#278 baababbba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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