Skip to content

#427 aaabababba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a b &\rightarrow c \\ c a b^{2} &\rightarrow d \\ c a^{2} &\rightarrow a^{3} d a \\ b a c &\rightarrow c a b \\ c a b c &\rightarrow d a b \\ b a^{4} d a &\rightarrow c a b a^{2} \\ b a d &\rightarrow c a c b \\ c a b a^{3} d a &\rightarrow d a b a^{2} \\ c a b d &\rightarrow d a c b \end{aligned} \)