#306 aabababbaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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