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 TDG 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 graph: sel#(s(X),cons(Y,Z)) -> activate#(Z) -> activate#(n__from(X)) -> from#(X) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) -> sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) -> sel#(s(X),cons(Y,Z)) -> activate#(Z) SCC Processor: #sccs: 1 #rules: 1 #arcs: 3/9 DPs: sel#(s(X),cons(Y,Z)) -> sel#(X,activate(Z)) 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(sel#) = 0 precedence: sel > activate > from > sel# ~ 0 ~ cons ~ n__from ~ s 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