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#450 baabababaa=aabbaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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