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#415 bbabaaabba=abbabaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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