#407 abbabbabaa=baabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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