#018 aaabaaabba=baaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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