#400 baaaabbaaa=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow a^{2} \\ a b^{2} &\rightarrow d \\ b a^{3} d a^{3} &\rightarrow a \\ b a^{3} d a^{2} d &\rightarrow d \\ a b a &\rightarrow d a^{3} d a^{3} \\ a b d &\rightarrow d a^{3} d a^{2} d \\ d a^{3} d a^{5} d a^{2} d &\rightarrow a d \\ d a^{3} d a^{5} d a^{3} &\rightarrow a^{2} \\ b a^{4} d &\rightarrow a d a^{5} d a^{2} d \\ b a^{5} &\rightarrow a d a^{5} d a^{3} \\ d a^{3} d a^{6} d &\rightarrow a^{2} d a^{5} d a^{2} d \\ d a^{3} d a^{7} &\rightarrow a^{2} d a^{5} d a^{3} \end{aligned} \)