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#260 baaabbaa=abaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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