let R be the TRS under consideration length(cons(_1,_2)) -> length(activate(_2)) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 0 is a position in r0 we have r0|p0 = activate(_2) activate(n__zeros) -> zeros is in R let l'0 be the left-hand side of this rule theta0 = {_2/n__zeros} is a mgu of r0|p0 and l'0 ==> length(cons(_1,n__zeros)) -> length(zeros) is in EU_R^1 let r1 be the right-hand side of this rule p1 = 0 is a position in r1 we have r1|p1 = zeros zeros -> cons(0,n__zeros) is in R let l'1 be the left-hand side of this rule theta1 = {} is a mgu of r1|p1 and l'1 ==> length(cons(_1,n__zeros)) -> length(cons(0,n__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 = {_1/0} let theta' = {} we have r|p = length(cons(0,n__zeros)) and theta'(theta(l)) = theta(r|p) so, theta(l) = length(cons(0,n__zeros)) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=2, depth k=3 64 rule(s) generated