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#205 baababbaa=aaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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