let R be the TRS under consideration U11(tt,_1) -> U12(tt,activate(_1)) is in elim_R(R) let r0 be the right-hand side of this rule p0 = 1 is a position in r0 we have r0|p0 = activate(_1) activate(n__zeros) -> zeros is in R let l'0 be the left-hand side of this rule theta0 = {_1/n__zeros} is a mgu of r0|p0 and l'0 ==> U11(tt,n__zeros) -> U12(tt,zeros) is in EU_R^1 let l1 be the left-hand side of this rule p1 = 1 is a position in l1 we have l1|p1 = n__zeros activate(_1) -> _1 is in R let r'1 be the right-hand side of this rule theta1 = {_1/n__zeros} is a mgu of l1|p1 and r'1 ==> U11(tt,activate(n__zeros)) -> U12(tt,zeros) is in EU_R^2 let l2 be the left-hand side of this rule p2 = epsilon is a position in l2 we have l2|p2 = U11(tt,activate(n__zeros)) length(cons(_1,_2)) -> U11(tt,activate(_2)) is in R let r'2 be the right-hand side of this rule theta2 = {_2/n__zeros} is a mgu of l2|p2 and r'2 ==> length(cons(_1,n__zeros)) -> U12(tt,zeros) is in EU_R^3 let l3 be the left-hand side of this rule p3 = 0 is a position in l3 we have l3|p3 = cons(_1,n__zeros) zeros -> cons(0,n__zeros) is in R let r'3 be the right-hand side of this rule theta3 = {_1/0} is a mgu of l3|p3 and r'3 ==> length(zeros) -> U12(tt,zeros) is in EU_R^4 let l4 be the left-hand side of this rule p4 = 0 is a position in l4 we have l4|p4 = zeros activate(_1) -> _1 is in R let r'4 be the right-hand side of this rule theta4 = {_1/zeros} is a mgu of l4|p4 and r'4 ==> length(activate(zeros)) -> U12(tt,zeros) is in EU_R^5 let r5 be the right-hand side of this rule p5 = epsilon is a position in r5 we have r5|p5 = U12(tt,zeros) U12(tt,_1) -> s(length(activate(_1))) is in R let l'5 be the left-hand side of this rule theta5 = {_1/zeros} is a mgu of r5|p5 and l'5 ==> length(activate(zeros)) -> s(length(activate(zeros))) is in EU_R^6 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 = length(activate(zeros)) and theta'(theta(l)) = theta(r|p) so, theta(l) = length(activate(zeros)) is non-terminating w.r.t. R Termination disproved by the forward+backward process proof stopped at iteration i=6, depth k=2 126 rule(s) generated