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#210 baaabbaaba=abbabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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