Skip to content

#352 baabaaaba=abaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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