YES
* Step 1: TrivialSCCs 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) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1]                                                    (?,1)
          4. f2(A,B,C,D,E) -> f3(A,B,C,C,E)      [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C]                                                    (?,1)
          5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E)  [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1)
          6. f3(A,B,C,D,E) -> f4(A,B,C,D,D)      [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A]     (?,1)
          7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0                                                                                (?,1)
                                                  && B + -1*E >= 0                                                                                  
                                                  && -1*C + E >= 0                                                                                  
                                                  && B + -1*D >= 0                                                                                  
                                                  && -1*C + D >= 0                                                                                  
                                                  && -1*A + D >= 0                                                                                  
                                                  && -1*C >= 0                                                                                      
                                                  && B + -1*C >= 0                                                                                  
                                                  && -1*A + B >= 0                                                                                  
                                                  && E >= 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:
        TrivialSCCs
    + Details:
        All trivial SCCs of the transition graph admit timebound 1.
* Step 2: Looptree 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]                                                                                      (1,1)
          3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1]                                                    (?,1)
          4. f2(A,B,C,D,E) -> f3(A,B,C,C,E)      [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C]                                                    (1,1)
          5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E)  [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1)
          6. f3(A,B,C,D,E) -> f4(A,B,C,D,D)      [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A]     (1,1)
          7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0                                                                                (?,1)
                                                  && B + -1*E >= 0                                                                                  
                                                  && -1*C + E >= 0                                                                                  
                                                  && B + -1*D >= 0                                                                                  
                                                  && -1*C + D >= 0                                                                                  
                                                  && -1*A + D >= 0                                                                                  
                                                  && -1*C >= 0                                                                                      
                                                  && B + -1*C >= 0                                                                                  
                                                  && -1*A + B >= 0                                                                                  
                                                  && E >= 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:
        Looptree
    + 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]

YES