#036 aababbaaaa=baaaaaba

Original presentation

\( \left\langle a, b \;\middle|\; a^{2} b a b^{2} a^{4} = b a^{5} b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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