Skip to content

#258 aabbaabbaa=baabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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