#300 aabbaabbba=baabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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