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#008 aabaaaabba=baaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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