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#083 baabaabbaa=aabbaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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