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#453 aabbababaa=baaabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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