#047 ababbababa=babababa

Original presentation

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

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; d c^{3} = c^{4},\; c = b a,\; d = a c b \right\rangle \)

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ a c b &\rightarrow d \\ d c^{3} &\rightarrow c^{4} \\ b d &\rightarrow c^{2} b \\ a c^{2} &\rightarrow d a \\ b c^{4} &\rightarrow c^{2} b c^{3} \end{aligned} \)