#354 baabbaaaba=aabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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