#330 abaaababba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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