#393 babaaaabba=ababaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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