WORST_CASE(?,O(n^1))
* Step 1: RestrictVarsProcessor WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B,C,D,E,F) -> f2(-1 + A,-1 + B,A,B,-2 + A,F) [A >= 1 && B >= 1] (?,1)
          1. f3(A,B,C,D,E,F) -> f2(A,B,C,D,E,F)                True               (1,1)
          2. f2(A,B,C,D,E,F) -> f4(A,G,C,D,E,H)                [0 >= B && 0 >= G] (?,1)
          3. f2(A,B,C,D,E,F) -> f4(A,B,C,D,E,H)                [B >= 1 && 0 >= A] (?,1)
        Signature:
          {(f2,6);(f3,6);(f4,6)}
        Flow Graph:
          [0->{0,2,3},1->{0,2,3},2->{},3->{}]
        
    + Applied Processor:
        RestrictVarsProcessor
    + Details:
        We removed the arguments [C,D,E,F] .
* Step 2: LocalSizeboundsProc WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(-1 + A,-1 + B) [A >= 1 && B >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)           True               (1,1)
          2. f2(A,B) -> f4(A,G)           [0 >= B && 0 >= G] (?,1)
          3. f2(A,B) -> f4(A,B)           [B >= 1 && 0 >= A] (?,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2,3},1->{0,2,3},2->{},3->{}]
        
    + Applied Processor:
        LocalSizeboundsProc
    + Details:
        LocalSizebounds generated; rvgraph
          (<0,0,A>, 1 + A, .+ 1) (<0,0,B>, 1 + B, .+ 1) 
          (<1,0,A>,     A, .= 0) (<1,0,B>,     B, .= 0) 
          (<2,0,A>,     A, .= 0) (<2,0,B>,     ?,   .?) 
          (<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(-1 + A,-1 + B) [A >= 1 && B >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)           True               (1,1)
          2. f2(A,B) -> f4(A,G)           [0 >= B && 0 >= G] (?,1)
          3. f2(A,B) -> f4(A,B)           [B >= 1 && 0 >= A] (?,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2,3},1->{0,2,3},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>, ?) (<3,0,B>, ?) 
* Step 4: LeafRules WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(-1 + A,-1 + B) [A >= 1 && B >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)           True               (1,1)
          2. f2(A,B) -> f4(A,G)           [0 >= B && 0 >= G] (?,1)
          3. f2(A,B) -> f4(A,B)           [B >= 1 && 0 >= A] (?,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0,2,3},1->{0,2,3},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>, ?) (<3,0,B>, ?) 
    + Applied Processor:
        LeafRules
    + Details:
        The following transitions are estimated by its predecessors and are removed [2,3]
* Step 5: PolyRank WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(-1 + A,-1 + B) [A >= 1 && B >= 1] (?,1)
          1. f3(A,B) -> f2(A,B)           True               (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0},1->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
    + Applied Processor:
        PolyRank {useFarkas = True, withSizebounds = [], shape = Linear}
    + Details:
        We apply a polynomial interpretation of shape linear:
          p(f2) = x2
          p(f3) = x2
        
        The following rules are strictly oriented:
        [A >= 1 && B >= 1] ==>                  
                   f2(A,B)   = B                
                             > -1 + B           
                             = f2(-1 + A,-1 + B)
        
        
        The following rules are weakly oriented:
             True ==>        
          f3(A,B)   = B      
                   >= B      
                    = f2(A,B)
        
        
* Step 6: KnowledgePropagation WORST_CASE(?,O(n^1))
    + Considered Problem:
        Rules:
          0. f2(A,B) -> f2(-1 + A,-1 + B) [A >= 1 && B >= 1] (B,1)
          1. f3(A,B) -> f2(A,B)           True               (1,1)
        Signature:
          {(f2,2);(f3,2);(f4,2)}
        Flow Graph:
          [0->{0},1->{0}]
        Sizebounds:
          (<0,0,A>, ?) (<0,0,B>, ?) 
          (<1,0,A>, A) (<1,0,B>, B) 
    + Applied Processor:
        KnowledgePropagation
    + Details:
        The problem is already solved.

WORST_CASE(?,O(n^1))