#108 baabbabba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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