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#285 baaabaaaba=aaabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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