#279 abbabaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ b c a e &\rightarrow e c^{2} \\ c a e a &\rightarrow a e \\ c e &\rightarrow e c^{2} a \\ a e c^{2} &\rightarrow e c^{2} a c^{2} a^{2} \\ a e a c^{2} &\rightarrow e c^{2} a^{2} \\ a e a^{2} c a e &\rightarrow e a^{2} e a \\ a e a^{2} c^{2} &\rightarrow e a \\ d &\rightarrow a e a^{3} \\ b c^{2} &\rightarrow a e a^{2} \\ a e a^{4} e a^{2} &\rightarrow e \\ a e a^{3} e &\rightarrow e a^{2} e a^{2} \\ a^{2} e a^{3} &\rightarrow c^{2} \\ b e &\rightarrow e c^{2} a^{5} e a^{2} \\ a e a^{2} e &\rightarrow e c^{2} a^{3} e a^{2} \\ a e a c a e &\rightarrow e c^{2} a^{3} e a \\ a e c a e &\rightarrow e c^{2} a c^{2} a^{3} e a \\ a e^{2} &\rightarrow e c^{2} a c^{2} a c^{2} a^{3} e a^{2} \\ a e a e &\rightarrow e c^{2} a c^{2} a^{3} e a^{2} \end{aligned} \)