#239 abaabaabba=baababaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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