Skip to content

#385 bbaaabbbba=aa

Original presentation

\( \left\langle a, b \;\middle|\; b^{2} a^{3} b^{4} a = a^{2} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; b^{2} c d b a = c,\; c = a^{2},\; d = a b^{3} \right\rangle \)

Complete rewriting system

Using recursive path order (RPOCmp) with \(a < d < b < c\):

\( \begin{aligned} c &\rightarrow a^{2} \\ b^{2} a^{2} d b a &\rightarrow a^{2} \\ a b^{3} &\rightarrow d \\ b^{2} a^{2} d b d &\rightarrow a d \\ a b^{2} a^{2} &\rightarrow d b a^{2} d b a \\ a b a^{2} &\rightarrow d a^{2} d b a \\ a b^{2} a d &\rightarrow d b a^{2} d b d \\ d b a^{2} d b a d b d &\rightarrow a^{2} d \\ d b a^{2} d b a d b a &\rightarrow a^{3} \\ a b a d &\rightarrow d a^{2} d b d \\ b^{2} a^{4} d &\rightarrow a^{3} d b a d b d \\ b^{2} a^{5} &\rightarrow a^{3} d b a d b a \\ d b a^{2} d b a^{3} d &\rightarrow a^{4} d b a d b d \\ d b a^{2} d b a^{4} &\rightarrow a^{4} d b a d b a \end{aligned} \)