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#478 babbabbaba=abbabba

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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