YES Proof: This system is quasi-decreasing. By \cite{O02}, p. 214, Proposition 7.2.50. This system is of type 3 or smaller. This system is deterministic. System R transformed to U(R). Call external tool: ttt2 - trs 30 Input: isnoc(cons(y, nil)) -> tp2(nil, y) ?1(tp2(xs, y), x, ys) -> tp2(cons(x, xs), y) isnoc(cons(x, ys)) -> ?1(isnoc(ys), x, ys) DP Processor: DPs: isnoc#(cons(x,ys)) -> isnoc#(ys) isnoc#(cons(x,ys)) -> ?1#(isnoc(ys),x,ys) TRS: isnoc(cons(y,nil())) -> tp2(nil(),y) ?1(tp2(xs,y),x,ys) -> tp2(cons(x,xs),y) isnoc(cons(x,ys)) -> ?1(isnoc(ys),x,ys) TDG Processor: DPs: isnoc#(cons(x,ys)) -> isnoc#(ys) isnoc#(cons(x,ys)) -> ?1#(isnoc(ys),x,ys) TRS: isnoc(cons(y,nil())) -> tp2(nil(),y) ?1(tp2(xs,y),x,ys) -> tp2(cons(x,xs),y) isnoc(cons(x,ys)) -> ?1(isnoc(ys),x,ys) graph: isnoc#(cons(x,ys)) -> isnoc#(ys) -> isnoc#(cons(x,ys)) -> ?1#(isnoc(ys),x,ys) isnoc#(cons(x,ys)) -> isnoc#(ys) -> isnoc#(cons(x,ys)) -> isnoc#(ys) SCC Processor: #sccs: 1 #rules: 1 #arcs: 2/4 DPs: isnoc#(cons(x,ys)) -> isnoc#(ys) TRS: isnoc(cons(y,nil())) -> tp2(nil(),y) ?1(tp2(xs,y),x,ys) -> tp2(cons(x,xs),y) isnoc(cons(x,ys)) -> ?1(isnoc(ys),x,ys) Subterm Criterion Processor: simple projection: pi(isnoc#) = 0 problem: DPs: TRS: isnoc(cons(y,nil())) -> tp2(nil(),y) ?1(tp2(xs,y),x,ys) -> tp2(cons(x,xs),y) isnoc(cons(x,ys)) -> ?1(isnoc(ys),x,ys) Qed