#447 baaababa=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} c e c^{2} &\rightarrow d^{2} \\ c e c d c^{3} d &\rightarrow e c d c^{2} \\ d c^{2} e c d c^{2} &\rightarrow c e \\ b e &\rightarrow c^{3} e c d c^{2} \\ a &\rightarrow c e c d c^{4} \\ c e c d c^{6} e c d c^{2} &\rightarrow e \\ c^{2} e c d c^{4} &\rightarrow d \\ c e c d c^{5} e &\rightarrow e c^{4} e c d c^{2} \\ c e c d c^{4} e &\rightarrow e c d c^{4} e c d c^{2} \\ c e c d c^{4} d &\rightarrow e c^{2} \\ b c e c d c^{4} &\rightarrow c \\ c e c d c^{3} e &\rightarrow e c d c d c^{4} e c d c^{2} \\ c e c d c^{2} d &\rightarrow e c d c d c^{2} \\ d c e c d c^{2} &\rightarrow c e c d \\ c e c d c d &\rightarrow e c d c d c d c^{2} \\ d e &\rightarrow e c d c d \\ c e c d^{2} &\rightarrow e c d c d c d c d c^{2} \\ c e d &\rightarrow e c d c d c d c d c d c^{4} \\ c e c e &\rightarrow e c d c d c d c d c d c^{6} e c d c^{2} \\ c e c d c^{2} e &\rightarrow e c d c d c d c^{4} e c d c^{2} \\ c e c d c e &\rightarrow e c d c d c d c d c^{4} e c d c^{2} \\ c e^{2} &\rightarrow e c d c d c d c d c d c^{3} d c^{4} e c d c^{2} \end{aligned} \)