#132 baabaababa=abaabbaa

Original presentation

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

Modified presentation

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

Complete rewriting system

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

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