YES
* Step 1: TrivialSCCs YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D) -> f4(0,B,C,D)      True                   (1,1)
          1. f4(A,B,C,D) -> f7(A,B,1 + A,D)  [A >= 0 && B >= 1 + A] (?,1)
          2. f7(A,B,C,D) -> f7(A,B,1 + C,0)  [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C]             
          3. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C              
                                              && 0 >= 1 + E]             
          4. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C              
                                              && E >= 1]                 
          5. f7(A,B,C,D) -> f4(1 + A,B,C,D)  [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && C >= B]                 
          6. f4(A,B,C,D) -> f19(A,B,C,D)     [A >= 0 && A >= B]     (?,1)
        Signature:
          {(f0,4);(f19,4);(f4,4);(f7,4)}
        Flow Graph:
          [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{}]
        
    + 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) -> f4(0,B,C,D)      True                   (1,1)
          1. f4(A,B,C,D) -> f7(A,B,1 + A,D)  [A >= 0 && B >= 1 + A] (?,1)
          2. f7(A,B,C,D) -> f7(A,B,1 + C,0)  [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C]             
          3. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C              
                                              && 0 >= 1 + E]             
          4. f7(A,B,C,D) -> f7(A,-1 + B,C,E) [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && B >= 1 + C              
                                              && E >= 1]                 
          5. f7(A,B,C,D) -> f4(1 + A,B,C,D)  [B + -1*C >= 0         (?,1)
                                              && -1 + C >= 0             
                                              && -2 + B + C >= 0         
                                              && -1 + A + C >= 0         
                                              && -1 + -1*A + C >= 0      
                                              && -1 + B >= 0             
                                              && -1 + A + B >= 0         
                                              && -1 + -1*A + B >= 0      
                                              && A >= 0                  
                                              && C >= B]                 
          6. f4(A,B,C,D) -> f19(A,B,C,D)     [A >= 0 && A >= B]     (1,1)
        Signature:
          {(f0,4);(f19,4);(f4,4);(f7,4)}
        Flow Graph:
          [0->{1,6},1->{2,3,4,5},2->{2,3,4,5},3->{2,3,4,5},4->{2,3,4,5},5->{1,6},6->{}]
        
    + Applied Processor:
        Looptree
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5,6]
          |
          `- p:[1,5,2,3,4] c: [5]
             |
             `- p:[2,3,4] c: [4]
                |
                `- p:[2,3] c: [3]
                   |
                   `- p:[2] c: [2]

YES