WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C) -> f2(A + -1*B,1 + B,C) [A >= 1] (?,1)
          1. f3(A,B,C) -> f2(A,B,C)            [B >= 1] (1,1)
          2. f2(A,B,C) -> f4(A,B,D)            [0 >= A] (?,1)
          3. f3(A,B,C) -> f4(A,B,D)            [0 >= B] (1,1)
        Signature:
          {(f2,3);(f3,3);(f4,3)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          2. f2(A,B) -> f4(A,B)            [0 >= A] (?,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, A + B, .* 0) (<0,0,B>, 1 + B, .+ 1) 
          (<1,0,A>,     A, .= 0) (<1,0,B>,     B, .= 0) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,     B, .= 0) 
          (<3,0,A>,     A, .= 0) (<3,0,B>,     B, .= 0) 
* Step 3: SizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          2. f2(A,B) -> f4(A,B)            [0 >= A] (?,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},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>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          2. f2(A,B) -> f4(A,B)            [0 >= A] (?,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2},1->{0,2},2->{},3->{}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
          (<2,0,A>, ?) (<2,0,B>, ?) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2]
* Step 5: LocationConstraintsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0},1->{0},3->{}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        LocationConstraintsProc
    + Details:
        We computed the location constraints  0 :  [B >= 1 && B >= 1] 1 :  True 3 :  True .
* Step 6: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0},1->{0},3->{}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f2) = x1
          p(f3) = x1
          p(f4) = x1
        
        The following rules are strictly oriented:
         [A >= 1] ==>                   
          f2(A,B)   = A                 
                    > A + -1*B          
                    = f2(A + -1*B,1 + B)
        
        
        The following rules are weakly oriented:
         [B >= 1] ==>        
          f3(A,B)   = A      
                   >= A      
                    = f2(A,B)
        
         [0 >= B] ==>        
          f3(A,B)   = A      
                   >= A      
                    = f4(A,B)
        
        
* Step 7: UnsatPaths WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(A + -1*B,1 + B) [A >= 1] (A,1)
          1. f3(A,B) -> f2(A,B)            [B >= 1] (1,1)
          3. f3(A,B) -> f4(A,B)            [0 >= B] (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0},1->{0},3->{}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
          (<3,0,A>, A) (<3,0,B>, B) 
    + Applied Processor:
        UnsatPaths
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))