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#127 baaabbabaa=abaaabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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