#356 baabaabaa=ababaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} a b a &\rightarrow c \\ b a^{2} &\rightarrow d \\ a d &\rightarrow c a \\ a b c &\rightarrow c b a \\ b a c &\rightarrow d b a \\ c d &\rightarrow d^{3} \\ a b d^{3} &\rightarrow c b c a \\ b c^{3} a &\rightarrow d b c a \\ b c^{4} &\rightarrow d b c^{2} \\ b d^{9} &\rightarrow d b d^{5} \end{aligned} \)