WORST_CASE(?,O(1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1)
          3. f3(A) -> f13(A)    [A >= 42]               (?,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     0, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) 
          (<2,0,A>, 1 + A, .+ 1) 
          (<3,0,A>,     A, .= 0) 
* Step 2: SizeboundsProc WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1)
          3. f3(A) -> f13(A)    [A >= 42]               (?,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        Sizebounds:
          (<0,0,A>, ?) 
          (<1,0,A>, ?) 
          (<2,0,A>, ?) 
          (<3,0,A>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
          (<3,0,A>, 42) 
* Step 3: UnsatPaths WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1)
          3. f3(A) -> f13(A)    [A >= 42]               (?,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2,3},1->{1,2,3},2->{1,2,3},3->{}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
          (<3,0,A>, 42) 
    + Applied Processor:
        UnsatPaths
    + Details:
        We remove following edges from the transition graph: [(0,3)]
* Step 4: LeafRules WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1)
          3. f3(A) -> f13(A)    [A >= 42]               (?,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2},1->{1,2,3},2->{1,2,3},3->{}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
          (<3,0,A>, 42) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [3]
* Step 5: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1)
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (?,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 42        
          p(f3) = 42 + -1*x1
        
        The following rules are strictly oriented:
        [41 >= A && 0 >= 1 + B] ==>          
                          f3(A)   = 42 + -1*A
                                  > 41 + -1*A
                                  = f3(1 + A)
        
        
        The following rules are weakly oriented:
             True ==>          
            f0(A)   = 42       
                   >= 42       
                    = f3(0)    
        
        [41 >= A] ==>          
            f3(A)   = 42 + -1*A
                   >= 41 + -1*A
                    = f3(1 + A)
        
        
* Step 6: PolyRank WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1) 
          1. f3(A) -> f3(1 + A) [41 >= A]               (?,1) 
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (42,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f0) = 42        
          p(f3) = 42 + -1*x1
        
        The following rules are strictly oriented:
                      [41 >= A] ==>          
                          f3(A)   = 42 + -1*A
                                  > 41 + -1*A
                                  = f3(1 + A)
        
        [41 >= A && 0 >= 1 + B] ==>          
                          f3(A)   = 42 + -1*A
                                  > 41 + -1*A
                                  = f3(1 + A)
        
        
        The following rules are weakly oriented:
           True ==>      
          f0(A)   = 42   
                 >= 42   
                  = f3(0)
        
        
* Step 7: KnowledgePropagation WORST_CASE(?,O(1))
    + Considered Problem:
        Rules:
          0. f0(A) -> f3(0)     True                    (1,1) 
          1. f3(A) -> f3(1 + A) [41 >= A]               (42,1)
          2. f3(A) -> f3(1 + A) [41 >= A && 0 >= 1 + B] (42,1)
        Signature:
          {(f0,1);(f13,1);(f3,1)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>,  0) 
          (<1,0,A>, 42) 
          (<2,0,A>, 42) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(1))