WORST_CASE(?,O(1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                     (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C]             (?,1)
          2. f8(A,B,C) -> f6(A,B,C)         [2*B >= 1 + A && C >= B] (?,1)
          3. f8(A,B,C) -> f6(A,B,C)         [A >= 2*B && C >= B]     (?,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     0, .= 0) (<0,0,B>, 10, .= 10) (<0,0,C>,     0, .= 0) 
          (<1,0,A>, 2 + A, .+ 2) (<1,0,B>,  B,  .= 0) (<1,0,C>, 1 + C, .+ 1) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,  B,  .= 0) (<2,0,C>,     C, .= 0) 
          (<3,0,A>,     A, .= 0) (<3,0,B>,  B,  .= 0) (<3,0,C>,     C, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                     (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C]             (?,1)
          2. f8(A,B,C) -> f6(A,B,C)         [2*B >= 1 + A && C >= B] (?,1)
          3. f8(A,B,C) -> f6(A,B,C)         [A >= 2*B && C >= B]     (?,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) (<0,0,C>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) (<1,0,C>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) (<2,0,C>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) (<3,0,C>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>,  0) 
          (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) 
          (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) 
          (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 10) 
* Step 3: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                     (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C]             (?,1)
          2. f8(A,B,C) -> f6(A,B,C)         [2*B >= 1 + A && C >= B] (?,1)
          3. f8(A,B,C) -> f6(A,B,C)         [A >= 2*B && C >= B]     (?,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>,  0) 
          (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) 
          (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) 
          (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 10) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2),(0,3)]
* Step 4: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True                     (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C]             (?,1)
          2. f8(A,B,C) -> f6(A,B,C)         [2*B >= 1 + A && C >= B] (?,1)
          3. f8(A,B,C) -> f6(A,B,C)         [A >= 2*B && C >= B]     (?,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1,2,3},2->{},3->{}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>,  0) 
          (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) 
          (<2,0,A>, ?) (<2,0,B>, 10) (<2,0,C>, 10) 
          (<3,0,A>, ?) (<3,0,B>, 10) (<3,0,C>, 10) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2,3]
* Step 5: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True         (1,1)
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (?,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>,  0) 
          (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10        
          p(f8) = x2 + -1*x3
        
        The following rules are strictly oriented:
        [B >= 1 + C] ==>                  
           f8(A,B,C)   = B + -1*C         
                       > -1 + B + -1*C    
                       = f8(2 + A,B,1 + C)
        
        
        The following rules are weakly oriented:
               True ==>           
          f0(A,B,C)   = 10        
                     >= 10        
                      = f8(0,10,0)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B,C) -> f8(0,10,0)        True         (1,1) 
          1. f8(A,B,C) -> f8(2 + A,B,1 + C) [B >= 1 + C] (10,1)
        Signature:
          {(f0,3);(f6,3);(f8,3)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, 10) (<0,0,C>,  0) 
          (<1,0,A>, ?) (<1,0,B>, 10) (<1,0,C>, 10) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))