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#131 babbaaabba=abbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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