WORST_CASE(?,O(1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B) -> f6(C,0)     True      (1,1)
          1. f6(A,B) -> f6(A,1 + B) [9 >= B]  (?,1)
          2. f6(A,B) -> f15(A,B)    [B >= 10] (?,1)
        Signature:
          {(f0,2);(f15,2);(f6,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [A] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True      (1,1)
          1. f6(B) -> f6(1 + B) [9 >= B]  (?,1)
          2. f6(B) -> f15(B)    [B >= 10] (?,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,B>,     0, .= 0) 
          (<1,0,B>, 1 + B, .+ 1) 
          (<2,0,B>,     B, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True      (1,1)
          1. f6(B) -> f6(1 + B) [9 >= B]  (?,1)
          2. f6(B) -> f15(B)    [B >= 10] (?,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>, ?) 
          (<1,0,B>, ?) 
          (<2,0,B>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,B>,  0) 
          (<1,0,B>, 10) 
          (<2,0,B>, 10) 
* Step 4: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True      (1,1)
          1. f6(B) -> f6(1 + B) [9 >= B]  (?,1)
          2. f6(B) -> f15(B)    [B >= 10] (?,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>,  0) 
          (<1,0,B>, 10) 
          (<2,0,B>, 10) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,2)]
* Step 5: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True      (1,1)
          1. f6(B) -> f6(1 + B) [9 >= B]  (?,1)
          2. f6(B) -> f15(B)    [B >= 10] (?,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>,  0) 
          (<1,0,B>, 10) 
          (<2,0,B>, 10) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True     (1,1)
          1. f6(B) -> f6(1 + B) [9 >= B] (?,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>,  0) 
          (<1,0,B>, 10) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 10        
          p(f6) = 10 + -1*x1
        
        The following rules are strictly oriented:
        [9 >= B] ==>          
           f6(B)   = 10 + -1*B
                   > 9 + -1*B 
                   = f6(1 + B)
        
        
        The following rules are weakly oriented:
           True ==>      
          f0(B)   = 10   
                 >= 10   
                  = f6(0)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(B) -> f6(0)     True     (1,1) 
          1. f6(B) -> f6(1 + B) [9 >= B] (10,1)
        Signature:
          {(f0,1);(f15,1);(f6,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>,  0) 
          (<1,0,B>, 10) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))