#336 baababbbaa=abba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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