#252 baaaaaabba=aaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{6} b^{2} a = a^{3} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow a^{2} \\ a b^{2} &\rightarrow d \\ b a^{5} d a &\rightarrow a^{3} \\ a b a^{3} &\rightarrow d a^{5} d a \\ b a^{5} d^{2} &\rightarrow a^{2} d \\ a b a^{2} d &\rightarrow d a^{5} d^{2} \\ d a^{5} d a^{3} d^{2} &\rightarrow a^{3} d \\ d a^{5} d a^{3} d a &\rightarrow a^{4} \\ b a^{8} d &\rightarrow a^{7} d a^{3} d^{2} \\ b a^{9} &\rightarrow a^{7} d a^{3} d a \\ d a^{5} d a^{6} d &\rightarrow a^{8} d a^{3} d^{2} \\ d a^{5} d a^{7} &\rightarrow a^{8} d a^{3} d a \end{aligned} \)