#067 baaaaabba=aabaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{5} b^{2} a = a^{2} b a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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