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#324 baabaaba=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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