WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (?,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (?,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     A, .= 0) (<0,0,B>,     B, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) (<1,0,B>, 1 + B, .+ 1) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,     B, .= 0) 
          (<3,0,A>,     A, .= 0) (<3,0,B>, 1 + B, .+ 1) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (?,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (?,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        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>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
* Step 3: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (?,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (?,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(l0) = 2
          p(l1) = 2
          p(l2) = 1
        
        The following rules are strictly oriented:
         [0 >= A] ==>        
          l1(A,B)   = 2      
                    > 1      
                    = l2(A,B)
        
        
        The following rules are weakly oriented:
             True ==>                 
          l0(A,B)   = 2               
                   >= 2               
                    = l1(A,B)         
        
         [A >= 1] ==>                 
          l1(A,B)   = 2               
                   >= 2               
                    = l1(-1 + A,1 + B)
        
         [B >= 1] ==>                 
          l2(A,B)   = 1               
                   >= 1               
                    = l2(A,-1 + B)    
        
        
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (?,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (2,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(l0) = x1
          p(l1) = x1
          p(l2) = x1
        
        The following rules are strictly oriented:
         [A >= 1] ==>                 
          l1(A,B)   = A               
                    > -1 + A          
                    = l1(-1 + A,1 + B)
        
        
        The following rules are weakly oriented:
             True ==>             
          l0(A,B)   = A           
                   >= A           
                    = l1(A,B)     
        
         [0 >= A] ==>             
          l1(A,B)   = A           
                   >= A           
                    = l2(A,B)     
        
         [B >= 1] ==>             
          l2(A,B)   = A           
                   >= A           
                    = l2(A,-1 + B)
        
        
* Step 5: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (A,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (2,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, 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>,     B) 
          (<1,0,A>, 2*A) (<1,0,B>, A + B) 
          (<2,0,A>, 2*A) (<2,0,B>, A + B) 
          (<3,0,A>, 2*A) (<3,0,B>,     ?) 
* Step 6: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (A,1)
          2. l1(A,B) -> l2(A,B)          [0 >= A] (2,1)
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (?,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        Sizebounds:
          (<0,0,A>,   A) (<0,0,B>,     B) 
          (<1,0,A>, 2*A) (<1,0,B>, A + B) 
          (<2,0,A>, 2*A) (<2,0,B>, A + B) 
          (<3,0,A>, 2*A) (<3,0,B>,     ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [3], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(l2) = x2
        
        The following rules are strictly oriented:
         [B >= 1] ==>             
          l2(A,B)   = B           
                    > -1 + B      
                    = l2(A,-1 + B)
        
        
        The following rules are weakly oriented:
        
        We use the following global sizebounds:
        (<0,0,A>,   A) (<0,0,B>,     B) 
        (<1,0,A>, 2*A) (<1,0,B>, A + B) 
        (<2,0,A>, 2*A) (<2,0,B>, A + B) 
        (<3,0,A>, 2*A) (<3,0,B>,     ?) 
* Step 7: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. l0(A,B) -> l1(A,B)          True     (1,1)        
          1. l1(A,B) -> l1(-1 + A,1 + B) [A >= 1] (A,1)        
          2. l1(A,B) -> l2(A,B)          [0 >= A] (2,1)        
          3. l2(A,B) -> l2(A,-1 + B)     [B >= 1] (2*A + 2*B,1)
        Signature:
          {(l0,2);(l1,2);(l2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{3},3->{3}]
        Sizebounds:
          (<0,0,A>,   A) (<0,0,B>,     B) 
          (<1,0,A>, 2*A) (<1,0,B>, A + B) 
          (<2,0,A>, 2*A) (<2,0,B>, A + B) 
          (<3,0,A>, 2*A) (<3,0,B>,     ?) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))