#388 babaabaaba=aabbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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