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#493 ababbbabba=bbabbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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