WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)    -> evalfentryin(A,B)   True         (1,1)
          1. evalfentryin(A,B)  -> evalfbb1in(B,A)     True         (?,1)
          2. evalfbb1in(A,B)    -> evalfbbin(A,B)      [A >= B]     (?,1)
          3. evalfbb1in(A,B)    -> evalfreturnin(A,B)  [B >= 1 + A] (?,1)
          4. evalfbbin(A,B)     -> evalfbb1in(A,1 + B) True         (?,1)
          5. evalfreturnin(A,B) -> evalfstop(A,B)      True         (?,1)
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A, .= 0) (<0,0,B>,     B, .= 0) 
          (<1,0,A>, B, .= 0) (<1,0,B>,     A, .= 0) 
          (<2,0,A>, A, .= 0) (<2,0,B>,     B, .= 0) 
          (<3,0,A>, A, .= 0) (<3,0,B>,     B, .= 0) 
          (<4,0,A>, A, .= 0) (<4,0,B>, 1 + B, .+ 1) 
          (<5,0,A>, A, .= 0) (<5,0,B>,     B, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)    -> evalfentryin(A,B)   True         (1,1)
          1. evalfentryin(A,B)  -> evalfbb1in(B,A)     True         (?,1)
          2. evalfbb1in(A,B)    -> evalfbbin(A,B)      [A >= B]     (?,1)
          3. evalfbb1in(A,B)    -> evalfreturnin(A,B)  [B >= 1 + A] (?,1)
          4. evalfbbin(A,B)     -> evalfbb1in(A,1 + B) True         (?,1)
          5. evalfreturnin(A,B) -> evalfstop(A,B)      True         (?,1)
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}]
        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>, ?) 
          (<4,0,A>, ?) (<4,0,B>, ?) 
          (<5,0,A>, ?) (<5,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) (<0,0,B>,     B) 
          (<1,0,A>, B) (<1,0,B>,     A) 
          (<2,0,A>, B) (<2,0,B>,     B) 
          (<3,0,A>, B) (<3,0,B>, A + B) 
          (<4,0,A>, B) (<4,0,B>,     B) 
          (<5,0,A>, B) (<5,0,B>, A + B) 
* Step 3: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)    -> evalfentryin(A,B)   True         (1,1)
          1. evalfentryin(A,B)  -> evalfbb1in(B,A)     True         (?,1)
          2. evalfbb1in(A,B)    -> evalfbbin(A,B)      [A >= B]     (?,1)
          3. evalfbb1in(A,B)    -> evalfreturnin(A,B)  [B >= 1 + A] (?,1)
          4. evalfbbin(A,B)     -> evalfbb1in(A,1 + B) True         (?,1)
          5. evalfreturnin(A,B) -> evalfstop(A,B)      True         (?,1)
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2,3},2->{4},3->{5},4->{2,3},5->{}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>,     B) 
          (<1,0,A>, B) (<1,0,B>,     A) 
          (<2,0,A>, B) (<2,0,B>,     B) 
          (<3,0,A>, B) (<3,0,B>, A + B) 
          (<4,0,A>, B) (<4,0,B>,     B) 
          (<5,0,A>, B) (<5,0,B>, A + B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [3,5]
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)   -> evalfentryin(A,B)   True     (1,1)
          1. evalfentryin(A,B) -> evalfbb1in(B,A)     True     (?,1)
          2. evalfbb1in(A,B)   -> evalfbbin(A,B)      [A >= B] (?,1)
          4. evalfbbin(A,B)    -> evalfbb1in(A,1 + B) True     (?,1)
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{4},4->{2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, B) (<1,0,B>, A) 
          (<2,0,A>, B) (<2,0,B>, B) 
          (<4,0,A>, B) (<4,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
            p(evalfbb1in) = 2 + x1 + -1*x2
             p(evalfbbin) = 1 + x1 + -1*x2
          p(evalfentryin) = 2 + -1*x1 + x2
            p(evalfstart) = 2 + -1*x1 + x2
        
        The following rules are strictly oriented:
                 [A >= B] ==>               
          evalfbb1in(A,B)   = 2 + A + -1*B  
                            > 1 + A + -1*B  
                            = evalfbbin(A,B)
        
        
        The following rules are weakly oriented:
                       True ==>                    
            evalfstart(A,B)   = 2 + -1*A + B       
                             >= 2 + -1*A + B       
                              = evalfentryin(A,B)  
        
                       True ==>                    
          evalfentryin(A,B)   = 2 + -1*A + B       
                             >= 2 + -1*A + B       
                              = evalfbb1in(B,A)    
        
                       True ==>                    
             evalfbbin(A,B)   = 1 + A + -1*B       
                             >= 1 + A + -1*B       
                              = evalfbb1in(A,1 + B)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)   -> evalfentryin(A,B)   True     (1,1)        
          1. evalfentryin(A,B) -> evalfbb1in(B,A)     True     (?,1)        
          2. evalfbb1in(A,B)   -> evalfbbin(A,B)      [A >= B] (2 + A + B,1)
          4. evalfbbin(A,B)    -> evalfbb1in(A,1 + B) True     (?,1)        
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{4},4->{2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, B) (<1,0,B>, A) 
          (<2,0,A>, B) (<2,0,B>, B) 
          (<4,0,A>, B) (<4,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        We propagate bounds from predecessors.
* Step 6: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. evalfstart(A,B)   -> evalfentryin(A,B)   True     (1,1)        
          1. evalfentryin(A,B) -> evalfbb1in(B,A)     True     (1,1)        
          2. evalfbb1in(A,B)   -> evalfbbin(A,B)      [A >= B] (2 + A + B,1)
          4. evalfbbin(A,B)    -> evalfbb1in(A,1 + B) True     (2 + A + B,1)
        Signature:
          {(evalfbb1in,2);(evalfbbin,2);(evalfentryin,2);(evalfreturnin,2);(evalfstart,2);(evalfstop,2)}
        Flow Graph:
          [0->{1},1->{2},2->{4},4->{2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, B) (<1,0,B>, A) 
          (<2,0,A>, B) (<2,0,B>, B) 
          (<4,0,A>, B) (<4,0,B>, B) 
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))