let R be the TRS under consideration incr(cons(_1,_2)) -> activate(_2) is in elim_R(R) let r0 be the right-hand side of this rule p0 = epsilon is a position in r0 we have r0|p0 = activate(_2) activate(n__incr(_3)) -> incr(activate(_3)) is in R let l'0 be the left-hand side of this rule theta0 = {_2/n__incr(_3)} is a mgu of r0|p0 and l'0 ==> incr(cons(_1,n__incr(_2))) -> incr(activate(_2)) 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 = activate(_2) activate(n__oddNs) -> oddNs is in R let l'1 be the left-hand side of this rule theta1 = {_2/n__oddNs} is a mgu of r1|p1 and l'1 ==> incr(cons(_1,n__incr(n__oddNs))) -> incr(oddNs) is in EU_R^2 let r2 be the right-hand side of this rule p2 = 0 is a position in r2 we have r2|p2 = oddNs oddNs -> incr(pairNs) is in R let l'2 be the left-hand side of this rule theta2 = {} is a mgu of r2|p2 and l'2 ==> incr(cons(_1,n__incr(n__oddNs))) -> incr(incr(pairNs)) is in EU_R^3 let r3 be the right-hand side of this rule p3 = 0.0 is a position in r3 we have r3|p3 = pairNs pairNs -> cons(0,n__incr(n__oddNs)) is in R let l'3 be the left-hand side of this rule theta3 = {} is a mgu of r3|p3 and l'3 ==> incr(cons(_1,n__incr(n__oddNs))) -> incr(incr(cons(0,n__incr(n__oddNs)))) 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 = {_1/0} let theta' = {} we have r|p = incr(cons(0,n__incr(n__oddNs))) and theta'(theta(l)) = theta(r|p) so, theta(l) = incr(cons(0,n__incr(n__oddNs))) is non-terminating w.r.t. R Termination disproved by the forward process proof stopped at iteration i=4, depth k=3 1727 rule(s) generated