YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [B >= 10]            (?,1)
          3. f1(A,B,C,D,E)   -> f300(1000,B,C,D,E)   True                 (1,1)
        Signature:
          {(f1,5);(f2,5);(f300,5)}
        Flow Graph:
          [0->{0,1,2},1->{},2->{},3->{0,1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(3,1)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E) [A >= 101 && 9 >= B] (?,1)
          1. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [100 >= A && 9 >= B] (?,1)
          2. f300(A,B,C,D,E) -> f2(A,B,0,0,0)        [B >= 10]            (?,1)
          3. f1(A,B,C,D,E)   -> f300(1000,B,C,D,E)   True                 (1,1)
        Signature:
          {(f1,5);(f2,5);(f300,5)}
        Flow Graph:
          [0->{0,1},1->{},2->{},3->{0,2}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E)  [A >= 101 && 9 >= B]
          f300(A,B,C,D,E) -> f2(A,B,0,0,0)         [100 >= A && 9 >= B]
          f300(A,B,C,D,E) -> f2(A,B,0,0,0)         [B >= 10]
          f1(A,B,C,D,E)   -> f300(1000,B,C,D,E)    True
        Signature:
          {(f1,5);(f2,5);(f300,5)}
        Rule Graph:
          [0->{0,1},1->{},2->{},3->{0,2}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0] c: [0]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f300(A,B,C,D,E) -> f300(-1 + A,B,C,D,E)  [A >= 101 && 9 >= B]
          f300(A,B,C,D,E) -> f2(A,B,0,0,0)         [100 >= A && 9 >= B]
          f300(A,B,C,D,E) -> f2(A,B,0,0,0)         [B >= 10]
          f1(A,B,C,D,E)   -> f300(1000,B,C,D,E)    True
        Signature:
          {(f1,5);(f2,5);(f300,5)}
        Rule Graph:
          [0->{0,1},1->{},2->{},3->{0,2}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[0] c: [0])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES