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#134 baabbbba=aa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{2} b^{4} a = a^{2} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; b a^{2} c^{2} a = a^{2},\; c = b^{2},\; d = b^{4} \right\rangle \)

Complete rewriting system

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

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