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#225 abbaabbaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ b c a &\rightarrow d \\ a d^{2} &\rightarrow c^{2} \\ b c^{2} &\rightarrow c d^{2} \\ c d^{2} c &\rightarrow d^{3} \\ b c d^{3} &\rightarrow c d^{4} c \\ c d^{5} &\rightarrow d^{5} c \\ b d^{5} c &\rightarrow c d^{4} c d^{2} \\ b d^{8} &\rightarrow c d^{4} c d^{4} c \end{aligned} \)