#066 abababbba=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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