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#177 abbababbaa=bababa

Original presentation

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

Modified presentation

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

Complete rewriting system

Using reversed recursive path order (RevRPOCmp) with \(a < c < e < d < b\):

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