#457 ababaabbaa=baaababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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