#011 babaaababa=aabababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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