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#382 aaabbababa=babaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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