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#346 baababbaa=abaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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