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#154 aababaabba=babaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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