NO
* Step 1: UnsatPaths NO
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(A,A)         [A = B]      (1,1)
          1. f1(A,B) -> f1(1 + A,1 + B) True         (?,1)
          2. f1(A,B) -> f2(A,B)         True         (?,1)
          3. f1(A,B) -> f10000(A,B)     [A >= 1 + B] (?,1)
        Signature:
          {(f0,2);(f1,2);(f10000,2);(f2,2)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3)]
* Step 2: FromIts NO
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f1(A,A)         [A = B]      (1,1)
          1. f1(A,B) -> f1(1 + A,1 + B) True         (?,1)
          2. f1(A,B) -> f2(A,B)         True         (?,1)
          3. f1(A,B) -> f10000(A,B)     [A >= 1 + B] (?,1)
        Signature:
          {(f0,2);(f1,2);(f10000,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: CloseWith NO
    + Considered Problem:
        Rules:
          f0(A,B) -> f1(A,A)          [A = B]
          f1(A,B) -> f1(1 + A,1 + B)  True
          f1(A,B) -> f2(A,B)          True
          f1(A,B) -> f10000(A,B)      [A >= 1 + B]
        Signature:
          {(f0,2);(f1,2);(f10000,2);(f2,2)}
        Rule Graph:
          [0->{1,2},1->{1,2,3},2->{},3->{}]
    + Applied Processor:
        CloseWith False
    + Details:
        ()

NO