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#322 abaabaaba=baabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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