diff --git a/AutFN.jl b/AutFN.jl
index 09a7da1..6063a25 100644
--- a/AutFN.jl
+++ b/AutFN.jl
@@ -115,7 +115,7 @@ function hashed_product{T}(image::T, B, images_dict::Dict{T, Int})
     return column
 end
 
-function create_product_matrix(basis::Vector{AutWord}, images)
+function create_product_matrix(images, basis::Vector{AutWord})
     n = length(basis)
     product_matrix = zeros(Int, (n, n));
     print("Creating hashtable of images...")
@@ -129,41 +129,36 @@ function create_product_matrix(basis::Vector{AutWord}, images)
     return product_matrix
 end
 
-function ΔandSDPconstraints(identity::AutWord, S::Vector{AutWord})
-
-    println("Generating Balls of increasing radius...")
-    @time B₁ = vcat([identity], S)
-    @time B₂ = products(B₁,B₁);
-    @show length(B₂)
-    if length(B₂) != length(B₁)
-        @time B₃ = products(B₁, B₂)
-        @show length(B₃)
-        if length(B₃) != length(B₂)
-            @time B₄_images = products_images(B₁, B₃)
-        else
-            B₄_images = unique([f(domain) for f in B₃])
-        end
-    else
-        B₃ = B₂
-        B₄ = B₂
-        B₄_images = unique([f(domain) for f in B₃])
+function generate_balls{T}(S::Vector{T}, Id::T; radius=4)
+    sizes = Vector{Int}()
+    S = vcat([Id], S)
+    B = [Id]
+    for i in 1:radius
+        B = products(B, S);
+        push!(sizes, length(B))
     end
+    return B, sizes
+end
 
-    @show length(B₄_images)
+
+function ΔandSDPconstraints(Id::AutWord, S::Vector{AutWord}, r::Int=2)
+    B, sizes = generate_balls(S, Id, radius=2*r)
+    basis = B[1:sizes[r]]
+    B_images = unique([f(domain) for f in B])
+
+    println("Generated balls of sizes $sizes")
 
     println("Creating product matrix...")
-    @time pm = create_product_matrix(B₂, B₄_images)
+    @time pm = create_product_matrix(B_images, basis)
     println("Creating sdp_constratints...")
     @time sdp_constraints = PropertyT.constraints_from_pm(pm)
 
-    L_coeff = PropertyT.splaplacian_coeff(S, B₂, length(B₄_images))
+    L_coeff = PropertyT.splaplacian_coeff(S, basis, length(B_images))
     Δ = PropertyT.GroupAlgebraElement(L_coeff, Array{Int,2}(pm))
 
     return Δ, sdp_constraints
 end
 
-ΔandSDPconstraints(identity::AutWord, S::Vector{AutWord}, r::Int) = ΔandSDPconstraints(identity, S)
-
 const symbols =  [FGSymbol("x₁",1), FGSymbol("x₂",1), FGSymbol("x₃",1), FGSymbol("x₄",1), FGSymbol("x₅",1), FGSymbol("x₆",1)]
 
 const TOL=1e-8