YES
* Step 1: UnreachableRules YES
    + Considered Problem:
        Rules:
          0. f8(A,B,C) -> f12(2,1,C) [A = 2]  (?,1)
          1. f8(A,B,C) -> f12(A,0,C) [1 >= A] (?,1)
          2. f8(A,B,C) -> f12(A,0,C) [A >= 3] (?,1)
          3. f0(A,B,C) -> f12(1,1,1) True     (1,1)
        Signature:
          {(f0,3);(f12,3);(f8,3)}
        Flow Graph:
          [0->{},1->{},2->{},3->{}]
        
    + Applied Processor:
        UnreachableRules
    + Details:
        Following transitions are not reachable from the starting states and are revomed: [0,1,2]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          3. f0(A,B,C) -> f12(1,1,1) True (1,1)
        Signature:
          {(f0,3);(f12,3);(f8,3)}
        Flow Graph:
          [3->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C) -> f12(1,1,1)  True
        Signature:
          {(f0,3);(f12,3);(f8,3)}
        Rule Graph:
          [3->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [3]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C) -> f12(1,1,1)  True
        Signature:
          {(f0,3);(f12,3);(f8,3)}
        Rule Graph:
          [3->{}]
        ,We construct a looptree:
          P: [3])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES