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#500 abbbababaa=baabbba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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