Skip to content

#297 baabaabba=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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