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#123 baabbaaba=abbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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