#416 baaaababaa=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow a^{2} \\ a b a b &\rightarrow d \\ b a^{3} d a^{2} &\rightarrow a^{2} \\ a b d &\rightarrow d a b \\ a b a^{3} &\rightarrow d a^{3} d a^{2} \\ b a^{3} d a d &\rightarrow a d \\ a b a^{2} d &\rightarrow d a^{3} d a d \\ d a^{3} d a^{2} d a d &\rightarrow a^{2} d \\ d a^{3} d a^{2} d a^{2} &\rightarrow a^{3} \\ b a^{5} d &\rightarrow a^{3} d a^{2} d a d \\ b a^{6} &\rightarrow a^{3} d a^{2} d a^{2} \\ d a^{3} d a^{4} d &\rightarrow a^{4} d a^{2} d a d \\ d a^{3} d a^{5} &\rightarrow a^{4} d a^{2} d a^{2} \end{aligned} \)