#451 baaabaaba=a

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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