1. f3(A,B,C) -> f1(A,B,C)     [B >= 1 + C]           (1,1)
          2. f1(A,B,C) -> f1(A,B,1 + C) [B >= 2 + C && B >= A] (?,1)
        Signature:
          {(f1,3);(f3,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f1(A,B,C) -> f1(A,1 + B,C)  [A >= 1 + B]
          f3(A,B,C) -> f1(A,B,C)      [B >= 1 + C]
          f1(A,B,C) -> f1(A,B,1 + C)  [B >= 2 + C && B >= A]
        Signature:
          {(f1,3);(f3,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{2}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          +- p:[0] c: [0]
          |
          `- p:[2] c: [2]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f1(A,B,C) -> f1(A,1 + B,C)  [A >= 1 + B]
          f3(A,B,C) -> f1(A,B,C)      [B >= 1 + C]
          f1(A,B,C) -> f1(A,B,1 + C)  [B >= 2 + C && B >= A]
        Signature:
          {(f1,3);(f3,3)}
        Rule Graph:
          [0->{0,2},1->{0,2},2->{2}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          +- p:[0] c: [0]
          |
          `- p:[2] c: [2])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES