#203 baabbabbaa=aba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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