let R be the TRS under consideration a__length(cons(_1,_2)) -> a__length(mark(_2)) is in elim_R(R) let l0 be the left-hand side of this rule p0 = 0 is a position in l0 we have l0|p0 = cons(_1,_2) a__zeros -> cons(0,zeros) is in R let r'0 be the right-hand side of this rule theta0 = {_1/0, _2/zeros} is a mgu of l0|p0 and r'0 ==> a__length(a__zeros) -> a__length(mark(zeros)) 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 = a__zeros mark(zeros) -> a__zeros is in R let r'1 be the right-hand side of this rule theta1 = {} is a mgu of l1|p1 and r'1 ==> a__length(mark(zeros)) -> a__length(mark(zeros)) is in EU_R^2 let l be the left-hand side and r be the right-hand side of this rule let p = epsilon 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 backward process proof stopped at iteration i=2, depth k=3 338 rule(s) generated