WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. init(Xs,Zs,Ys)    -> split(Xs,Zs,Ys) True                                                    (1,1)
          1. split(Xs,Zs,Ys)   -> return(Xs)      [Xs = 0 && Zs = 0 && Ys = 0 && False && False && False] (?,1)
          2. split(XXs,XYs,Zs) -> split(Xs,Zs,Ys) [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0]    (?,1)
        Signature:
          {(init,3);(return,1);(split,3)}
        Flow Graph:
          [0->{1,2},1->{},2->{1,2}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,Xs>, Xs, .= 0) (<0,0,Zs>, Zs, .= 0) (<0,0,Ys>, Ys, .= 0) 
          (<1,0,Xs>, Xs, .= 0) (<2,0,Zs>, Zs, .= 0) (<2,0,Ys>, Ys, .= 0) 
          (<2,0,Xs>, Xs, .= 0)                                           
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. init(Xs,Zs,Ys)    -> split(Xs,Zs,Ys) True                                                    (1,1)
          1. split(Xs,Zs,Ys)   -> return(Xs)      [Xs = 0 && Zs = 0 && Ys = 0 && False && False && False] (?,1)
          2. split(XXs,XYs,Zs) -> split(Xs,Zs,Ys) [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0]    (?,1)
        Signature:
          {(init,3);(return,1);(split,3)}
        Flow Graph:
          [0->{1,2},1->{},2->{1,2}]
        Sizebounds:
          (<0,0,Xs>, ?) (<0,0,Zs>, ?) (<0,0,Ys>, ?) 
          (<1,0,Xs>, ?) (<2,0,Zs>, ?) (<2,0,Ys>, ?) 
          (<2,0,Xs>, ?)                             
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,Xs>, Xs) (<0,0,Zs>, Zs) (<0,0,Ys>, Ys) 
          (<1,0,Xs>, Xs) (<2,0,Zs>, Zs) (<2,0,Ys>, Ys) 
          (<2,0,Xs>, Xs)                               
* Step 3: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. init(Xs,Zs,Ys)    -> split(Xs,Zs,Ys) True                                                    (1,1)
          1. split(Xs,Zs,Ys)   -> return(Xs)      [Xs = 0 && Zs = 0 && Ys = 0 && False && False && False] (?,1)
          2. split(XXs,XYs,Zs) -> split(Xs,Zs,Ys) [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0]    (?,1)
        Signature:
          {(init,3);(return,1);(split,3)}
        Flow Graph:
          [0->{1,2},1->{},2->{1,2}]
        Sizebounds:
          (<0,0,Xs>, Xs) (<0,0,Zs>, Zs) (<0,0,Ys>, Ys) 
          (<1,0,Xs>, Xs) (<2,0,Zs>, Zs) (<2,0,Ys>, Ys) 
          (<2,0,Xs>, Xs)                               
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [1]
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. init(Xs,Zs,Ys)    -> split(Xs,Zs,Ys) True                                                 (1,1)
          2. split(XXs,XYs,Zs) -> split(Xs,Zs,Ys) [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0] (?,1)
        Signature:
          {(init,3);(return,1);(split,3)}
        Flow Graph:
          [0->{2},2->{2}]
        Sizebounds:
          (<0,0,Xs>, Xs) (<0,0,Zs>, Zs) (<0,0,Ys>, Ys) 
          (<2,0,Xs>, Xs) (<2,0,Zs>, Zs) (<2,0,Ys>, Ys) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(init) = x1
          p(split) = x1
        
        The following rules are strictly oriented:
        [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0] ==>                
                                           split(XXs,XYs,Zs)   = XXs            
                                                               > Xs             
                                                               = split(Xs,Zs,Ys)
        
        
        The following rules are weakly oriented:
                    True ==>                
          init(Xs,Zs,Ys)   = Xs             
                          >= Xs             
                           = split(Xs,Zs,Ys)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. init(Xs,Zs,Ys)    -> split(Xs,Zs,Ys) True                                                 (1,1) 
          2. split(XXs,XYs,Zs) -> split(Xs,Zs,Ys) [XXs = 1 + Xs && XYs = 1 + Ys && Xs >= 0 && Ys >= 0] (Xs,1)
        Signature:
          {(init,3);(return,1);(split,3)}
        Flow Graph:
          [0->{2},2->{2}]
        Sizebounds:
          (<0,0,Xs>, Xs) (<0,0,Zs>, Zs) (<0,0,Ys>, Ys) 
          (<2,0,Xs>, Xs) (<2,0,Zs>, Zs) (<2,0,Ys>, Ys) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))