Exercício 08.39

Converta para a Forma Normal de Greibach a gramática:

G = ({S, A, B, C}, {a, b}, P, S)
P = {< S >  ->  < S > < C >
            |   < A > < A >
            |   a
     < A >  ->  < C > < A >
            |   < A > < B >
            |   a
     < B >  ->  < A > < C >
            |   b
     < C >  ->  < C > < A >
            |   < A > < S >
            |   b }

Resposta

1. Simplificação da gramática livre do contexto

A gramática livre do contexto já está simplificada.

G = ({S, A, B, C}, {a, b}, P, S)
P = {< S >  ->  < S > < C >
            |   < A > < A >
            |   a
     < A >  ->  < C > < A >
            |   < A > < B >
            |   a
     < B >  ->  < A > < C >
            |   b
     < C >  ->  < C > < A >
            |   < A > < S >
            |   b }

2. Renomeação das variáveis em uma ordem crescente qualquer

G = ({A, B, C, D}, {a, b}, P, A)
P = {< A >  ->  < A > < D >
            |   < B > < B >
            |   a
     < B >  ->  < D > < B >
            |   < B > < C >
            |   a
     < C >  ->  < B > < D >
            |   b
     < D >  ->  < D > < B >
            |   < B > < A >
            |   b }

4. Exclusão das recursões da forma < Ar > -> < Ar > α

G = ({A, A₀, B, B₀, C, D, D₀}, {a, b}, P, A)
P = {< A >  ->  < B > < B > < A₀ >
            |   a < A₀ >
            |   < B > < B >
            |   a
     < A₀ > ->  < D > < A₀ >
            |   < D >
     < B >  ->  < D > < B > < B₀ >
            |   a < B₀ >
            |   < D > < B >
            |   a
     < B₀ > ->  < C > < B₀ >
            |   < C >
     < C >  ->  < B > < D >
            |   b
     < D >  ->  < B > < A > < D₀ >
            |   b < D₀ >
            |   < B > < A >
            |   b
     < D₀ > ->  < B > < D₀ >
            |   < B > }

3. Transformação de produções para a forma < Ar > -> < As > α, onde r ≤ s

G = ({A, A₀, B, B₀, C, D, D₀}, {a, b}, P, A)
P = {< A >  ->  < B > < B > < A₀ >
            |   a < A₀ >
            |   < B > < B >
            |   a
     < A₀ > ->  < D > < A₀ >
            |   < D >
     < B >  ->  < D > < B > < B₀ >
            |   a < B₀ >
            |   < D > < B >
            |   a
     < B₀ > ->  < C > < B₀ >
            |   < C >
     < C >  ->  < D > < B > < B₀ > < D >
            |   a < B₀ > < D >
            |   < D > < B > < D >
            |   a < D >
            |   b
     < D >  ->  < D > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ >
            |   < D > < B > < A > < D₀ >
            |   a < A > < D₀ >
            |   b < D₀ >
            |   < D > < B > < B₀ > < A >
            |   a < B₀ > < A >
            |   < D > < B > < A >
            |   a < A >
            |   b
     < D₀ > ->  < B > < D₀ >
            |   < B > }

4. Exclusão das recursões da forma < Ar > -> < Ar > α

G = ({A, A₀, B, B₀, C, D, D₀, D₁}, {a, b}, P, A)
P = {< A >  ->  < B > < B > < A₀ >
            |   a < A₀ >
            |   < B > < B >
            |   a
     < A₀ > ->  < D > < A₀ >
            |   < D >
     < B >  ->  < D > < B > < B₀ >
            |   a < B₀ >
            |   < D > < B >
            |   a
     < B₀ > ->  < C > < B₀ >
            |   < C >
     < C >  ->  < D > < B > < B₀ > < D >
            |   a < B₀ > < D >
            |   < D > < B > < D >
            |   a < D >
            |   b
     < D >  ->  a < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < A > < D₁ >
            |   b < D₁ >
            |   a < B₀ > < A > < D₀ >
            |   a < A > < D₀ >
            |   b < D₀ >
            |   a < B₀ > < A >
            |   a < A >
            |   b
     < D₀ > ->  < B > < D₀ >
            |   < B >
     < D₁ > ->  < B > < B₀ > < A > < D₀ > < D₁ >
            |   < B > < A > < D₀ > < D₁ >
            |   < B > < B₀ > < A > < D₁ >
            |   < B > < A > < D₁ >
            |   < B > < B₀ > < A > < D₀ >
            |   < B > < A > < D₀ >
            |   < B > < B₀ > < A >
            |   < B > < A > }

5. Um terminal no início do lado direito de cada produção

G = ({A, A₀, B, B₀, C, D, D₀, D₁}, {a, b}, P, A)
P = {< A >  ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₁ > < B > < B₀ > < B > < A₀ >
            |   b < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₀ > < B > < B₀ > < B > < A₀ >
            |   b < D₀ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < B > < B₀ > < B > < A₀ >
            |   a < A > < B > < B₀ > < B > < A₀ >
            |   b < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B > < A₀ >
            |   a < A > < D₀ > < D₁ > < B > < B > < A₀ >
            |   b < D₀ > < D₁ > < B > < B > < A₀ >
            |   a < B₀ > < A > < D₁ > < B > < B > < A₀ >
            |   a < A > < D₁ > < B > < B > < A₀ >
            |   b < D₁ > < B > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < B > < B > < A₀ >
            |   a < A > < D₀ > < B > < B > < A₀ >
            |   b < D₀ > < B > < B > < A₀ >
            |   a < B₀ > < A > < B > < B > < A₀ >
            |   a < A > < B > < B > < A₀ >
            |   b < B > < B > < A₀ >
            |   a < B > < A₀ >
            |   a < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B >
            |   b < D₀ > < D₁ > < B > < B₀ > < B >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B >
            |   a < A > < D₁ > < B > < B₀ > < B >
            |   b < D₁ > < B > < B₀ > < B >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B >
            |   a < A > < D₀ > < B > < B₀ > < B >
            |   b < D₀ > < B > < B₀ > < B >
            |   a < B₀ > < A > < B > < B₀ > < B >
            |   a < A > < B > < B₀ > < B >
            |   b < B > < B₀ > < B >
            |   a < B₀ > < B >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B >
            |   a < A > < D₀ > < D₁ > < B > < B >
            |   b < D₀ > < D₁ > < B > < B >
            |   a < B₀ > < A > < D₁ > < B > < B >
            |   a < A > < D₁ > < B > < B >
            |   b < D₁ > < B > < B >
            |   a < B₀ > < A > < D₀ > < B > < B >
            |   a < A > < D₀ > < B > < B >
            |   b < D₀ > < B > < B >
            |   a < B₀ > < A > < B > < B >
            |   a < A > < B > < B >
            |   b < B > < B >
            |   a < B >
            |   a
     < A₀ > ->  a < B₀ > < A > < D₀ > < D₁ > < A₀ >
            |   a < A > < D₀ > < D₁ > < A₀ >
            |   b < D₀ > < D₁ > < A₀ >
            |   a < B₀ > < A > < D₁ > < A₀ >
            |   a < A > < D₁ > < A₀ >
            |   b < D₁ > < A₀ >
            |   a < B₀ > < A > < D₀ > < A₀ >
            |   a < A > < D₀ > < A₀ >
            |   b < D₀ > < A₀ >
            |   a < B₀ > < A > < A₀ >
            |   a < A > < A₀ >
            |   b < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < A > < D₁ >
            |   b < D₁ >
            |   a < B₀ > < A > < D₀ >
            |   a < A > < D₀ >
            |   b < D₀ >
            |   a < B₀ > < A >
            |   a < A >
            |   b
     < B >  ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ >
            |   b < D₀ > < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ >
            |   a < A > < D₁ > < B > < B₀ >
            |   b < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ >
            |   a < A > < D₀ > < B > < B₀ >
            |   b < D₀ > < B > < B₀ >
            |   a < B₀ > < A > < B > < B₀ >
            |   a < A > < B > < B₀ >
            |   b < B > < B₀ >
            |   a < B₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B >
            |   a < A > < D₀ > < D₁ > < B >
            |   b < D₀ > < D₁ > < B >
            |   a < B₀ > < A > < D₁ > < B >
            |   a < A > < D₁ > < B >
            |   b < D₁ > < B >
            |   a < B₀ > < A > < D₀ > < B >
            |   a < A > < D₀ > < B >
            |   b < D₀ > < B >
            |   a < B₀ > < A > < B >
            |   a < A > < B >
            |   b < B >
            |   a
     < B₀ > ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₁ > < B > < B₀ > < D > < B₀ >
            |   b < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₀ > < B > < B₀ > < D > < B₀ >
            |   b < D₀ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < B > < B₀ > < D > < B₀ >
            |   a < A > < B > < B₀ > < D > < B₀ >
            |   b < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < D > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < D > < B₀ >
            |   b < D₀ > < D₁ > < B > < D > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < D > < B₀ >
            |   a < A > < D₁ > < B > < D > < B₀ >
            |   b < D₁ > < B > < D > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < D > < B₀ >
            |   a < A > < D₀ > < B > < D > < B₀ >
            |   b < D₀ > < B > < D > < B₀ >
            |   a < B₀ > < A > < B > < D > < B₀ >
            |   a < A > < B > < D > < B₀ >
            |   b < B > < D > < B₀ >
            |   a < D > < B₀ >
            |   b < B₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < D >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < D >
            |   b < D₀ > < D₁ > < B > < B₀ > < D >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < D >
            |   a < A > < D₁ > < B > < B₀ > < D >
            |   b < D₁ > < B > < B₀ > < D >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < D >
            |   a < A > < D₀ > < B > < B₀ > < D >
            |   b < D₀ > < B > < B₀ > < D >
            |   a < B₀ > < A > < B > < B₀ > < D >
            |   a < A > < B > < B₀ > < D >
            |   b < B > < B₀ > < D >
            |   a < B₀ > < D >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < D >
            |   a < A > < D₀ > < D₁ > < B > < D >
            |   b < D₀ > < D₁ > < B > < D >
            |   a < B₀ > < A > < D₁ > < B > < D >
            |   a < A > < D₁ > < B > < D >
            |   b < D₁ > < B > < D >
            |   a < B₀ > < A > < D₀ > < B > < D >
            |   a < A > < D₀ > < B > < D >
            |   b < D₀ > < B > < D >
            |   a < B₀ > < A > < B > < D >
            |   a < A > < B > < D >
            |   b < B > < D >
            |   a < D >
            |   b
     < C >  ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < D >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < D >
            |   b < D₀ > < D₁ > < B > < B₀ > < D >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < D >
            |   a < A > < D₁ > < B > < B₀ > < D >
            |   b < D₁ > < B > < B₀ > < D >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < D >
            |   a < A > < D₀ > < B > < B₀ > < D >
            |   b < D₀ > < B > < B₀ > < D >
            |   a < B₀ > < A > < B > < B₀ > < D >
            |   a < A > < B > < B₀ > < D >
            |   b < B > < B₀ > < D >
            |   a < B₀ > < D >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < D >
            |   a < A > < D₀ > < D₁ > < B > < D >
            |   b < D₀ > < D₁ > < B > < D >
            |   a < B₀ > < A > < D₁ > < B > < D >
            |   a < A > < D₁ > < B > < D >
            |   b < D₁ > < B > < D >
            |   a < B₀ > < A > < D₀ > < B > < D >
            |   a < A > < D₀ > < B > < D >
            |   b < D₀ > < B > < D >
            |   a < B₀ > < A > < B > < D >
            |   a < A > < B > < D >
            |   b < B > < D >
            |   a < D >
            |   b
     < D >  ->  a < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < A > < D₁ >
            |   b < D₁ >
            |   a < B₀ > < A > < D₀ >
            |   a < A > < D₀ >
            |   b < D₀ >
            |   a < B₀ > < A >
            |   a < A >
            |   b
     < D₀ > ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < D₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < D₀ >
            |   a < A > < D₁ > < B > < B₀ > < D₀ >
            |   b < D₁ > < B > < B₀ > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < D₀ >
            |   a < A > < D₀ > < B > < B₀ > < D₀ >
            |   b < D₀ > < B > < B₀ > < D₀ >
            |   a < B₀ > < A > < B > < B₀ > < D₀ >
            |   a < A > < B > < B₀ > < D₀ >
            |   b < B > < B₀ > < D₀ >
            |   a < B₀ > < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < D₀ >
            |   b < D₀ > < D₁ > < B > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < D₀ >
            |   a < A > < D₁ > < B > < D₀ >
            |   b < D₁ > < B > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < D₀ >
            |   a < A > < D₀ > < B > < D₀ >
            |   b < D₀ > < B > < D₀ >
            |   a < B₀ > < A > < B > < D₀ >
            |   a < A > < B > < D₀ >
            |   b < B > < D₀ >
            |   a < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ >
            |   b < D₀ > < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ >
            |   a < A > < D₁ > < B > < B₀ >
            |   b < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ >
            |   a < A > < D₀ > < B > < B₀ >
            |   b < D₀ > < B > < B₀ >
            |   a < B₀ > < A > < B > < B₀ >
            |   a < A > < B > < B₀ >
            |   b < B > < B₀ >
            |   a < B₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B >
            |   a < A > < D₀ > < D₁ > < B >
            |   b < D₀ > < D₁ > < B >
            |   a < B₀ > < A > < D₁ > < B >
            |   a < A > < D₁ > < B >
            |   b < D₁ > < B >
            |   a < B₀ > < A > < D₀ > < B >
            |   a < A > < D₀ > < B >
            |   b < D₀ > < B >
            |   a < B₀ > < A > < B >
            |   a < A > < B >
            |   b < B >
            |   a
     < D₁ > ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₁ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   b < B > < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₁ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < D₀ > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < B > < B₀ > < A > < D₀ > < D₁ >
            |   b < B > < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ > < B > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < A > < D₀ > < D₁ >
            |   a < A > < D₁ > < B > < A > < D₀ > < D₁ >
            |   b < D₁ > < B > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < B > < A > < D₀ > < D₁ >
            |   b < D₀ > < B > < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < B > < A > < D₀ > < D₁ >
            |   a < A > < B > < A > < D₀ > < D₁ >
            |   b < B > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   b < D₁ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   b < D₀ > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < A > < B > < B₀ > < B₀ > < A > < D₁ >
            |   b < B > < B₀ > < B₀ > < A > < D₁ >
            |   a < B₀ > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₁ >
            |   b < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₁ >
            |   b < D₀ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₁ >
            |   a < A > < B > < B₀ > < A > < D₁ >
            |   b < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₁ >
            |   b < D₁ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₁ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₁ >
            |   b < D₀ > < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₁ >
            |   a < A > < B > < B₀ > < A > < D₁ >
            |   b < B > < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < A > < D₁ >
            |   a < A > < D₀ > < D₁ > < B > < A > < D₁ >
            |   b < D₀ > < D₁ > < B > < A > < D₁ >
            |   a < B₀ > < A > < D₁ > < B > < A > < D₁ >
            |   a < A > < D₁ > < B > < A > < D₁ >
            |   b < D₁ > < B > < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < B > < A > < D₁ >
            |   a < A > < D₀ > < B > < A > < D₁ >
            |   b < D₀ > < B > < A > < D₁ >
            |   a < B₀ > < A > < B > < A > < D₁ >
            |   a < A > < B > < A > < D₁ >
            |   b < B > < A > < D₁ >
            |   a < A > < D₁ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < A > < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   b < D₁ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   b < D₀ > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < A > < B > < B₀ > < B₀ > < A > < D₀ >
            |   b < B > < B₀ > < B₀ > < A > < D₀ >
            |   a < B₀ > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₀ >
            |   b < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₀ >
            |   b < D₀ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₀ >
            |   a < A > < B > < B₀ > < A > < D₀ >
            |   b < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₁ > < B > < B₀ > < A > < D₀ >
            |   b < D₁ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A > < D₀ >
            |   a < A > < D₀ > < B > < B₀ > < A > < D₀ >
            |   b < D₀ > < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < B > < B₀ > < A > < D₀ >
            |   a < A > < B > < B₀ > < A > < D₀ >
            |   b < B > < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < A > < D₀ >
            |   a < A > < D₀ > < D₁ > < B > < A > < D₀ >
            |   b < D₀ > < D₁ > < B > < A > < D₀ >
            |   a < B₀ > < A > < D₁ > < B > < A > < D₀ >
            |   a < A > < D₁ > < B > < A > < D₀ >
            |   b < D₁ > < B > < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < B > < A > < D₀ >
            |   a < A > < D₀ > < B > < A > < D₀ >
            |   b < D₀ > < B > < A > < D₀ >
            |   a < B₀ > < A > < B > < A > < D₀ >
            |   a < A > < B > < A > < D₀ >
            |   b < B > < A > < D₀ >
            |   a < A > < D₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B₀ > < A >
            |   b < D₀ > < D₁ > < B > < B₀ > < B₀ > < A >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B₀ > < A >
            |   a < A > < D₁ > < B > < B₀ > < B₀ > < A >
            |   b < D₁ > < B > < B₀ > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B₀ > < A >
            |   a < A > < D₀ > < B > < B₀ > < B₀ > < A >
            |   b < D₀ > < B > < B₀ > < B₀ > < A >
            |   a < B₀ > < A > < B > < B₀ > < B₀ > < A >
            |   a < A > < B > < B₀ > < B₀ > < A >
            |   b < B > < B₀ > < B₀ > < A >
            |   a < B₀ > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   b < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₁ > < B > < B₀ > < A >
            |   b < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A >
            |   a < A > < D₀ > < B > < B₀ > < A >
            |   b < D₀ > < B > < B₀ > < A >
            |   a < B₀ > < A > < B > < B₀ > < A >
            |   a < A > < B > < B₀ > < A >
            |   b < B > < B₀ > < A >
            |   a < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   b < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₁ > < B > < B₀ > < A >
            |   b < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A >
            |   a < A > < D₀ > < B > < B₀ > < A >
            |   b < D₀ > < B > < B₀ > < A >
            |   a < B₀ > < A > < B > < B₀ > < A >
            |   a < A > < B > < B₀ > < A >
            |   b < B > < B₀ > < A >
            |   a < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < A >
            |   a < A > < D₀ > < D₁ > < B > < A >
            |   b < D₀ > < D₁ > < B > < A >
            |   a < B₀ > < A > < D₁ > < B > < A >
            |   a < A > < D₁ > < B > < A >
            |   b < D₁ > < B > < A >
            |   a < B₀ > < A > < D₀ > < B > < A >
            |   a < A > < D₀ > < B > < A >
            |   b < D₀ > < B > < A >
            |   a < B₀ > < A > < B > < A >
            |   a < A > < B > < A >
            |   b < B > < A >
            |   a < A > }

6. Produções da forma < Ar > -> a α onde α é composto por variáveis

G = ({A, A₀, B, B₀, C, D, D₀, D₁}, {a, b}, P, A)
P = {< A >  ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₁ > < B > < B₀ > < B > < A₀ >
            |   b < D₁ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B > < A₀ >
            |   a < A > < D₀ > < B > < B₀ > < B > < A₀ >
            |   b < D₀ > < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < B > < B₀ > < B > < A₀ >
            |   a < A > < B > < B₀ > < B > < A₀ >
            |   b < B > < B₀ > < B > < A₀ >
            |   a < B₀ > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B > < A₀ >
            |   a < A > < D₀ > < D₁ > < B > < B > < A₀ >
            |   b < D₀ > < D₁ > < B > < B > < A₀ >
            |   a < B₀ > < A > < D₁ > < B > < B > < A₀ >
            |   a < A > < D₁ > < B > < B > < A₀ >
            |   b < D₁ > < B > < B > < A₀ >
            |   a < B₀ > < A > < D₀ > < B > < B > < A₀ >
            |   a < A > < D₀ > < B > < B > < A₀ >
            |   b < D₀ > < B > < B > < A₀ >
            |   a < B₀ > < A > < B > < B > < A₀ >
            |   a < A > < B > < B > < A₀ >
            |   b < B > < B > < A₀ >
            |   a < B > < A₀ >
            |   a < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < B >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < B >
            |   b < D₀ > < D₁ > < B > < B₀ > < B >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < B >
            |   a < A > < D₁ > < B > < B₀ > < B >
            |   b < D₁ > < B > < B₀ > < B >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < B >
            |   a < A > < D₀ > < B > < B₀ > < B >
            |   b < D₀ > < B > < B₀ > < B >
            |   a < B₀ > < A > < B > < B₀ > < B >
            |   a < A > < B > < B₀ > < B >
            |   b < B > < B₀ > < B >
            |   a < B₀ > < B >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B >
            |   a < A > < D₀ > < D₁ > < B > < B >
            |   b < D₀ > < D₁ > < B > < B >
            |   a < B₀ > < A > < D₁ > < B > < B >
            |   a < A > < D₁ > < B > < B >
            |   b < D₁ > < B > < B >
            |   a < B₀ > < A > < D₀ > < B > < B >
            |   a < A > < D₀ > < B > < B >
            |   b < D₀ > < B > < B >
            |   a < B₀ > < A > < B > < B >
            |   a < A > < B > < B >
            |   b < B > < B >
            |   a < B >
            |   a
     < A₀ > ->  a < B₀ > < A > < D₀ > < D₁ > < A₀ >
            |   a < A > < D₀ > < D₁ > < A₀ >
            |   b < D₀ > < D₁ > < A₀ >
            |   a < B₀ > < A > < D₁ > < A₀ >
            |   a < A > < D₁ > < A₀ >
            |   b < D₁ > < A₀ >
            |   a < B₀ > < A > < D₀ > < A₀ >
            |   a < A > < D₀ > < A₀ >
            |   b < D₀ > < A₀ >
            |   a < B₀ > < A > < A₀ >
            |   a < A > < A₀ >
            |   b < A₀ >
            |   a < B₀ > < A > < D₀ > < D₁ >
            |   a < A > < D₀ > < D₁ >
            |   b < D₀ > < D₁ >
            |   a < B₀ > < A > < D₁ >
            |   a < A > < D₁ >
            |   b < D₁ >
            |   a < B₀ > < A > < D₀ >
            |   a < A > < D₀ >
            |   b < D₀ >
            |   a < B₀ > < A >
            |   a < A >
            |   b
     < B >  ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ >
            |   b < D₀ > < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ >
            |   a < A > < D₁ > < B > < B₀ >
            |   b < D₁ > < B > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ >
            |   a < A > < D₀ > < B > < B₀ >
            |   b < D₀ > < B > < B₀ >
            |   a < B₀ > < A > < B > < B₀ >
            |   a < A > < B > < B₀ >
            |   b < B > < B₀ >
            |   a < B₀ >
            |   a < B₀ > < A > < D₀ > < D₁ > < B >
            |   a < A > < D₀ > < D₁ > < B >
            |   b < D₀ > < D₁ > < B >
            |   a < B₀ > < A > < D₁ > < B >
            |   a < A > < D₁ > < B >
            |   b < D₁ > < B >
            |   a < B₀ > < A > < D₀ > < B >
            |   a < A > < D₀ > < B >
            |   b < D₀ > < B >
            |   a < B₀ > < A > < B >
            |   a < A > < B >
            |   b < B >
            |   a
     < B₀ > ->  a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   b < D₀ > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₁ > < B > < B₀ > < D > < B₀ >
            |   b < D₁ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < D > < B₀ >
            |   a < A > < D₀ > < B > < B₀ > < D > < B₀ >
            |   b < D₀ > < B > < B₀ > < D > < B₀ >
            |   a < B₀ > < A > < B > < B₀ > < D > < B₀ >
            |   a < A > < B > < B₀ > < D > < B₀ >
            |   b < B > < B₀ > < D > < B₀ >
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            |   b < B > < B₀ > < B₀ > < A >
            |   a < B₀ > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   b < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₁ > < B > < B₀ > < A >
            |   b < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A >
            |   a < A > < D₀ > < B > < B₀ > < A >
            |   b < D₀ > < B > < B₀ > < A >
            |   a < B₀ > < A > < B > < B₀ > < A >
            |   a < A > < B > < B₀ > < A >
            |   b < B > < B₀ > < A >
            |   a < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₀ > < D₁ > < B > < B₀ > < A >
            |   b < D₀ > < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₁ > < B > < B₀ > < A >
            |   a < A > < D₁ > < B > < B₀ > < A >
            |   b < D₁ > < B > < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < B > < B₀ > < A >
            |   a < A > < D₀ > < B > < B₀ > < A >
            |   b < D₀ > < B > < B₀ > < A >
            |   a < B₀ > < A > < B > < B₀ > < A >
            |   a < A > < B > < B₀ > < A >
            |   b < B > < B₀ > < A >
            |   a < B₀ > < A >
            |   a < B₀ > < A > < D₀ > < D₁ > < B > < A >
            |   a < A > < D₀ > < D₁ > < B > < A >
            |   b < D₀ > < D₁ > < B > < A >
            |   a < B₀ > < A > < D₁ > < B > < A >
            |   a < A > < D₁ > < B > < A >
            |   b < D₁ > < B > < A >
            |   a < B₀ > < A > < D₀ > < B > < A >
            |   a < A > < D₀ > < B > < A >
            |   b < D₀ > < B > < A >
            |   a < B₀ > < A > < B > < A >
            |   a < A > < B > < A >
            |   b < B > < A >
            |   a < A > }

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