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#103 abbabbaa=babba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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