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#007 abaaabaaba=babaaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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