Skip to content

#233 abaababaaa=baaabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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