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#163 aabbaababa=baaabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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