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#331 abaabaaaba=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c &\rightarrow b a \\ a^{2} b &\rightarrow d \\ b d^{2} &\rightarrow d^{2} a d a d^{2} \\ b d a &\rightarrow d^{2} a d a d a \\ a d^{2} a d a &\rightarrow d^{2} a \\ a d^{2} a d^{2} &\rightarrow d^{3} \\ a d^{4} a &\rightarrow d^{3} a d a \\ a d^{5} &\rightarrow d^{3} a d^{2} \end{aligned} \)