#471 abaaababa=baabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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