#093 aabaaaabba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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