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#110 abbaababa=baabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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