#355 baaabbaba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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