YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D,E) -> f1(A,B,C,D,E)      True         (1,1)
          1. f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E)  [A >= 1 + B] (?,1)
          2. f1(A,B,C,D,E) -> f2(A,B,B,D,E)      [B >= A]     (?,1)
          3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [C >= 1]     (?,1)
          4. f2(A,B,C,D,E) -> f3(A,B,C,C,E)      [0 >= C]     (?,1)
          5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E)  [A >= 1 + D] (?,1)
          6. f3(A,B,C,D,E) -> f4(A,B,C,D,D)      [D >= A]     (?,1)
          7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [E >= 1]     (?,1)
        Signature:
          {(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7},7->{7}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D,E) -> f1(A,B,C,D,E)       True
          f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E)   [A >= 1 + B]
          f1(A,B,C,D,E) -> f2(A,B,B,D,E)       [B >= A]
          f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E)  [C >= 1]
          f2(A,B,C,D,E) -> f3(A,B,C,C,E)       [0 >= C]
          f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E)   [A >= 1 + D]
          f3(A,B,C,D,E) -> f4(A,B,C,D,D)       [D >= A]
          f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E)  [E >= 1]
        Signature:
          {(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7},7->{7}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6,7]
          |
          +- p:[1] c: [1]
          |
          +- p:[3] c: [3]
          |
          +- p:[5] c: [5]
          |
          `- p:[7] c: [7]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D,E) -> f1(A,B,C,D,E)       True
          f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E)   [A >= 1 + B]
          f1(A,B,C,D,E) -> f2(A,B,B,D,E)       [B >= A]
          f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E)  [C >= 1]
          f2(A,B,C,D,E) -> f3(A,B,C,C,E)       [0 >= C]
          f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E)   [A >= 1 + D]
          f3(A,B,C,D,E) -> f4(A,B,C,D,D)       [D >= A]
          f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E)  [E >= 1]
        Signature:
          {(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7},7->{7}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5,6,7]
          |
          +- p:[1] c: [1]
          |
          +- p:[3] c: [3]
          |
          +- p:[5] c: [5]
          |
          `- p:[7] c: [7])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES