#060 baabbbabba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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