#171 baaabbabaa=aaabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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