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#113 abbababbaa=babba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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