cykp v1.2 starting
adding production S -> a	X	b	
adding production S -> a	A	
adding production S -> A	B	
adding production S -> a	S	a	S	a	
adding production A -> B	
adding production A -> a	
adding production B -> A	
adding production C -> a	
adding production S -> #e	
adding production C -> #e	
reading input finished.
Start symbol: S
Variables: A B C S X 
Terminals: a b 
Sorted productions:
A -> B	
A -> a	
B -> A	
C -> #e	
C -> a	
S -> #e	
S -> A	B	
S -> a	A	
S -> a	S	a	S	a	
S -> a	X	b	
cyk_eliminate 1a)
newv= A  C  S  
cyk_eliminate 1a) n
newv= A  B  C  S  
eliminate temp= X  
lemma 4.1 variables removed: X 
cyk_eliminate 1b)
newv= A  B  S  
newt= a  
lemma 4.2 variables removed: C 
lemma 4.2 terminals removed: b 
deleting useless production:
C -> #e 
deleting useless production:
C -> a 
deleting useless production:
S -> a X b 
cyk_eliminate 2)
Eliminate epslion Productions
nullable variable: S
nullable variable: S
deleting epsilon production:
S -> #e 
adding with no #e:0
S -> a a a 
adding with no #e:1
S -> a S a a 
adding with no #e:2
S -> a a S a 
cyk_eliminate 3)
Eliminate Unit Productions
after eliminate, Variables:
A B S 
after eliminate, Terminals:
a 
after eliminate, sorted productions:
A -> a 
B -> a 
S -> A B 
S -> a A 
S -> a S a S a 
S -> a S a a 
S -> a a S a 
S -> a a a 
Chomsky 1, replace terminal with variable
Chomsky part 1, sorted productions:
A ->  a
B ->  a
S ->  A  B
S ->  T_a  A
S ->  T_a  S  T_a  S  T_a
S ->  T_a  S  T_a  T_a
S ->  T_a  T_a  S  T_a
S ->  T_a  T_a  T_a
T_a ->  a
Chomsky Part 2 generated productions
C_ST_a ->  S  T_a
C_T_aS ->  T_a  S
C_ST_a ->  S  T_a
C_T_aT_a ->  T_a  T_a
C_ST_a ->  S  T_a
C_ST_a ->  S  T_a
C_T_aS ->  T_a  S
C_T_aT_a ->  T_a  T_a
after Chomsky, sorted productions:
A ->  a
B ->  a
C_ST_a ->  S  T_a
C_T_aS ->  T_a  S
C_T_aT_a ->  T_a  T_a
S ->  A  B
S ->  T_a  A
S ->  T_a  C_ST_a
S ->  T_a  C_T_aS
S ->  T_a  C_T_aT_a
T_a ->  a
after Chomsky, Variables:
A  B  C_ST_a  C_T_aS  C_T_aT_a  S  T_a  

about to parse aa
run CYK algorithm to build array, size=2
Finished first row of VV table
VV(1,1)= A B T_a 
VV(2,1)= A B T_a 
Finished 2 row of VV table
VV(1,2)= C_T_aT_a S 
VV(2,2)= 
finish CYK algorithm, check for S in VV[1][n]and thus Accepted 
string accepted by G, string is in L(G)

about to parse 
run CYK algorithm to build array, size=0
null string accepted by G, string is in L(G)

about to parse a
run CYK algorithm to build array, size=1
Finished first row of VV table
VV(1,1)= A B T_a 
finish CYK algorithm, check for S in VV[1][n]and thus Accepted 
string rejected by G, string is not in L(G)