Skip to content

#219 bababaaaba=aababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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