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#183 abbabbabba=bbabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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