#265 baaaabbaba=aa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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