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#220 baaabbaaba=abaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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