WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. div(A,B)   -> end(A,B)        [0 >= A]               (?,1)
          1. div(A,B)   -> end(A,B)        [A >= B]               (?,1)
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [0->{},1->{},2->{0,1,2},3->{0,1,2}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>,         B, .= 0) 
          (<1,0,A>, A, .= 0) (<1,0,B>,         B, .= 0) 
          (<2,0,A>, A, .= 0) (<2,0,B>, 1 + A + B, .* 1) 
          (<3,0,A>, A, .= 0) (<3,0,B>,         B, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. div(A,B)   -> end(A,B)        [0 >= A]               (?,1)
          1. div(A,B)   -> end(A,B)        [A >= B]               (?,1)
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [0->{},1->{},2->{0,1,2},3->{0,1,2}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, ?) 
          (<2,0,A>, A) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
* Step 3: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. div(A,B)   -> end(A,B)        [0 >= A]               (?,1)
          1. div(A,B)   -> end(A,B)        [A >= B]               (?,1)
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [0->{},1->{},2->{0,1,2},3->{0,1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, ?) 
          (<2,0,A>, A) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(2,0)]
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. div(A,B)   -> end(A,B)        [0 >= A]               (?,1)
          1. div(A,B)   -> end(A,B)        [A >= B]               (?,1)
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [0->{},1->{},2->{1,2},3->{0,1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, ?) 
          (<2,0,A>, A) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [0,1]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (?,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [2->{2},3->{2}]
        Sizebounds:
          (<2,0,A>, A) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
            p(div) = -1*x1 + x2
          p(start) = -1*x1 + x2
        
        The following rules are strictly oriented:
        [B >= 1 + A && A >= 1] ==>                
                      div(A,B)   = -1*A + B       
                                 > -2*A + B       
                                 = div(A,-1*A + B)
        
        
        The following rules are weakly oriented:
                True ==>         
          start(A,B)   = -1*A + B
                      >= -1*A + B
                       = div(A,B)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          2. div(A,B)   -> div(A,-1*A + B) [B >= 1 + A && A >= 1] (A + B,1)
          3. start(A,B) -> div(A,B)        True                   (1,1)    
        Signature:
          {(div,2);(end,2);(start,2)}
        Flow Graph:
          [2->{2},3->{2}]
        Sizebounds:
          (<2,0,A>, A) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))