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#032 baaabababa=abbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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