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#250 ababbbbaaa=baba

Original presentation

\( \left\langle a, b \;\middle|\; a b a b^{4} a^{3} = b a b a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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