#074 abaababaa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

\( \begin{aligned} b a &\rightarrow c \\ c^{2} a &\rightarrow d \\ c a c &\rightarrow a c a d \\ a c a d a d &\rightarrow d c \\ c a^{2} c a d &\rightarrow a c a d a c \\ a c a d c a &\rightarrow c a d \\ b c a d &\rightarrow d^{2} c a \\ b d c &\rightarrow d^{2} a d \\ d c a d c a &\rightarrow c d^{2} \\ c d c &\rightarrow d c a d \\ a c a d a c a d &\rightarrow c a d c \\ b c d^{2} &\rightarrow d^{2} a d a d c a \\ b d^{2} &\rightarrow d^{2} a d c a \\ b d a c a d &\rightarrow d^{2} a d a c \\ d c a d a c a d &\rightarrow c d^{2} c \\ c^{2} d^{2} &\rightarrow d c a d a d c a \\ c d^{2} c a d &\rightarrow d c a d^{2} c \\ c d a c a d &\rightarrow d c a d a c \\ c a d c a d &\rightarrow a c a d^{2} c \\ a c a d a c d^{2} &\rightarrow d^{3} c a \\ c d^{3} c a &\rightarrow d a c a d^{3} \\ c a d^{2} c a &\rightarrow a^{2} c a d^{3} \\ c a^{3} c a d^{3} &\rightarrow d^{2} c a d a \\ b d a^{2} c a d^{3} &\rightarrow d^{2} a d a d^{2} c a \\ b d a^{3} c a d^{3} &\rightarrow d^{2} a d a d c a d a \\ c d^{2} c d^{2} &\rightarrow d a c a d^{4} c a \\ c d^{2} a c a d^{3} &\rightarrow d c a d^{4} c a \\ c d a^{2} c a d^{3} &\rightarrow d c a d a d^{2} c a \\ c a d c d^{2} &\rightarrow a^{2} c a d^{4} c a \\ c a d a c a d^{3} &\rightarrow a c a d^{4} c a \\ c a d^{2} a c a d &\rightarrow a^{2} c a d^{3} c \\ c a d^{2} a^{2} c a d^{3} &\rightarrow a^{2} c a d^{5} c a \\ c d^{2} a^{2} c a d^{3} &\rightarrow d c a d^{3} c a d a \\ c d a^{3} c a d^{3} &\rightarrow d c a d a d c a d a \\ d a c a d^{2} c &\rightarrow c d^{3} \\ c a d a^{2} c a d^{3} &\rightarrow a c a d^{3} c a d a \\ a^{2} c a d^{2} c &\rightarrow c a d^{2} \\ d a c a d^{3} a c a d^{3} &\rightarrow c d^{6} c a \\ d a c a d^{3} c a d &\rightarrow c d^{4} c \\ d a c a d^{3} a^{2} c a d^{3} &\rightarrow c d^{5} c a d a \\ c a d^{2} a^{3} c a d^{3} &\rightarrow a^{2} c a d^{4} c a d a \\ a^{2} c a d^{3} a^{2} c a d^{3} &\rightarrow c a d^{4} c a d a \\ a^{2} c a d^{3} a c a d^{3} &\rightarrow c a d^{5} c a \\ a^{2} c a d^{3} c a d &\rightarrow c a d^{3} c \\ c d^{3} a &\rightarrow d a^{3} c a d^{3} \\ c d^{2} a^{3} c a d^{3} &\rightarrow d c a d^{4} a \\ c a d a^{3} c a d^{3} &\rightarrow a c a d^{4} a \\ d a c a d^{3} a^{3} c a d^{3} &\rightarrow c d^{6} a \\ a^{2} c a d^{3} a^{3} c a d^{3} &\rightarrow c a d^{5} a \\ a^{4} c a d^{3} &\rightarrow c a d^{2} a \end{aligned} \)