YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          1. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(1,2),(2,1)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f1(A,B,2)      [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1)
          1. f1(A,B,C) -> f1(A,1 + B,C)  [A + C >= 1 + 2*B]                     (?,1)
          2. f1(A,B,C) -> f1(A,-1 + B,C) [2*B >= 2 + A + C]                     (?,1)
        Signature:
          {(f0,3);(f1,3)}
        Flow Graph:
          [0->{1,2},1->{1},2->{2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C) -> f1(A,B,2)       [A >= 0 && 3 >= A && 3 >= B && B >= 0]
          f1(A,B,C) -> f1(A,1 + B,C)   [A + C >= 1 + 2*B]
          f1(A,B,C) -> f1(A,-1 + B,C)  [2*B >= 2 + A + C]
        Signature:
          {(f0,3);(f1,3)}
        Rule Graph:
          [0->{1,2},1->{1},2->{2}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          +- p:[2] c: [2]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C) -> f1(A,B,2)       [A >= 0 && 3 >= A && 3 >= B && B >= 0]
          f1(A,B,C) -> f1(A,1 + B,C)   [A + C >= 1 + 2*B]
          f1(A,B,C) -> f1(A,-1 + B,C)  [2*B >= 2 + A + C]
        Signature:
          {(f0,3);(f1,3)}
        Rule Graph:
          [0->{1,2},1->{1},2->{2}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          +- p:[2] c: [2]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES