Consider the following context-free grammar:

S AB

A ABCD|BCD

B CD

C a|Cb

D AB|C

Show the process of deriving each of the following strings based on the context-free grammar (here, each step when a substitution rule is used should be given).

1. aaaaaa

2. abaabaaba

3. ) Provide a PDA which recognises the language of this grammar.