#428 aabbaabbaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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