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#137 abaabbbbba=babaa

Original presentation

\( \left\langle a, b \;\middle|\; a b a^{2} b^{5} a = b a b a^{2} \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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