#056 abbabbabaa=baba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ d &\rightarrow a e \\ b c^{2} &\rightarrow c^{2} e a \\ c e c a e &\rightarrow e c^{2} e a \\ a c e a &\rightarrow c^{2} \\ c^{3} e a &\rightarrow a e \\ c e c^{2} &\rightarrow e \\ b c a e &\rightarrow c^{2} e a c^{2} e a \\ c e c e &\rightarrow e^{2} c^{2} \\ c e a e &\rightarrow e c e a \\ a e c e a &\rightarrow c^{2} e \\ b c e &\rightarrow e^{2} c^{2} a c^{2} \\ b e &\rightarrow e^{2} c^{2} a c^{4} \\ c e^{2} &\rightarrow e^{2} c^{4} \\ a e^{2} &\rightarrow e^{2} c^{6} a \end{aligned} \)