#191 baaaaaabba=aaaaaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{6} b^{2} a = a^{6} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow a^{2} \\ a b^{2} &\rightarrow d \\ b a^{5} d a &\rightarrow a^{6} \\ a b a^{6} &\rightarrow d a^{5} d a \\ b a^{5} d^{2} &\rightarrow a^{5} d \\ a b a^{5} d &\rightarrow d a^{5} d^{2} \\ d a^{5} d^{3} &\rightarrow a^{6} d \\ d a^{5} d^{2} a &\rightarrow a^{7} \\ b a^{11} d &\rightarrow a^{10} d^{3} \\ b a^{12} &\rightarrow a^{10} d^{2} a \\ d a^{5} d a^{6} d &\rightarrow a^{11} d^{3} \\ d a^{5} d a^{7} &\rightarrow a^{11} d^{2} a \end{aligned} \)