#483 aabaabbaaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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