#112 baababba=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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