Skip to content

#061 baaababbba=abaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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