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#021 aaaabaabba=baabaaa

Original presentation

\( \left\langle a, b \;\middle|\; a^{4} b a^{2} b^{2} a = b a^{2} b a^{3} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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