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#410 baaaaaabba=abaaaaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{6} b^{2} a = a b a^{5} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; c a d = a c,\; c = b a^{5},\; d = b^{2} a \right\rangle \)

Complete rewriting system

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

\( \begin{aligned} b^{2} a &\rightarrow d \\ b a^{5} &\rightarrow c \\ a c &\rightarrow c a d \\ b c &\rightarrow d a^{4} \\ d a^{5} d a d a d a d a d &\rightarrow c^{2} \\ b d a^{5} d &\rightarrow d c \\ b d c a d a d a d a d a d c &\rightarrow d c a^{5} d a d a d a d a d \\ d a^{5} d a d a d a d c a d c &\rightarrow c^{2} a^{5} d a d a d a d a d \end{aligned} \)