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#053 baaababbaa=abababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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