#499 baaaaaabba=aaabaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{6} b^{2} a = a^{3} b a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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