WORST_CASE(?,O(n^1))
* Step 1: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f2(A,B)      [A >= 1 && B >= 1] (1,1)
          1. f2(A,B) -> f2(-1 + A,B) [A >= 2 && B >= 1] (?,1)
          2. f2(A,B) -> f2(A,-1 + B) [A >= 1 && B >= 2] (?,1)
        Signature:
          {(f1,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        
    + 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>,     B, .= 0) 
          (<2,0,A>,     A, .= 0) (<2,0,B>, 1 + B, .+ 1) 
* Step 2: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f2(A,B)      [A >= 1 && B >= 1] (1,1)
          1. f2(A,B) -> f2(-1 + A,B) [A >= 2 && B >= 1] (?,1)
          2. f2(A,B) -> f2(A,-1 + B) [A >= 1 && B >= 2] (?,1)
        Signature:
          {(f1,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,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>, ?) 
* Step 3: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f2(A,B)      [A >= 1 && B >= 1] (1,1)
          1. f2(A,B) -> f2(-1 + A,B) [A >= 2 && B >= 1] (?,1)
          2. f2(A,B) -> f2(A,-1 + B) [A >= 1 && B >= 2] (?,1)
        Signature:
          {(f1,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = x2     
          p(f2) = -1 + x2
        
        The following rules are strictly oriented:
        [A >= 1 && B >= 1] ==>             
                   f1(A,B)   = B           
                             > -1 + B      
                             = f2(A,B)     
        
        [A >= 1 && B >= 2] ==>             
                   f2(A,B)   = -1 + B      
                             > -2 + B      
                             = f2(A,-1 + B)
        
        
        The following rules are weakly oriented:
        [A >= 2 && B >= 1] ==>             
                   f2(A,B)   = -1 + B      
                            >= -1 + B      
                             = f2(-1 + A,B)
        
        
* Step 4: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f2(A,B)      [A >= 1 && B >= 1] (1,1)
          1. f2(A,B) -> f2(-1 + A,B) [A >= 2 && B >= 1] (?,1)
          2. f2(A,B) -> f2(A,-1 + B) [A >= 1 && B >= 2] (B,1)
        Signature:
          {(f1,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f1) = x1
          p(f2) = x1
        
        The following rules are strictly oriented:
        [A >= 2 && B >= 1] ==>             
                   f2(A,B)   = A           
                             > -1 + A      
                             = f2(-1 + A,B)
        
        
        The following rules are weakly oriented:
        [A >= 1 && B >= 1] ==>             
                   f1(A,B)   = A           
                            >= A           
                             = f2(A,B)     
        
        [A >= 1 && B >= 2] ==>             
                   f2(A,B)   = A           
                            >= A           
                             = f2(A,-1 + B)
        
        
* Step 5: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f1(A,B) -> f2(A,B)      [A >= 1 && B >= 1] (1,1)
          1. f2(A,B) -> f2(-1 + A,B) [A >= 2 && B >= 1] (A,1)
          2. f2(A,B) -> f2(A,-1 + B) [A >= 1 && B >= 2] (B,1)
        Signature:
          {(f1,2);(f2,2)}
        Flow Graph:
          [0->{1,2},1->{1,2},2->{1,2}]
        Sizebounds:
          (<0,0,A>, A) (<0,0,B>, B) 
          (<1,0,A>, ?) (<1,0,B>, ?) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))