YES(?,O(n^1))
* Step 1: FromIts WORST_CASE(?,O(n^1))
    + 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: AddSinks WORST_CASE(?,O(n^1))
    + 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:
        AddSinks
    + Details:
        ()
* Step 3: Decompose WORST_CASE(?,O(n^1))
    + 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]
          end(A,B,C,D)  -> exitus616(A,B,C,D)          True
        Signature:
          {(end,4);(exitus616,4);(f,4);(sqrt,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3}]
    + Applied Processor:
        Decompose Greedy
    + Details:
        We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1]
* Step 4: AbstractSize WORST_CASE(?,O(n^1))
    + 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]
          end(A,B,C,D)  -> exitus616(A,B,C,D)          True
        Signature:
          {(end,4);(exitus616,4);(f,4);(sqrt,4)}
        Rule Graph:
          [0->{1,2},1->{1,2},2->{3}]
        ,We construct a looptree:
          P: [0,1,2,3]
          |
          `- p:[1] c: [1])
    + Applied Processor:
        AbstractSize Minimize
    + Details:
        ()
* Step 5: AbstractFlow WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [A,B,C,D,0.0]
           sqrt  ~>  f           [A <= 0*K, B <= K, C <= K, D <= D]
           f     ~>  f           [A <= D, B <= B + C + D, C <= 2*K + B + C, D <= D]
           f     ~>  end         [A <= A, B <= B, C <= C, D <= D]
           end   ~>  exitus616   [A <= A, B <= B, C <= C, D <= D]
          + Loop: [0.0 <= K + A + B + C + D]
               f  ~>  f   [A <= D, B <= B + C + D, C <= 2*K + B + C, D <= D]
    + Applied Processor:
        AbstractFlow
    + Details:
        ()
* Step 6: Lare WORST_CASE(?,O(n^1))
    + Considered Problem:
        Program:
          Domain: [tick,huge,K,A,B,C,D,0.0]
           sqrt  ~>  f           [K ~=> A,K ~=> B,K ~=> C]
           f     ~>  f           [D ~=> A,B ~+> B,B ~+> C,C ~+> B,C ~+> C,D ~+> B,K ~*> C]
           f     ~>  end         []
           end   ~>  exitus616   []
          + Loop: [A ~+> 0.0,B ~+> 0.0,C ~+> 0.0,D ~+> 0.0,K ~+> 0.0]
               f  ~>  f   [D ~=> A,B ~+> B,B ~+> C,C ~+> B,C ~+> C,D ~+> B,K ~*> C]
    + Applied Processor:
        Lare
    + Details:
         sqrt  ~>  exitus616   [D ~=> A
                               ,K ~=> A
                               ,K ~=> B
                               ,K ~=> C
                               ,D ~+> B
                               ,D ~+> C
                               ,D ~+> 0.0
                               ,D ~+> tick
                               ,tick ~+> tick
                               ,K ~+> B
                               ,K ~+> C
                               ,K ~+> 0.0
                               ,K ~+> tick
                               ,D ~*> B
                               ,D ~*> C
                               ,K ~*> B
                               ,K ~*> C
                               ,K ~*> 0.0
                               ,K ~*> tick
                               ,D ~^> B
                               ,D ~^> C
                               ,K ~^> B
                               ,K ~^> C]
        + <f  ~>  f>  [D ~=> A
                      ,A ~+> 0.0
                      ,A ~+> tick
                      ,B ~+> B
                      ,B ~+> C
                      ,B ~+> 0.0
                      ,B ~+> tick
                      ,C ~+> B
                      ,C ~+> C
                      ,C ~+> 0.0
                      ,C ~+> tick
                      ,D ~+> B
                      ,D ~+> C
                      ,D ~+> 0.0
                      ,D ~+> tick
                      ,tick ~+> tick
                      ,K ~+> 0.0
                      ,K ~+> tick
                      ,A ~*> B
                      ,A ~*> C
                      ,B ~*> B
                      ,B ~*> C
                      ,C ~*> B
                      ,C ~*> C
                      ,D ~*> B
                      ,D ~*> C
                      ,K ~*> B
                      ,K ~*> C
                      ,A ~^> B
                      ,A ~^> C
                      ,B ~^> B
                      ,B ~^> C
                      ,C ~^> B
                      ,C ~^> C
                      ,D ~^> B
                      ,D ~^> C
                      ,K ~^> B
                      ,K ~^> C]

YES(?,O(n^1))