#476 abababbaaa=baaababa

Original presentation

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

Modified presentation

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

Complete rewriting system

Using reversed recursive path order (RevRPOCmp) with \(c < e < d < a < b\):

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