#111 baabbabaa=aabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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