#392 baababbaba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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