YES
* Step 1: UnsatPaths YES
    + Considered Problem:
        Rules:
          0. l0(A,B,C,D) -> l1(0,B,C,D)          True                                                                                                       (1,1)
          1. l1(A,B,C,D) -> l1(1 + A,-1 + B,C,D) [A >= 0 && B >= 1]                                                                                         (?,1)
          2. l1(A,B,C,D) -> l2(A,B,A,D)          [A >= 0 && 0 >= B]                                                                                         (?,1)
          3. l2(A,B,C,D) -> l3(A,B,C,C)          [A + -1*C >= 0 && C >= 0 && -1*B + C >= 0 && A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && A >= 0 && C >= 1] (?,1)
          4. l3(A,B,C,D) -> l3(A,B,C,-1 + D)     [C + -1*D >= 0                                                                                             (?,1)
                                                  && A + -1*D >= 0                                                                                               
                                                  && A + -1*C >= 0                                                                                               
                                                  && -1 + C >= 0                                                                                                 
                                                  && -1 + -1*B + C >= 0                                                                                          
                                                  && -2 + A + C >= 0                                                                                             
                                                  && -1*B >= 0                                                                                                   
                                                  && -1 + A + -1*B >= 0                                                                                          
                                                  && -1 + A >= 0                                                                                                 
                                                  && D >= 1                                                                                                      
                                                  && C >= 1]                                                                                                     
          5. l3(A,B,C,D) -> l2(A,B,-1 + C,D)     [C + -1*D >= 0                                                                                             (?,1)
                                                  && A + -1*D >= 0                                                                                               
                                                  && A + -1*C >= 0                                                                                               
                                                  && -1 + C >= 0                                                                                                 
                                                  && -1 + -1*B + C >= 0                                                                                          
                                                  && -2 + A + C >= 0                                                                                             
                                                  && -1*B >= 0                                                                                                   
                                                  && -1 + A + -1*B >= 0                                                                                          
                                                  && -1 + A >= 0                                                                                                 
                                                  && 0 >= D                                                                                                      
                                                  && C >= 1]                                                                                                     
        Signature:
          {(l0,4);(l1,4);(l2,4);(l3,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{4,5},4->{4,5},5->{3}]
        
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(3,5)]
* Step 2: FromIts YES
    + Considered Problem:
        Rules:
          0. l0(A,B,C,D) -> l1(0,B,C,D)          True                                                                                                       (1,1)
          1. l1(A,B,C,D) -> l1(1 + A,-1 + B,C,D) [A >= 0 && B >= 1]                                                                                         (?,1)
          2. l1(A,B,C,D) -> l2(A,B,A,D)          [A >= 0 && 0 >= B]                                                                                         (?,1)
          3. l2(A,B,C,D) -> l3(A,B,C,C)          [A + -1*C >= 0 && C >= 0 && -1*B + C >= 0 && A + C >= 0 && -1*B >= 0 && A + -1*B >= 0 && A >= 0 && C >= 1] (?,1)
          4. l3(A,B,C,D) -> l3(A,B,C,-1 + D)     [C + -1*D >= 0                                                                                             (?,1)
                                                  && A + -1*D >= 0                                                                                               
                                                  && A + -1*C >= 0                                                                                               
                                                  && -1 + C >= 0                                                                                                 
                                                  && -1 + -1*B + C >= 0                                                                                          
                                                  && -2 + A + C >= 0                                                                                             
                                                  && -1*B >= 0                                                                                                   
                                                  && -1 + A + -1*B >= 0                                                                                          
                                                  && -1 + A >= 0                                                                                                 
                                                  && D >= 1                                                                                                      
                                                  && C >= 1]                                                                                                     
          5. l3(A,B,C,D) -> l2(A,B,-1 + C,D)     [C + -1*D >= 0                                                                                             (?,1)
                                                  && A + -1*D >= 0                                                                                               
                                                  && A + -1*C >= 0                                                                                               
                                                  && -1 + C >= 0                                                                                                 
                                                  && -1 + -1*B + C >= 0                                                                                          
                                                  && -2 + A + C >= 0                                                                                             
                                                  && -1*B >= 0                                                                                                   
                                                  && -1 + A + -1*B >= 0                                                                                          
                                                  && -1 + A >= 0                                                                                                 
                                                  && 0 >= D                                                                                                      
                                                  && C >= 1]                                                                                                     
        Signature:
          {(l0,4);(l1,4);(l2,4);(l3,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{4},4->{4,5},5->{3}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 3: Decompose YES
    + Considered Problem:
        Rules:
          l0(A,B,C,D) -> l1(0,B,C,D)           True
          l1(A,B,C,D) -> l1(1 + A,-1 + B,C,D)  [A >= 0 && B >= 1]
          l1(A,B,C,D) -> l2(A,B,A,D)           [A >= 0 && 0 >= B]
          l2(A,B,C,D) -> l3(A,B,C,C)           [A + -1*C >= 0
                                                && C >= 0
                                                && -1*B + C >= 0
                                                && A + C >= 0
                                                && -1*B >= 0
                                                && A + -1*B >= 0
                                                && A >= 0
                                                && C >= 1]
          l3(A,B,C,D) -> l3(A,B,C,-1 + D)      [C + -1*D >= 0
                                                && A + -1*D >= 0
                                                && A + -1*C >= 0
                                                && -1 + C >= 0
                                                && -1 + -1*B + C >= 0
                                                && -2 + A + C >= 0
                                                && -1*B >= 0
                                                && -1 + A + -1*B >= 0
                                                && -1 + A >= 0
                                                && D >= 1
                                                && C >= 1]
          l3(A,B,C,D) -> l2(A,B,-1 + C,D)      [C + -1*D >= 0
                                                && A + -1*D >= 0
                                                && A + -1*C >= 0
                                                && -1 + C >= 0
                                                && -1 + -1*B + C >= 0
                                                && -2 + A + C >= 0
                                                && -1*B >= 0
                                                && -1 + A + -1*B >= 0
                                                && -1 + A >= 0
                                                && 0 >= D
                                                && C >= 1]
        Signature:
          {(l0,4);(l1,4);(l2,4);(l3,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3},3->{4},4->{4,5},5->{3}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[3,5,4] c: [3,5]
             |
             `- p:[4] c: [4]
* Step 4: CloseWith YES
    + Considered Problem:
        (Rules:
          l0(A,B,C,D) -> l1(0,B,C,D)           True
          l1(A,B,C,D) -> l1(1 + A,-1 + B,C,D)  [A >= 0 && B >= 1]
          l1(A,B,C,D) -> l2(A,B,A,D)           [A >= 0 && 0 >= B]
          l2(A,B,C,D) -> l3(A,B,C,C)           [A + -1*C >= 0
                                                && C >= 0
                                                && -1*B + C >= 0
                                                && A + C >= 0
                                                && -1*B >= 0
                                                && A + -1*B >= 0
                                                && A >= 0
                                                && C >= 1]
          l3(A,B,C,D) -> l3(A,B,C,-1 + D)      [C + -1*D >= 0
                                                && A + -1*D >= 0
                                                && A + -1*C >= 0
                                                && -1 + C >= 0
                                                && -1 + -1*B + C >= 0
                                                && -2 + A + C >= 0
                                                && -1*B >= 0
                                                && -1 + A + -1*B >= 0
                                                && -1 + A >= 0
                                                && D >= 1
                                                && C >= 1]
          l3(A,B,C,D) -> l2(A,B,-1 + C,D)      [C + -1*D >= 0
                                                && A + -1*D >= 0
                                                && A + -1*C >= 0
                                                && -1 + C >= 0
                                                && -1 + -1*B + C >= 0
                                                && -2 + A + C >= 0
                                                && -1*B >= 0
                                                && -1 + A + -1*B >= 0
                                                && -1 + A >= 0
                                                && 0 >= D
                                                && C >= 1]
        Signature:
          {(l0,4);(l1,4);(l2,4);(l3,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3},3->{4},4->{4,5},5->{3}]
        ,We construct a looptree:
          P: [0,1,2,3,4,5]
          |
          +- p:[1] c: [1]
          |
          `- p:[3,5,4] c: [3,5]
             |
             `- p:[4] c: [4])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES