#264 abaabbaaba=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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