#463 baabababba=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ b d c b c b d &\rightarrow d c^{3} \\ b d c b c^{3} b d &\rightarrow d c b^{2} d \\ b d c b c^{2} b d &\rightarrow d c b^{2} d c b c \\ a b d &\rightarrow b d c b c^{2} b^{2} d \\ c b d c b c &\rightarrow b d \\ b d c b c^{4} &\rightarrow d c b c \\ a c &\rightarrow b d c b c^{2} b c \\ b d c b c^{2} b^{2} d c b c &\rightarrow d \\ a d &\rightarrow d c b^{2} d c b c \\ b d c b^{2} d &\rightarrow d c^{4} b c \\ b^{2} d c b c^{2} b c &\rightarrow c^{2} \\ b^{2} d c b c^{2} b^{2} d &\rightarrow c b d \\ c d &\rightarrow d c^{4} b c^{2} b c \\ b d c b d &\rightarrow d c^{4} b c^{2} b c^{2} b^{2} d c b c \\ b d b d &\rightarrow d c^{4} b c^{2} b c^{4} \\ b d c^{2} b d &\rightarrow d c^{4} b c^{2} b c^{2} b^{2} d \\ b d c^{3} &\rightarrow d c^{4} b c^{2} b c^{2} b c \\ b d^{2} &\rightarrow d c^{4} b c^{2} b c^{5} b c^{2} b^{2} d c b c \end{aligned} \)