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#389 baaababaa=aababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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