WORST_CASE(?,O(1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                   (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A]               (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2]               (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1,5},1->{1,5},2->{2,3,4},3->{},4->{},5->{2,3,4}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     0, .= 0) (<0,0,B>,     B, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) (<1,0,B>,     B, .= 0) 
          (<2,0,A>,     A, .= 0) (<2,0,B>, 1 + B, .+ 1) 
          (<3,0,A>,     A, .= 0) (<3,0,B>,     B, .= 0) 
          (<4,0,A>,     A, .= 0) (<4,0,B>,     B, .= 0) 
          (<5,0,A>,     A, .= 0) (<5,0,B>,     0, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                   (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A]               (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2]               (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1,5},1->{1,5},2->{2,3,4},3->{},4->{},5->{2,3,4}]
        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>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<3,0,A>, 2) (<3,0,B>, 2) 
          (<4,0,A>, 2) (<4,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
* Step 3: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                   (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A]               (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2]               (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1,5},1->{1,5},2->{2,3,4},3->{},4->{},5->{2,3,4}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<3,0,A>, 2) (<3,0,B>, 2) 
          (<4,0,A>, 2) (<4,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,5),(5,3),(5,4)]
* Step 4: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True                   (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A]               (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B]               (?,1)
          3. f10(A,B) -> f18(A,B)     [B >= 2 && 0 >= 1 + C] (?,1)
          4. f10(A,B) -> f18(A,B)     [B >= 2]               (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2]               (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2,3,4},3->{},4->{},5->{2}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<3,0,A>, 2) (<3,0,B>, 2) 
          (<4,0,A>, 2) (<4,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [3,4]
* Step 5: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True     (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A] (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B] (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2] (?,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2},5->{2}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(f0) = 1
          p(f10) = 0
           p(f4) = 1
        
        The following rules are strictly oriented:
         [A >= 2] ==>         
          f4(A,B)   = 1       
                    > 0       
                    = f10(A,0)
        
        
        The following rules are weakly oriented:
              True ==>             
           f0(A,B)   = 1           
                    >= 1           
                     = f4(0,B)     
        
          [1 >= A] ==>             
           f4(A,B)   = 1           
                    >= 1           
                     = f4(1 + A,B) 
        
          [1 >= B] ==>             
          f10(A,B)   = 0           
                    >= 0           
                     = f10(A,1 + B)
        
        
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True     (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A] (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B] (?,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2] (1,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2},5->{2}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(f0) = 2        
          p(f10) = 2 + -1*x2
           p(f4) = 2        
        
        The following rules are strictly oriented:
          [1 >= B] ==>             
          f10(A,B)   = 2 + -1*B    
                     > 1 + -1*B    
                     = f10(A,1 + B)
        
        
        The following rules are weakly oriented:
             True ==>            
          f0(A,B)   = 2          
                   >= 2          
                    = f4(0,B)    
        
         [1 >= A] ==>            
          f4(A,B)   = 2          
                   >= 2          
                    = f4(1 + A,B)
        
         [A >= 2] ==>            
          f4(A,B)   = 2          
                   >= 2          
                    = f10(A,0)   
        
        
* Step 7: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True     (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A] (?,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B] (2,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2] (1,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2},5->{2}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
           p(f0) = 2        
          p(f10) = -1*x1    
           p(f4) = 2 + -1*x1
        
        The following rules are strictly oriented:
         [1 >= A] ==>            
          f4(A,B)   = 2 + -1*A   
                    > 1 + -1*A   
                    = f4(1 + A,B)
        
        
        The following rules are weakly oriented:
              True ==>             
           f0(A,B)   = 2           
                    >= 2           
                     = f4(0,B)     
        
          [1 >= B] ==>             
          f10(A,B)   = -1*A        
                    >= -1*A        
                     = f10(A,1 + B)
        
          [A >= 2] ==>             
           f4(A,B)   = 2 + -1*A    
                    >= -1*A        
                     = f10(A,0)    
        
        
* Step 8: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A,B)  -> f4(0,B)      True     (1,1)
          1. f4(A,B)  -> f4(1 + A,B)  [1 >= A] (2,1)
          2. f10(A,B) -> f10(A,1 + B) [1 >= B] (2,1)
          5. f4(A,B)  -> f10(A,0)     [A >= 2] (1,1)
        Signature:
          {(f0,2);(f10,2);(f18,2);(f4,2)}
        Flow Graph:
          [0->{1},1->{1,5},2->{2},5->{2}]
        Sizebounds:
          (<0,0,A>, 0) (<0,0,B>, B) 
          (<1,0,A>, 2) (<1,0,B>, B) 
          (<2,0,A>, 2) (<2,0,B>, 2) 
          (<5,0,A>, 2) (<5,0,B>, 0) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))