Skip to content

#157 bababaabba=ababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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