WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(0,B)          True     (1,1)
          1. l1(A,B) -> l1(1 + A,-1 + B) [B >= 1] (?,1)
          2. l1(A,B) -> l2(A,B)          [0 >= B] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [A] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(B) -> l1(B)      True     (1,1)
          1. l1(B) -> l1(-1 + B) [B >= 1] (?,1)
          2. l1(B) -> l2(B)      [0 >= B] (?,1)
        Signature:
          {(l0,1);(l1,1);(l2,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,B>,     B, .= 0) 
          (<1,0,B>, 1 + B, .+ 1) 
          (<2,0,B>,     B, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(B) -> l1(B)      True     (1,1)
          1. l1(B) -> l1(-1 + B) [B >= 1] (?,1)
          2. l1(B) -> l2(B)      [0 >= B] (?,1)
        Signature:
          {(l0,1);(l1,1);(l2,1)}
        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>, B) 
          (<1,0,B>, ?) 
          (<2,0,B>, ?) 
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(B) -> l1(B)      True     (1,1)
          1. l1(B) -> l1(-1 + B) [B >= 1] (?,1)
          2. l1(B) -> l2(B)      [0 >= B] (?,1)
        Signature:
          {(l0,1);(l1,1);(l2,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{}]
        Sizebounds:
          (<0,0,B>, B) 
          (<1,0,B>, ?) 
          (<2,0,B>, ?) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(B) -> l1(B)      True     (1,1)
          1. l1(B) -> l1(-1 + B) [B >= 1] (?,1)
        Signature:
          {(l0,1);(l1,1);(l2,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>, B) 
          (<1,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(l0) = x1
          p(l1) = x1
        
        The following rules are strictly oriented:
        [B >= 1] ==>           
           l1(B)   = B         
                   > -1 + B    
                   = l1(-1 + B)
        
        
        The following rules are weakly oriented:
           True ==>      
          l0(B)   = B    
                 >= B    
                  = l1(B)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(B) -> l1(B)      True     (1,1)
          1. l1(B) -> l1(-1 + B) [B >= 1] (B,1)
        Signature:
          {(l0,1);(l1,1);(l2,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,B>, B) 
          (<1,0,B>, ?) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))