#290 abaabbaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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