#038 babaabbbba=abbbbaba

Original presentation

\( \left\langle a, b \;\middle|\; b a b a^{2} b^{4} a = a b^{4} a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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