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#381 babbaaaba=ababba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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