#280 abaabbabaa=babaaaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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