#156 ababaabaaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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