#070 abababbaaa=baababa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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