#017 aababbabba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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