WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A) -> f1(A)      [A >= 0] (1,1)
          1. f1(A) -> f1(-1 + A) [A >= 1] (?,1)
        Signature:
          {(f1,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>,     A, .= 0) 
          (<1,0,A>, 1 + A, .+ 1) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A) -> f1(A)      [A >= 0] (1,1)
          1. f1(A) -> f1(-1 + A) [A >= 1] (?,1)
        Signature:
          {(f1,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, ?) 
          (<1,0,A>, ?) 
    + Applied Processor:
        SizeboundsProc
    + Details:
        Sizebounds computed:
          (<0,0,A>, A) 
          (<1,0,A>, ?) 
* Step 3: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A) -> f1(A)      [A >= 0] (1,1)
          1. f1(A) -> f1(-1 + A) [A >= 1] (?,1)
        Signature:
          {(f1,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) 
          (<1,0,A>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = x1
          p(f3) = x1
        
        The following rules are strictly oriented:
        [A >= 1] ==>           
           f1(A)   = A         
                   > -1 + A    
                   = f1(-1 + A)
        
        
        The following rules are weakly oriented:
        [A >= 0] ==>      
           f3(A)   = A    
                  >= A    
                   = f1(A)
        
        
* Step 4: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f3(A) -> f1(A)      [A >= 0] (1,1)
          1. f1(A) -> f1(-1 + A) [A >= 1] (A,1)
        Signature:
          {(f1,1);(f3,1)}
        Flow Graph:
          [0->{1},1->{1}]
        Sizebounds:
          (<0,0,A>, A) 
          (<1,0,A>, ?) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))