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#397 abbabbbbaa=bbaabba

Original presentation

\( \left\langle a, b \;\middle|\; a b^{2} a b^{4} a^{2} = b^{2} a^{2} b^{2} a \right\rangle \)

Modified presentation

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

Complete rewriting system

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

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