let R be the TRS under consideration a__U11(tt,_1) -> a__U12(tt,_1) is in elim_R(R) let l0 be the left-hand side of this rule p0 = epsilon is a position in l0 we have l0|p0 = a__U11(tt,_1) a__length(cons(_2,_3)) -> a__U11(tt,_3) is in R let r'0 be the right-hand side of this rule theta0 = {_1/_3} is a mgu of l0|p0 and r'0 ==> a__length(cons(_1,_2)) -> a__U12(tt,_2) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 0 is a position in l1 we have l1|p1 = cons(_1,_2) a__zeros -> cons(0,zeros) is in R let r'1 be the right-hand side of this rule theta1 = {_1/0, _2/zeros} is a mgu of l1|p1 and r'1 ==> a__length(a__zeros) -> a__U12(tt,zeros) is in EU_R^2 let l2 be the left-hand side of this rule p2 = 0 is a position in l2 we have l2|p2 = a__zeros mark(zeros) -> a__zeros is in R let r'2 be the right-hand side of this rule theta2 = {} is a mgu of l2|p2 and r'2 ==> a__length(mark(zeros)) -> a__U12(tt,zeros) is in EU_R^3 let r3 be the right-hand side of this rule p3 = epsilon is a position in r3 we have r3|p3 = a__U12(tt,zeros) a__U12(tt,_1) -> s(a__length(mark(_1))) is in R let l'3 be the left-hand side of this rule theta3 = {_1/zeros} is a mgu of r3|p3 and l'3 ==> a__length(mark(zeros)) -> s(a__length(mark(zeros))) is in EU_R^4 let l be the left-hand side and r be the right-hand side of this rule let p = 0 let theta = {} let theta' = {} we have r|p = a__length(mark(zeros)) and theta'(theta(l)) = theta(r|p) so, theta(l) = a__length(mark(zeros)) is non-terminating w.r.t. R Termination disproved by the forward+backward process proof stopped at iteration i=4, depth k=2 34211 rule(s) generated