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#473 abaabaaba=baaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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