YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E)  -> f4(0,B,C,D,E)      True       (1,1)
          1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [199 >= B] (?,1)
          2. f20(A,B,C,D,E) -> f31(A,B,C,D,E)     [B >= 200] (?,1)
          3. f4(A,B,C,D,E)  -> f4(1 + A,B,C,A,A)  [99 >= A]  (?,1)
          4. f4(A,B,C,D,E)  -> f20(A,100,C,D,E)   [A >= 100] (?,1)
        Signature:
          {(f0,5);(f20,5);(f31,5);(f4,5)}
        Flow Graph:
          [0->{3,4},1->{1,2},2->{},3->{3,4},4->{1,2}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,4),(4,2)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E)  -> f4(0,B,C,D,E)      True       (1,1)
          1. f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E) [199 >= B] (?,1)
          2. f20(A,B,C,D,E) -> f31(A,B,C,D,E)     [B >= 200] (?,1)
          3. f4(A,B,C,D,E)  -> f4(1 + A,B,C,A,A)  [99 >= A]  (?,1)
          4. f4(A,B,C,D,E)  -> f20(A,100,C,D,E)   [A >= 100] (?,1)
        Signature:
          {(f0,5);(f20,5);(f31,5);(f4,5)}
        Flow Graph:
          [0->{3},1->{1,2},2->{},3->{3,4},4->{1}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D,E)  -> f4(0,B,C,D,E)       True
          f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E)  [199 >= B]
          f20(A,B,C,D,E) -> f31(A,B,C,D,E)      [B >= 200]
          f4(A,B,C,D,E)  -> f4(1 + A,B,C,A,A)   [99 >= A]
          f4(A,B,C,D,E)  -> f20(A,100,C,D,E)    [A >= 100]
        Signature:
          {(f0,5);(f20,5);(f31,5);(f4,5)}
        Rule Graph:
          [0->{3},1->{1,2},2->{},3->{3,4},4->{1}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          +- p:[3] c: [3]
          |
          `- p:[1] c: [1]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D,E)  -> f4(0,B,C,D,E)       True
          f20(A,B,C,D,E) -> f20(A,1 + B,B,D,E)  [199 >= B]
          f20(A,B,C,D,E) -> f31(A,B,C,D,E)      [B >= 200]
          f4(A,B,C,D,E)  -> f4(1 + A,B,C,A,A)   [99 >= A]
          f4(A,B,C,D,E)  -> f20(A,100,C,D,E)    [A >= 100]
        Signature:
          {(f0,5);(f20,5);(f31,5);(f4,5)}
        Rule Graph:
          [0->{3},1->{1,2},2->{},3->{3,4},4->{1}]
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          +- p:[3] c: [3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES