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#362 abbaabbaba=bababbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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