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#296 ababbbabba=babbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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