#446 baaaaabba=aaaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{5} b^{2} a = a^{4} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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