#488 baababaaba=aababbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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