#049 baabaabba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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