k=0 
  
 L_(1,1)^0={b u e} 
 L_(1,2)^0=a 
 L_(1,3)^0={} 
 L_(2,1)^0=b 
 L_(2,2)^0={e} 
 L_(2,3)^0=a 
 L_(3,1)^0={} 
 L_(3,2)^0={} 
 L_(3,3)^0={a,b,e}

k=1 
  
 L_(1,1)^1={b u e} u ({b u e} o {b u e}* o {b u e})=b* 
 L_(1,2)^1=a u ({b u e} o {b u e}* o a)            =b*a 
 L_(1,3)^1={} u ({b u e} o {b u e}* o {})          ={} 
 L_(2,1)^1=b u (b o {b u e}* o {b u e})            =bb* 
 L_(2,2)^1={e} u (b o {b u e}* o a)                =e u bb*a 
 L_(2,3)^1=a u (b o {b u e}* o {})                 =a 
 L_(3,1)^1={} u ({} o {b u e}* o {b u e})          ={} 
 L_(3,2)^1={} u ({} o {b u e}* o a)                ={} 
 L_(3,3)^1={a,b,e} u ({} o {b u e}* o {})          ={a,b,e}

k=2 
  
 L_(1,1)^2=b* u (b*a o (e u bb*a)* o bb*)                      =b* u b*a(bb*a)*bb* 
 L_(1,2)^2=b*a u (b*a o (e u bb*a)* o (e u bb*a))              =b*a(bb*a)* 
 L_(1,3)^2={} u (b*a o (e u bb*a)* o a)                        =b*a(bb*a)*a 
 L_(2,1)^2=bb* u ((e u bb*a) o (e u bb*a)* o bb*)              =(bb*a)*bb* 
 L_(2,2)^2=(e u bb*a) u ((e u bb*a) o (e u bb*a)* o (e u bb*a))=(bb*a)* 
 L_(2,3)^2=a u ((e u bb*a) o (e u bb*a)* o a)                  =(bb*a)*a 
 L_(3,1)^2={} u ({} o (e u bb*a)* o bb*)                       ={} 
 L_(3,2)^2={} u ({} o (e u bb*a)* o (e u bb*a))                ={} 
 L_(3,3)^2={a,b,e} u ({} o (e u bb*a)* o a)                    ={a,b,e}

k=3 
  
 L_(1,1)^3=(b* u b*a(bb*a)*bb*) u (b*a(bb*a)*a o {a,b,e}* o {})=b* u b*a(bb*a)*bb* 
 L_(1,2)^3=b*a(bb*a)* u (b*a(bb*a)*a o {a,b,e}* o {})          =b*a(bb*a)* 
 L_(1,3)^3=b*a(bb*a)*a u (b*a(bb*a)*a o {a,b,e}* o {a,b,e})    =(b*a(bb*a)*a){a,b}* 
 L_(2,1)^3=(bb*a)*bb* u ((bb*a)*a o {a,b,e}* o {})             =(bb*a)*bb* 
 L_(2,2)^3=(bb*a)* u ((bb*a)*a o {a,b,e}* o {})                =(bb*a)* 
 L_(2,3)^3=(bb*a)*a u ((bb*a)*a o {a,b,e}* o {a,b,e})          =((bb*a)*a){a,b}* 
 L_(3,1)^3={} u ({a,b,e} o {a,b,e}* o {})                      ={} 
 L_(3,2)^3={} u ({a,b,e} o {a,b,e}* o {})                      ={} 
 L_(3,3)^3={a,b,e} u ({a,b,e} o {a,b,e}* o {a,b,e})            ={a,b}*