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#086 aaabbbaaba=baabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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