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#181 aabbaabaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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