#289 abbabbbaba=bababba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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