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Rules:
S –> AB
A –> aAA
A –> aA
A –> a
B –> bB
B –> b
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A leftmost derivation
E=>E*E
=>I*E
=>3*E+E
=>3*I+E
=>3*2+E
=>3*2+I
=>3*2+5
Another leftmost derivation
E=>E+E
=>E*E+E
=>I*E+E
=>3*E+E
=>3*I+E
=>3*2+I
=>3*2+5
17
E=>E*E
=>I*E
=>3*E+E
=>3*I+E
=>3*2+E
=>3*2+I
=>3*2+5
E
E
I
*
E
E
+
E
E
3
Another leftmost derivation
E=>E+E
=>E*E+E
=>I*E+E
E
=>3*E+E
=>3*I+E
=>3*2+I
I
=>3*2+5
3
+
E
*
E
I
I
2
5
E
I
5
I
2
18
Ambiguous grammar:
E -> I
E -> E + E
E -> E * E
E -> (E)
I -> ε | 0 | 1 | … | 9
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Rules:
S -> AB | C
A -> aAb | ab
B -> cBd | cd
String aabbccdd belongs to two different parts of the language:
L ={anbncmdm | n≥1, m ≥ 1}  {anbmcmdn | n ≥ 1, m ≥ 1}
C -> aCd | aDd
D -> bDc | bc
Derivation 2 of
aabbccdd:
S => C
=> aCd
=> aaDdd
=> aa bDc dd
=> aabbccdd
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