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#235 abaabababa=baaba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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