YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D)  -> f19(A,999,C,1)    True                        (1,1)
          1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*B + -1*D >= 0      
                                                && -1 + D >= 0                  
                                                && 998 + -1*B + D >= 0          
                                                && 999 + -1*B >= 0              
                                                && B >= 0]                      
          2. f19(A,B,C,D) -> f28(A,B,999,D)    [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*B + -1*D >= 0      
                                                && -1 + D >= 0                  
                                                && 998 + -1*B + D >= 0          
                                                && 999 + -1*B >= 0              
                                                && 0 >= 1 + B]                  
          3. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*C + -1*D >= 0      
                                                && -1*B + -1*D >= 0             
                                                && -1 + D >= 0                  
                                                && 998 + -1*C + D >= 0          
                                                && -2 + -1*B + D >= 0           
                                                && 999 + -1*C >= 0              
                                                && 998 + -1*B + -1*C >= 0       
                                                && -1 + -1*B >= 0               
                                                && C >= 0]                      
          4. f28(A,B,C,D) -> f36(A,B,C,D)      [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*C + -1*D >= 0      
                                                && -1*B + -1*D >= 0             
                                                && -1 + D >= 0                  
                                                && 998 + -1*C + D >= 0          
                                                && -2 + -1*B + D >= 0           
                                                && 999 + -1*C >= 0              
                                                && 998 + -1*B + -1*C >= 0       
                                                && -1 + -1*B >= 0               
                                                && 0 >= 1 + C]                  
        Signature:
          {(f0,4);(f19,4);(f28,4);(f36,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(2,4)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. f0(A,B,C,D)  -> f19(A,999,C,1)    True                        (1,1)
          1. f19(A,B,C,D) -> f19(A,-1 + B,C,D) [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*B + -1*D >= 0      
                                                && -1 + D >= 0                  
                                                && 998 + -1*B + D >= 0          
                                                && 999 + -1*B >= 0              
                                                && B >= 0]                      
          2. f19(A,B,C,D) -> f28(A,B,999,D)    [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*B + -1*D >= 0      
                                                && -1 + D >= 0                  
                                                && 998 + -1*B + D >= 0          
                                                && 999 + -1*B >= 0              
                                                && 0 >= 1 + B]                  
          3. f28(A,B,C,D) -> f28(A,B,-1 + C,D) [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*C + -1*D >= 0      
                                                && -1*B + -1*D >= 0             
                                                && -1 + D >= 0                  
                                                && 998 + -1*C + D >= 0          
                                                && -2 + -1*B + D >= 0           
                                                && 999 + -1*C >= 0              
                                                && 998 + -1*B + -1*C >= 0       
                                                && -1 + -1*B >= 0               
                                                && C >= 0]                      
          4. f28(A,B,C,D) -> f36(A,B,C,D)      [1 + -1*D >= 0              (?,1)
                                                && 1000 + -1*C + -1*D >= 0      
                                                && -1*B + -1*D >= 0             
                                                && -1 + D >= 0                  
                                                && 998 + -1*C + D >= 0          
                                                && -2 + -1*B + D >= 0           
                                                && 999 + -1*C >= 0              
                                                && 998 + -1*B + -1*C >= 0       
                                                && -1 + -1*B >= 0               
                                                && 0 >= 1 + C]                  
        Signature:
          {(f0,4);(f19,4);(f28,4);(f36,4)}
        Flow Graph:
          [0->{1},1->{1,2},2->{3},3->{3,4},4->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          f0(A,B,C,D)  -> f19(A,999,C,1)     True
          f19(A,B,C,D) -> f19(A,-1 + B,C,D)  [1 + -1*D >= 0
                                              && 1000 + -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*B + D >= 0
                                              && 999 + -1*B >= 0
                                              && B >= 0]
          f19(A,B,C,D) -> f28(A,B,999,D)     [1 + -1*D >= 0
                                              && 1000 + -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*B + D >= 0
                                              && 999 + -1*B >= 0
                                              && 0 >= 1 + B]
          f28(A,B,C,D) -> f28(A,B,-1 + C,D)  [1 + -1*D >= 0
                                              && 1000 + -1*C + -1*D >= 0
                                              && -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*C + D >= 0
                                              && -2 + -1*B + D >= 0
                                              && 999 + -1*C >= 0
                                              && 998 + -1*B + -1*C >= 0
                                              && -1 + -1*B >= 0
                                              && C >= 0]
          f28(A,B,C,D) -> f36(A,B,C,D)       [1 + -1*D >= 0
                                              && 1000 + -1*C + -1*D >= 0
                                              && -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*C + D >= 0
                                              && -2 + -1*B + D >= 0
                                              && 999 + -1*C >= 0
                                              && 998 + -1*B + -1*C >= 0
                                              && -1 + -1*B >= 0
                                              && 0 >= 1 + C]
        Signature:
          {(f0,4);(f19,4);(f28,4);(f36,4)}
        Rule Graph:
          [0->{1},1->{1,2},2->{3},3->{3,4},4->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4]
          |
          +- p:[1] c: [1]
          |
          `- p:[3] c: [3]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          f0(A,B,C,D)  -> f19(A,999,C,1)     True
          f19(A,B,C,D) -> f19(A,-1 + B,C,D)  [1 + -1*D >= 0
                                              && 1000 + -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*B + D >= 0
                                              && 999 + -1*B >= 0
                                              && B >= 0]
          f19(A,B,C,D) -> f28(A,B,999,D)     [1 + -1*D >= 0
                                              && 1000 + -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*B + D >= 0
                                              && 999 + -1*B >= 0
                                              && 0 >= 1 + B]
          f28(A,B,C,D) -> f28(A,B,-1 + C,D)  [1 + -1*D >= 0
                                              && 1000 + -1*C + -1*D >= 0
                                              && -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*C + D >= 0
                                              && -2 + -1*B + D >= 0
                                              && 999 + -1*C >= 0
                                              && 998 + -1*B + -1*C >= 0
                                              && -1 + -1*B >= 0
                                              && C >= 0]
          f28(A,B,C,D) -> f36(A,B,C,D)       [1 + -1*D >= 0
                                              && 1000 + -1*C + -1*D >= 0
                                              && -1*B + -1*D >= 0
                                              && -1 + D >= 0
                                              && 998 + -1*C + D >= 0
                                              && -2 + -1*B + D >= 0
                                              && 999 + -1*C >= 0
                                              && 998 + -1*B + -1*C >= 0
                                              && -1 + -1*B >= 0
                                              && 0 >= 1 + C]
        Signature:
          {(f0,4);(f19,4);(f28,4);(f36,4)}
        Rule Graph:
          [0->{1},1->{1,2},2->{3},3->{3,4},4->{}]
        ,We construct a looptree:
          P: [0,1,2,3,4]
          |
          +- p:[1] c: [1]
          |
          `- p:[3] c: [3])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES