YES
* Step 1: FromIts YES
    + Considered Problem:
        Rules:
          0. sqrt(A,B,C,D) -> f(0,1,1,D)                 True                   (1,1)
          1. f(A,B,C,D)    -> f(1 + A,2 + B,2 + B + C,D) [-1 + C >= 0           (?,1)
                                                          && -2 + B + C >= 0         
                                                          && -1*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                  
                                                          && D >= C                  
                                                          && B >= 0]                 
          2. f(A,B,C,D)    -> end(A,B,C,D)               [-1 + C >= 0           (?,1)
                                                          && -2 + B + C >= 0         
                                                          && -1*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 >= 1 + D]             
        Signature:
          {(end,4);(f,4);(sqrt,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        FromIts
    + Details:
        ()
* Step 2: Decompose YES
    + Considered Problem:
        Rules:
          sqrt(A,B,C,D) -> f(0,1,1,D)                  True
          f(A,B,C,D)    -> f(1 + A,2 + B,2 + B + C,D)  [-1 + C >= 0
                                                        && -2 + B + C >= 0
                                                        && -1*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
                                                        && D >= C
                                                        && B >= 0]
          f(A,B,C,D)    -> end(A,B,C,D)                [-1 + C >= 0
                                                        && -2 + B + C >= 0
                                                        && -1*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 >= 1 + D]
        Signature:
          {(end,4);(f,4);(sqrt,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{}]
    + Applied Processor:
        Decompose NoGreedy
    + Details:
        We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1]
* Step 3: CloseWith YES
    + Considered Problem:
        (Rules:
          sqrt(A,B,C,D) -> f(0,1,1,D)                  True
          f(A,B,C,D)    -> f(1 + A,2 + B,2 + B + C,D)  [-1 + C >= 0
                                                        && -2 + B + C >= 0
                                                        && -1*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
                                                        && D >= C
                                                        && B >= 0]
          f(A,B,C,D)    -> end(A,B,C,D)                [-1 + C >= 0
                                                        && -2 + B + C >= 0
                                                        && -1*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 >= 1 + D]
        Signature:
          {(end,4);(f,4);(sqrt,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{}]
        ,We construct a looptree:
          P: [0,1,2]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        CloseWith True
    + Details:
        ()

YES