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#126 baaaababba=aaa

Original presentation

\( \left\langle a, b \;\middle|\; b a^{4} b a b^{2} a = a^{3} \right\rangle \)

Modified presentation

\( \left\langle a, b, c, d \;\middle|\; b a^{4} b a c a = a^{3},\; c = b^{2},\; d = a b a c a^{2} b \right\rangle \)

Complete rewriting system

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

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