The extra arguments in a definite-clause grammar makes it strictly more powerful than a context-free grammar. The language {anbncn | n ≥ 0}, which consists of sentences that are made up of a number of as, followed by the same number of bs followed by the same number of cs cannot be defined with a context-free grammar. Define this language using a definite clause grammar.

[Hint: Define a predicate copies for a non-terminal that creates n copies of one of its arguments, and represent numbers using 0 for zero and s(N) for the numbers after n.]