#411 aabaabbaba=babaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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