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#179 babababbba=abbaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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