YES Problem: from(X) -> cons(X,n__from(s(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X Proof: DP Processor: DPs: sel#(s(X),cons(Y,Z)) -> activate#(Z) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) activate#(n__from(X)) -> from#(X) TRS: from(X) -> cons(X,n__from(s(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X LPO Processor: argument filtering: pi(from) = [0] pi(s) = [0] pi(n__from) = [0] pi(cons) = [0,1] pi(0) = [] pi(sel) = [0,1] pi(activate) = [0] pi(from#) = [] pi(sel#) = 0 pi(activate#) = [] precedence: sel > activate > from > s > activate# > sel# ~ from# ~ 0 ~ cons ~ n__from problem: DPs: TRS: from(X) -> cons(X,n__from(s(X))) sel(0(),cons(X,Y)) -> X sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X Qed