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#358 baaabbabaa=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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