WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor 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) [D >= C && B >= 0] (?,1)
          2. f(A,B,C,D)    -> end(A,B,C,D)               [C >= 1 + D]       (?,1)
        Signature:
          {(end,4);(f,4);(sqrt,4)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [A] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sqrt(B,C,D) -> f(1,1,D)             True               (1,1)
          1. f(B,C,D)    -> f(2 + B,2 + B + C,D) [D >= C && B >= 0] (?,1)
          2. f(B,C,D)    -> end(B,C,D)           [C >= 1 + D]       (?,1)
        Signature:
          {(end,3);(f,3);(sqrt,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,B>,     1, .= 1) (<0,0,C>,         1, .= 1) (<0,0,D>, D, .= 0) 
          (<1,0,B>, 2 + B, .+ 2) (<1,0,C>, 2 + B + C, .* 2) (<1,0,D>, D, .= 0) 
          (<2,0,B>,     B, .= 0) (<2,0,C>,         C, .= 0) (<2,0,D>, D, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sqrt(B,C,D) -> f(1,1,D)             True               (1,1)
          1. f(B,C,D)    -> f(2 + B,2 + B + C,D) [D >= C && B >= 0] (?,1)
          2. f(B,C,D)    -> end(B,C,D)           [C >= 1 + D]       (?,1)
        Signature:
          {(end,3);(f,3);(sqrt,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>, ?) (<0,0,C>, ?) (<0,0,D>, ?) 
          (<1,0,B>, ?) (<1,0,C>, ?) (<1,0,D>, ?) 
          (<2,0,B>, ?) (<2,0,C>, ?) (<2,0,D>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,B>, 1) (<0,0,C>,     1) (<0,0,D>, D) 
          (<1,0,B>, ?) (<1,0,C>, 3 + D) (<1,0,D>, D) 
          (<2,0,B>, ?) (<2,0,C>, 3 + D) (<2,0,D>, D) 
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sqrt(B,C,D) -> f(1,1,D)             True               (1,1)
          1. f(B,C,D)    -> f(2 + B,2 + B + C,D) [D >= C && B >= 0] (?,1)
          2. f(B,C,D)    -> end(B,C,D)           [C >= 1 + D]       (?,1)
        Signature:
          {(end,3);(f,3);(sqrt,3)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>, 1) (<0,0,C>,     1) (<0,0,D>, D) 
          (<1,0,B>, ?) (<1,0,C>, 3 + D) (<1,0,D>, D) 
          (<2,0,B>, ?) (<2,0,C>, 3 + D) (<2,0,D>, D) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sqrt(B,C,D) -> f(1,1,D)             True               (1,1)
          1. f(B,C,D)    -> f(2 + B,2 + B + C,D) [D >= C && B >= 0] (?,1)
        Signature:
          {(end,3);(f,3);(sqrt,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>, 1) (<0,0,C>,     1) (<0,0,D>, D) 
          (<1,0,B>, ?) (<1,0,C>, 3 + D) (<1,0,D>, D) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
             p(f) = 1 + -1*x2 + x3
          p(sqrt) = x3            
        
        The following rules are strictly oriented:
        [D >= C && B >= 0] ==>                     
                  f(B,C,D)   = 1 + -1*C + D        
                             > -1 + -1*B + -1*C + D
                             = f(2 + B,2 + B + C,D)
        
        
        The following rules are weakly oriented:
                 True ==>         
          sqrt(B,C,D)   = D       
                       >= D       
                        = f(1,1,D)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. sqrt(B,C,D) -> f(1,1,D)             True               (1,1)
          1. f(B,C,D)    -> f(2 + B,2 + B + C,D) [D >= C && B >= 0] (D,1)
        Signature:
          {(end,3);(f,3);(sqrt,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>, 1) (<0,0,C>,     1) (<0,0,D>, D) 
          (<1,0,B>, ?) (<1,0,C>, 3 + D) (<1,0,D>, D) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))