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#221 aaababbaba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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