MAYBE Problem: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Proof: DP Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(2nd(cons(X,XS))) -> head#(XS) active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(from(X)) -> active#(X) active#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(head(X)) -> active#(X) active#(head(X)) -> head#(active(X)) active#(2nd(X)) -> active#(X) active#(2nd(X)) -> 2nd#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) from#(mark(X)) -> from#(X) cons#(mark(X1),X2) -> cons#(X1,X2) s#(mark(X)) -> s#(X) head#(mark(X)) -> head#(X) 2nd#(mark(X)) -> 2nd#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(from(X)) -> proper#(X) proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(head(X)) -> proper#(X) proper#(head(X)) -> head#(proper(X)) proper#(2nd(X)) -> proper#(X) proper#(2nd(X)) -> 2nd#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) from#(ok(X)) -> from#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) s#(ok(X)) -> s#(X) head#(ok(X)) -> head#(X) 2nd#(ok(X)) -> 2nd#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) EDG Processor: DPs: active#(from(X)) -> s#(X) active#(from(X)) -> from#(s(X)) active#(from(X)) -> cons#(X,from(s(X))) active#(2nd(cons(X,XS))) -> head#(XS) active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(from(X)) -> active#(X) active#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) active#(s(X)) -> s#(active(X)) active#(head(X)) -> active#(X) active#(head(X)) -> head#(active(X)) active#(2nd(X)) -> active#(X) active#(2nd(X)) -> 2nd#(active(X)) active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) from#(mark(X)) -> from#(X) cons#(mark(X1),X2) -> cons#(X1,X2) s#(mark(X)) -> s#(X) head#(mark(X)) -> head#(X) 2nd#(mark(X)) -> 2nd#(X) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(from(X)) -> proper#(X) proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) proper#(s(X)) -> s#(proper(X)) proper#(head(X)) -> proper#(X) proper#(head(X)) -> head#(proper(X)) proper#(2nd(X)) -> proper#(X) proper#(2nd(X)) -> 2nd#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) from#(ok(X)) -> from#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) s#(ok(X)) -> s#(X) head#(ok(X)) -> head#(X) 2nd#(ok(X)) -> 2nd#(X) take#(ok(X1),ok(X2)) -> take#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) graph: top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X) top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> top#(proper(X)) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X) top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X)) top#(ok(X)) -> active#(X) -> active#(from(X)) -> s#(X) top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) top#(ok(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) top#(ok(X)) -> active#(X) -> active#(2nd(cons(X,XS))) -> head#(XS) top#(ok(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) top#(ok(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) top#(ok(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) top#(ok(X)) -> active#(X) -> active#(from(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) top#(ok(X)) -> active#(X) -> active#(head(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(head(X)) -> head#(active(X)) top#(ok(X)) -> active#(X) -> active#(2nd(X)) -> active#(X) top#(ok(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X)) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) top#(ok(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X) top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> top#(proper(X)) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X) top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X) top#(mark(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X)) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) top#(mark(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> head#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> head#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> proper#(X) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(mark(X1),X2) -> sel#(X1,X2) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(X1,mark(X2)) -> sel#(X1,X2) proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> head#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> head#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> proper#(X) proper#(take(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(mark(X1),X2) -> take#(X1,X2) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(X1,mark(X2)) -> take#(X1,X2) proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) proper#(2nd(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(2nd(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) proper#(2nd(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(2nd(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(2nd(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(2nd(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(2nd(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X) proper#(2nd(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X)) proper#(2nd(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X) proper#(2nd(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(2nd(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(2nd(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(2nd(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(2nd(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(2nd(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(2nd(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(2nd(X)) -> 2nd#(proper(X)) -> 2nd#(mark(X)) -> 2nd#(X) proper#(2nd(X)) -> 2nd#(proper(X)) -> 2nd#(ok(X)) -> 2nd#(X) proper#(head(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(head(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) proper#(head(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(head(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(head(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(head(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(head(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(head(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X) proper#(head(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X)) proper#(head(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X) proper#(head(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(head(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(head(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(head(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(head(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(head(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(head(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(head(X)) -> head#(proper(X)) -> head#(mark(X)) -> head#(X) proper#(head(X)) -> head#(proper(X)) -> head#(ok(X)) -> head#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(head(X)) -> head#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(from(X)) -> from#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(s(X)) -> s#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(head(X)) -> head#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X1) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(mark(X1),X2) -> cons#(X1,X2) proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X) proper#(s(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(s(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X) proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X) proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> proper#(X) proper#(from(X)) -> proper#(X) -> proper#(from(X)) -> from#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X) proper#(from(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(head(X)) -> proper#(X) proper#(from(X)) -> proper#(X) -> proper#(head(X)) -> head#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(2nd(X)) -> proper#(X) proper#(from(X)) -> proper#(X) -> proper#(2nd(X)) -> 2nd#(proper(X)) proper#(from(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(take(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(take(X1,X2)) -> take#(proper(X1),proper(X2)) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> proper#(X1) proper#(from(X)) -> proper#(X) -> proper#(sel(X1,X2)) -> sel#(proper(X1),proper(X2)) proper#(from(X)) -> from#(proper(X)) -> from#(mark(X)) -> from#(X) proper#(from(X)) -> from#(proper(X)) -> from#(ok(X)) -> from#(X) 2nd#(ok(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X) 2nd#(ok(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X) 2nd#(mark(X)) -> 2nd#(X) -> 2nd#(mark(X)) -> 2nd#(X) 2nd#(mark(X)) -> 2nd#(X) -> 2nd#(ok(X)) -> 2nd#(X) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(ok(X1),ok(X2)) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(ok(X1),ok(X2)) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(X1,mark(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) head#(ok(X)) -> head#(X) -> head#(mark(X)) -> head#(X) head#(ok(X)) -> head#(X) -> head#(ok(X)) -> head#(X) head#(mark(X)) -> head#(X) -> head#(mark(X)) -> head#(X) head#(mark(X)) -> head#(X) -> head#(ok(X)) -> head#(X) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(ok(X1),ok(X2)) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) from#(ok(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(ok(X)) -> from#(X) -> from#(ok(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(mark(X)) -> from#(X) from#(mark(X)) -> from#(X) -> from#(ok(X)) -> from#(X) s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X) s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X) active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(active(X1),X2) -> sel#(mark(X1),X2) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(active(X1),X2) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) -> sel#(X1,mark(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> sel#(X1,active(X2)) -> sel#(ok(X1),ok(X2)) -> sel#(X1,X2) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(sel(X1,X2)) -> active#(X2) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(sel(X1,X2)) -> active#(X2) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(sel(X1,X2)) -> active#(X2) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(head(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(head(X)) -> head#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(2nd(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X2) -> active#(2nd(X)) -> 2nd#(active(X)) active#(sel(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(sel(X1,X2)) -> active#(X1) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(sel(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(sel(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(head(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(head(X)) -> head#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> active#(X) active#(sel(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> 2nd#(active(X)) active#(sel(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(take(s(N),cons(X,XS))) -> take#(N,XS) -> take#(X1,mark(X2)) -> take#(X1,X2) active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(take(X1,X2)) -> take#(active(X1),X2) -> take#(mark(X1),X2) -> take#(X1,X2) active#(take(X1,X2)) -> take#(active(X1),X2) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(X1,active(X2)) -> take#(X1,mark(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> take#(X1,active(X2)) -> take#(ok(X1),ok(X2)) -> take#(X1,X2) active#(take(X1,X2)) -> active#(X2) -> active#(from(X)) -> s#(X) active#(take(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(s(X)) active#(take(X1,X2)) -> active#(X2) -> active#(from(X)) -> cons#(X,from(s(X))) active#(take(X1,X2)) -> active#(X2) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(take(X1,X2)) -> active#(X2) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(take(X1,X2)) -> active#(X2) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(take(X1,X2)) -> active#(X2) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(take(X1,X2)) -> active#(X2) -> active#(from(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(from(X)) -> from#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(s(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(head(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(head(X)) -> head#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(2nd(X)) -> active#(X) active#(take(X1,X2)) -> active#(X2) -> active#(2nd(X)) -> 2nd#(active(X)) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X2) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(take(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(take(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X2) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(take(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) active#(take(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(take(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(take(X1,X2)) -> active#(X1) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(take(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(take(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(take(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(take(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(head(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(head(X)) -> head#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> active#(X) active#(take(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> 2nd#(active(X)) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(take(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(take(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(2nd(cons(X,XS))) -> head#(XS) -> head#(mark(X)) -> head#(X) active#(2nd(cons(X,XS))) -> head#(XS) -> head#(ok(X)) -> head#(X) active#(2nd(X)) -> 2nd#(active(X)) -> 2nd#(mark(X)) -> 2nd#(X) active#(2nd(X)) -> 2nd#(active(X)) -> 2nd#(ok(X)) -> 2nd#(X) active#(2nd(X)) -> active#(X) -> active#(from(X)) -> s#(X) active#(2nd(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(2nd(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(2nd(X)) -> active#(X) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(2nd(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(2nd(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(2nd(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(2nd(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(2nd(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) active#(2nd(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(2nd(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(2nd(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(2nd(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(2nd(X)) -> active#(X) -> active#(head(X)) -> active#(X) active#(2nd(X)) -> active#(X) -> active#(head(X)) -> head#(active(X)) active#(2nd(X)) -> active#(X) -> active#(2nd(X)) -> active#(X) active#(2nd(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X)) active#(2nd(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(2nd(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(2nd(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(2nd(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(2nd(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(2nd(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(2nd(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(2nd(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(head(X)) -> head#(active(X)) -> head#(mark(X)) -> head#(X) active#(head(X)) -> head#(active(X)) -> head#(ok(X)) -> head#(X) active#(head(X)) -> active#(X) -> active#(from(X)) -> s#(X) active#(head(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(head(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(head(X)) -> active#(X) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(head(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(head(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(head(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(head(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(head(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) active#(head(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(head(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(head(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(head(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(head(X)) -> active#(X) -> active#(head(X)) -> active#(X) active#(head(X)) -> active#(X) -> active#(head(X)) -> head#(active(X)) active#(head(X)) -> active#(X) -> active#(2nd(X)) -> active#(X) active#(head(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X)) active#(head(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(head(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(head(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(head(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(head(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(head(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(head(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(head(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(mark(X1),X2) -> cons#(X1,X2) active#(cons(X1,X2)) -> cons#(active(X1),X2) -> cons#(ok(X1),ok(X2)) -> cons#(X1,X2) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> s#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(s(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> cons#(X,from(s(X))) active#(cons(X1,X2)) -> active#(X1) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(cons(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(cons(X1,X2)) -> active#(X1) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(from(X)) -> from#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(s(X)) -> s#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(head(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(head(X)) -> head#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) -> active#(2nd(X)) -> 2nd#(active(X)) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X1) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> active#(X2) active#(cons(X1,X2)) -> active#(X1) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X) active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X) active#(s(X)) -> active#(X) -> active#(from(X)) -> s#(X) active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(s(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(s(X)) -> active#(X) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(s(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(s(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(s(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(s(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(s(X)) -> active#(X) -> active#(head(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(head(X)) -> head#(active(X)) active#(s(X)) -> active#(X) -> active#(2nd(X)) -> active#(X) active#(s(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X)) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(s(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) active#(from(X)) -> from#(active(X)) -> from#(mark(X)) -> from#(X) active#(from(X)) -> from#(active(X)) -> from#(ok(X)) -> from#(X) active#(from(X)) -> active#(X) -> active#(from(X)) -> s#(X) active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(s(X)) active#(from(X)) -> active#(X) -> active#(from(X)) -> cons#(X,from(s(X))) active#(from(X)) -> active#(X) -> active#(2nd(cons(X,XS))) -> head#(XS) active#(from(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> take#(N,XS) active#(from(X)) -> active#(X) -> active#(take(s(N),cons(X,XS))) -> cons#(X,take(N,XS)) active#(from(X)) -> active#(X) -> active#(sel(s(N),cons(X,XS))) -> sel#(N,XS) active#(from(X)) -> active#(X) -> active#(from(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(from(X)) -> from#(active(X)) active#(from(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(cons(X1,X2)) -> cons#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(s(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(s(X)) -> s#(active(X)) active#(from(X)) -> active#(X) -> active#(head(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(head(X)) -> head#(active(X)) active#(from(X)) -> active#(X) -> active#(2nd(X)) -> active#(X) active#(from(X)) -> active#(X) -> active#(2nd(X)) -> 2nd#(active(X)) active#(from(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(take(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(take(X1,X2)) -> take#(X1,active(X2)) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(active(X1),X2) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> active#(X2) active#(from(X)) -> active#(X) -> active#(sel(X1,X2)) -> sel#(X1,active(X2)) SCC Processor: #sccs: 10 #rules: 37 #arcs: 522/3844 DPs: top#(ok(X)) -> top#(active(X)) top#(mark(X)) -> top#(proper(X)) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: proper#(sel(X1,X2)) -> proper#(X1) proper#(sel(X1,X2)) -> proper#(X2) proper#(take(X1,X2)) -> proper#(X1) proper#(take(X1,X2)) -> proper#(X2) proper#(2nd(X)) -> proper#(X) proper#(head(X)) -> proper#(X) proper#(s(X)) -> proper#(X) proper#(cons(X1,X2)) -> proper#(X1) proper#(cons(X1,X2)) -> proper#(X2) proper#(from(X)) -> proper#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [proper#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [sel](x0, x1) = x0 + x1 + 1, [nil] = 0, [take](x0, x1) = x0 + x1 + 1, [0] = 0, [2nd](x0) = x0 + 1, [head](x0) = x0 + 1, [mark](x0) = 1, [cons](x0, x1) = x0 + x1 + 1, [s](x0) = x0 + 1, [active](x0) = x0, [from](x0) = x0 + 1 orientation: proper#(sel(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(sel(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(take(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(take(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(2nd(X)) = X + 2 >= X + 1 = proper#(X) proper#(head(X)) = X + 2 >= X + 1 = proper#(X) proper#(s(X)) = X + 2 >= X + 1 = proper#(X) proper#(cons(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = proper#(X1) proper#(cons(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = proper#(X2) proper#(from(X)) = X + 2 >= X + 1 = proper#(X) active(from(X)) = X + 1 >= 1 = mark(cons(X,from(s(X)))) active(head(cons(X,XS))) = X + XS + 2 >= 1 = mark(X) active(2nd(cons(X,XS))) = X + XS + 2 >= 1 = mark(head(XS)) active(take(0(),XS)) = XS + 1 >= 1 = mark(nil()) active(take(s(N),cons(X,XS))) = N + X + XS + 3 >= 1 = mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) = X + XS + 2 >= 1 = mark(X) active(sel(s(N),cons(X,XS))) = N + X + XS + 3 >= 1 = mark(sel(N,XS)) active(from(X)) = X + 1 >= X + 1 = from(active(X)) active(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(active(X1),X2) active(s(X)) = X + 1 >= X + 1 = s(active(X)) active(head(X)) = X + 1 >= X + 1 = head(active(X)) active(2nd(X)) = X + 1 >= X + 1 = 2nd(active(X)) active(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(active(X1),X2) active(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,active(X2)) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(X1,active(X2)) from(mark(X)) = 2 >= 1 = mark(from(X)) cons(mark(X1),X2) = X2 + 2 >= 1 = mark(cons(X1,X2)) s(mark(X)) = 2 >= 1 = mark(s(X)) head(mark(X)) = 2 >= 1 = mark(head(X)) 2nd(mark(X)) = 2 >= 1 = mark(2nd(X)) take(mark(X1),X2) = X2 + 2 >= 1 = mark(take(X1,X2)) take(X1,mark(X2)) = X1 + 2 >= 1 = mark(take(X1,X2)) sel(mark(X1),X2) = X2 + 2 >= 1 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 2 >= 1 = mark(sel(X1,X2)) proper(from(X)) = X + 1 >= X + 1 = from(proper(X)) proper(cons(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = cons(proper(X1),proper(X2)) proper(s(X)) = X + 1 >= X + 1 = s(proper(X)) proper(head(X)) = X + 1 >= X + 1 = head(proper(X)) proper(2nd(X)) = X + 1 >= X + 1 = 2nd(proper(X)) proper(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(proper(X1),proper(X2)) proper(0()) = 0 >= 0 = ok(0()) proper(nil()) = 0 >= 0 = ok(nil()) proper(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(proper(X1),proper(X2)) from(ok(X)) = X + 1 >= X + 1 = ok(from(X)) cons(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(cons(X1,X2)) s(ok(X)) = X + 1 >= X + 1 = ok(s(X)) head(ok(X)) = X + 1 >= X + 1 = ok(head(X)) 2nd(ok(X)) = X + 1 >= X + 1 = ok(2nd(X)) take(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(take(X1,X2)) sel(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(sel(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: active#(sel(X1,X2)) -> active#(X2) active#(sel(X1,X2)) -> active#(X1) active#(take(X1,X2)) -> active#(X2) active#(take(X1,X2)) -> active#(X1) active#(2nd(X)) -> active#(X) active#(head(X)) -> active#(X) active#(s(X)) -> active#(X) active#(cons(X1,X2)) -> active#(X1) active#(from(X)) -> active#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = x0, [proper](x0) = x0, [sel](x0, x1) = x0 + x1 + 1, [nil] = 0, [take](x0, x1) = x0 + x1 + 1, [0] = 0, [2nd](x0) = x0, [head](x0) = x0, [mark](x0) = 1, [cons](x0, x1) = x0 + 1, [s](x0) = x0, [active](x0) = x0, [from](x0) = x0 + 1 orientation: active#(sel(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active#(sel(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(take(X1,X2)) = X1 + X2 + 2 >= X2 + 1 = active#(X2) active#(take(X1,X2)) = X1 + X2 + 2 >= X1 + 1 = active#(X1) active#(2nd(X)) = X + 1 >= X + 1 = active#(X) active#(head(X)) = X + 1 >= X + 1 = active#(X) active#(s(X)) = X + 1 >= X + 1 = active#(X) active#(cons(X1,X2)) = X1 + 2 >= X1 + 1 = active#(X1) active#(from(X)) = X + 2 >= X + 1 = active#(X) active(from(X)) = X + 1 >= 1 = mark(cons(X,from(s(X)))) active(head(cons(X,XS))) = X + 1 >= 1 = mark(X) active(2nd(cons(X,XS))) = X + 1 >= 1 = mark(head(XS)) active(take(0(),XS)) = XS + 1 >= 1 = mark(nil()) active(take(s(N),cons(X,XS))) = N + X + 2 >= 1 = mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) = X + 2 >= 1 = mark(X) active(sel(s(N),cons(X,XS))) = N + X + 2 >= 1 = mark(sel(N,XS)) active(from(X)) = X + 1 >= X + 1 = from(active(X)) active(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(active(X1),X2) active(s(X)) = X >= X = s(active(X)) active(head(X)) = X >= X = head(active(X)) active(2nd(X)) = X >= X = 2nd(active(X)) active(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(active(X1),X2) active(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(X1,active(X2)) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(X1,active(X2)) from(mark(X)) = 2 >= 1 = mark(from(X)) cons(mark(X1),X2) = 2 >= 1 = mark(cons(X1,X2)) s(mark(X)) = 1 >= 1 = mark(s(X)) head(mark(X)) = 1 >= 1 = mark(head(X)) 2nd(mark(X)) = 1 >= 1 = mark(2nd(X)) take(mark(X1),X2) = X2 + 2 >= 1 = mark(take(X1,X2)) take(X1,mark(X2)) = X1 + 2 >= 1 = mark(take(X1,X2)) sel(mark(X1),X2) = X2 + 2 >= 1 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 2 >= 1 = mark(sel(X1,X2)) proper(from(X)) = X + 1 >= X + 1 = from(proper(X)) proper(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(proper(X1),proper(X2)) proper(s(X)) = X >= X = s(proper(X)) proper(head(X)) = X >= X = head(proper(X)) proper(2nd(X)) = X >= X = 2nd(proper(X)) proper(take(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = take(proper(X1),proper(X2)) proper(0()) = 0 >= 0 = ok(0()) proper(nil()) = 0 >= 0 = ok(nil()) proper(sel(X1,X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = sel(proper(X1),proper(X2)) from(ok(X)) = X + 1 >= X + 1 = ok(from(X)) cons(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(cons(X1,X2)) s(ok(X)) = X >= X = ok(s(X)) head(ok(X)) = X >= X = ok(head(X)) 2nd(ok(X)) = X >= X = ok(2nd(X)) take(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(take(X1,X2)) sel(ok(X1),ok(X2)) = X1 + X2 + 1 >= X1 + X2 + 1 = ok(sel(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(2nd(X)) -> active#(X) active#(head(X)) -> active#(X) active#(s(X)) -> active#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0 + 1, [sel](x0, x1) = x0 + 1, [nil] = 0, [take](x0, x1) = 1, [0] = 1, [2nd](x0) = x0 + 1, [head](x0) = x0, [mark](x0) = 0, [cons](x0, x1) = x0, [s](x0) = x0 + 1, [active](x0) = x0, [from](x0) = x0 orientation: active#(2nd(X)) = X + 2 >= X + 1 = active#(X) active#(head(X)) = X + 1 >= X + 1 = active#(X) active#(s(X)) = X + 2 >= X + 1 = active#(X) active(from(X)) = X >= 0 = mark(cons(X,from(s(X)))) active(head(cons(X,XS))) = X >= 0 = mark(X) active(2nd(cons(X,XS))) = X + 1 >= 0 = mark(head(XS)) active(take(0(),XS)) = 1 >= 0 = mark(nil()) active(take(s(N),cons(X,XS))) = 1 >= 0 = mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) = 2 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = N + 2 >= 0 = mark(sel(N,XS)) active(from(X)) = X >= X = from(active(X)) active(cons(X1,X2)) = X1 >= X1 = cons(active(X1),X2) active(s(X)) = X + 1 >= X + 1 = s(active(X)) active(head(X)) = X >= X = head(active(X)) active(2nd(X)) = X + 1 >= X + 1 = 2nd(active(X)) active(take(X1,X2)) = 1 >= 1 = take(active(X1),X2) active(take(X1,X2)) = 1 >= 1 = take(X1,active(X2)) active(sel(X1,X2)) = X1 + 1 >= X1 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + 1 >= X1 + 1 = sel(X1,active(X2)) from(mark(X)) = 0 >= 0 = mark(from(X)) cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2)) s(mark(X)) = 1 >= 0 = mark(s(X)) head(mark(X)) = 0 >= 0 = mark(head(X)) 2nd(mark(X)) = 1 >= 0 = mark(2nd(X)) take(mark(X1),X2) = 1 >= 0 = mark(take(X1,X2)) take(X1,mark(X2)) = 1 >= 0 = mark(take(X1,X2)) sel(mark(X1),X2) = 1 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 1 >= 0 = mark(sel(X1,X2)) proper(from(X)) = X + 1 >= X + 1 = from(proper(X)) proper(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(proper(X1),proper(X2)) proper(s(X)) = X + 2 >= X + 2 = s(proper(X)) proper(head(X)) = X + 1 >= X + 1 = head(proper(X)) proper(2nd(X)) = X + 2 >= X + 2 = 2nd(proper(X)) proper(take(X1,X2)) = 2 >= 1 = take(proper(X1),proper(X2)) proper(0()) = 2 >= 0 = ok(0()) proper(nil()) = 1 >= 0 = ok(nil()) proper(sel(X1,X2)) = X1 + 2 >= X1 + 2 = sel(proper(X1),proper(X2)) from(ok(X)) = 0 >= 0 = ok(from(X)) cons(ok(X1),ok(X2)) = 0 >= 0 = ok(cons(X1,X2)) s(ok(X)) = 1 >= 0 = ok(s(X)) head(ok(X)) = 0 >= 0 = ok(head(X)) 2nd(ok(X)) = 1 >= 0 = ok(2nd(X)) take(ok(X1),ok(X2)) = 1 >= 0 = ok(take(X1,X2)) sel(ok(X1),ok(X2)) = 1 >= 0 = ok(sel(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: active#(head(X)) -> active#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [active#](x0) = x0 + 1, [top](x0) = 0, [ok](x0) = 0, [proper](x0) = x0 + 1, [sel](x0, x1) = x0 + 1, [nil] = 1, [take](x0, x1) = x0, [0] = 1, [2nd](x0) = x0, [head](x0) = x0 + 1, [mark](x0) = 0, [cons](x0, x1) = x0 + 1, [s](x0) = 1, [active](x0) = x0, [from](x0) = 0 orientation: active#(head(X)) = X + 2 >= X + 1 = active#(X) active(from(X)) = 0 >= 0 = mark(cons(X,from(s(X)))) active(head(cons(X,XS))) = X + 2 >= 0 = mark(X) active(2nd(cons(X,XS))) = X + 1 >= 0 = mark(head(XS)) active(take(0(),XS)) = 1 >= 0 = mark(nil()) active(take(s(N),cons(X,XS))) = 1 >= 0 = mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) = 2 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = 2 >= 0 = mark(sel(N,XS)) active(from(X)) = 0 >= 0 = from(active(X)) active(cons(X1,X2)) = X1 + 1 >= X1 + 1 = cons(active(X1),X2) active(s(X)) = 1 >= 1 = s(active(X)) active(head(X)) = X + 1 >= X + 1 = head(active(X)) active(2nd(X)) = X >= X = 2nd(active(X)) active(take(X1,X2)) = X1 >= X1 = take(active(X1),X2) active(take(X1,X2)) = X1 >= X1 = take(X1,active(X2)) active(sel(X1,X2)) = X1 + 1 >= X1 + 1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 + 1 >= X1 + 1 = sel(X1,active(X2)) from(mark(X)) = 0 >= 0 = mark(from(X)) cons(mark(X1),X2) = 1 >= 0 = mark(cons(X1,X2)) s(mark(X)) = 1 >= 0 = mark(s(X)) head(mark(X)) = 1 >= 0 = mark(head(X)) 2nd(mark(X)) = 0 >= 0 = mark(2nd(X)) take(mark(X1),X2) = 0 >= 0 = mark(take(X1,X2)) take(X1,mark(X2)) = X1 >= 0 = mark(take(X1,X2)) sel(mark(X1),X2) = 1 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 + 1 >= 0 = mark(sel(X1,X2)) proper(from(X)) = 1 >= 0 = from(proper(X)) proper(cons(X1,X2)) = X1 + 2 >= X1 + 2 = cons(proper(X1),proper(X2)) proper(s(X)) = 2 >= 1 = s(proper(X)) proper(head(X)) = X + 2 >= X + 2 = head(proper(X)) proper(2nd(X)) = X + 1 >= X + 1 = 2nd(proper(X)) proper(take(X1,X2)) = X1 + 1 >= X1 + 1 = take(proper(X1),proper(X2)) proper(0()) = 2 >= 0 = ok(0()) proper(nil()) = 2 >= 0 = ok(nil()) proper(sel(X1,X2)) = X1 + 2 >= X1 + 2 = sel(proper(X1),proper(X2)) from(ok(X)) = 0 >= 0 = ok(from(X)) cons(ok(X1),ok(X2)) = 1 >= 0 = ok(cons(X1,X2)) s(ok(X)) = 1 >= 0 = ok(s(X)) head(ok(X)) = 1 >= 0 = ok(head(X)) 2nd(ok(X)) = 0 >= 0 = ok(2nd(X)) take(ok(X1),ok(X2)) = 0 >= 0 = ok(take(X1,X2)) sel(ok(X1),ok(X2)) = 1 >= 0 = ok(sel(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Qed DPs: from#(ok(X)) -> from#(X) from#(mark(X)) -> from#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: cons#(ok(X1),ok(X2)) -> cons#(X1,X2) cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Matrix Interpretation Processor: dimension: 1 interpretation: [cons#](x0, x1) = x1 + 1, [top](x0) = 0, [ok](x0) = x0 + 1, [proper](x0) = 1, [sel](x0, x1) = x0, [nil] = 0, [take](x0, x1) = x1, [0] = 0, [2nd](x0) = x0, [head](x0) = x0, [mark](x0) = 0, [cons](x0, x1) = x0, [s](x0) = x0, [active](x0) = x0, [from](x0) = x0 orientation: cons#(ok(X1),ok(X2)) = X2 + 2 >= X2 + 1 = cons#(X1,X2) cons#(mark(X1),X2) = X2 + 1 >= X2 + 1 = cons#(X1,X2) active(from(X)) = X >= 0 = mark(cons(X,from(s(X)))) active(head(cons(X,XS))) = X >= 0 = mark(X) active(2nd(cons(X,XS))) = X >= 0 = mark(head(XS)) active(take(0(),XS)) = XS >= 0 = mark(nil()) active(take(s(N),cons(X,XS))) = X >= 0 = mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) = 0 >= 0 = mark(X) active(sel(s(N),cons(X,XS))) = N >= 0 = mark(sel(N,XS)) active(from(X)) = X >= X = from(active(X)) active(cons(X1,X2)) = X1 >= X1 = cons(active(X1),X2) active(s(X)) = X >= X = s(active(X)) active(head(X)) = X >= X = head(active(X)) active(2nd(X)) = X >= X = 2nd(active(X)) active(take(X1,X2)) = X2 >= X2 = take(active(X1),X2) active(take(X1,X2)) = X2 >= X2 = take(X1,active(X2)) active(sel(X1,X2)) = X1 >= X1 = sel(active(X1),X2) active(sel(X1,X2)) = X1 >= X1 = sel(X1,active(X2)) from(mark(X)) = 0 >= 0 = mark(from(X)) cons(mark(X1),X2) = 0 >= 0 = mark(cons(X1,X2)) s(mark(X)) = 0 >= 0 = mark(s(X)) head(mark(X)) = 0 >= 0 = mark(head(X)) 2nd(mark(X)) = 0 >= 0 = mark(2nd(X)) take(mark(X1),X2) = X2 >= 0 = mark(take(X1,X2)) take(X1,mark(X2)) = 0 >= 0 = mark(take(X1,X2)) sel(mark(X1),X2) = 0 >= 0 = mark(sel(X1,X2)) sel(X1,mark(X2)) = X1 >= 0 = mark(sel(X1,X2)) proper(from(X)) = 1 >= 1 = from(proper(X)) proper(cons(X1,X2)) = 1 >= 1 = cons(proper(X1),proper(X2)) proper(s(X)) = 1 >= 1 = s(proper(X)) proper(head(X)) = 1 >= 1 = head(proper(X)) proper(2nd(X)) = 1 >= 1 = 2nd(proper(X)) proper(take(X1,X2)) = 1 >= 1 = take(proper(X1),proper(X2)) proper(0()) = 1 >= 1 = ok(0()) proper(nil()) = 1 >= 1 = ok(nil()) proper(sel(X1,X2)) = 1 >= 1 = sel(proper(X1),proper(X2)) from(ok(X)) = X + 1 >= X + 1 = ok(from(X)) cons(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(cons(X1,X2)) s(ok(X)) = X + 1 >= X + 1 = ok(s(X)) head(ok(X)) = X + 1 >= X + 1 = ok(head(X)) 2nd(ok(X)) = X + 1 >= X + 1 = ok(2nd(X)) take(ok(X1),ok(X2)) = X2 + 1 >= X2 + 1 = ok(take(X1,X2)) sel(ok(X1),ok(X2)) = X1 + 1 >= X1 + 1 = ok(sel(X1,X2)) top(mark(X)) = 0 >= 0 = top(proper(X)) top(ok(X)) = 0 >= 0 = top(active(X)) problem: DPs: cons#(mark(X1),X2) -> cons#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: s#(ok(X)) -> s#(X) s#(mark(X)) -> s#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: head#(ok(X)) -> head#(X) head#(mark(X)) -> head#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: 2nd#(ok(X)) -> 2nd#(X) 2nd#(mark(X)) -> 2nd#(X) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: take#(ok(X1),ok(X2)) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(mark(X1),X2) -> take#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open DPs: sel#(ok(X1),ok(X2)) -> sel#(X1,X2) sel#(X1,mark(X2)) -> sel#(X1,X2) sel#(mark(X1),X2) -> sel#(X1,X2) TRS: active(from(X)) -> mark(cons(X,from(s(X)))) active(head(cons(X,XS))) -> mark(X) active(2nd(cons(X,XS))) -> mark(head(XS)) active(take(0(),XS)) -> mark(nil()) active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) active(sel(0(),cons(X,XS))) -> mark(X) active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) active(from(X)) -> from(active(X)) active(cons(X1,X2)) -> cons(active(X1),X2) active(s(X)) -> s(active(X)) active(head(X)) -> head(active(X)) active(2nd(X)) -> 2nd(active(X)) active(take(X1,X2)) -> take(active(X1),X2) active(take(X1,X2)) -> take(X1,active(X2)) active(sel(X1,X2)) -> sel(active(X1),X2) active(sel(X1,X2)) -> sel(X1,active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1),X2) -> mark(cons(X1,X2)) s(mark(X)) -> mark(s(X)) head(mark(X)) -> mark(head(X)) 2nd(mark(X)) -> mark(2nd(X)) take(mark(X1),X2) -> mark(take(X1,X2)) take(X1,mark(X2)) -> mark(take(X1,X2)) sel(mark(X1),X2) -> mark(sel(X1,X2)) sel(X1,mark(X2)) -> mark(sel(X1,X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) proper(s(X)) -> s(proper(X)) proper(head(X)) -> head(proper(X)) proper(2nd(X)) -> 2nd(proper(X)) proper(take(X1,X2)) -> take(proper(X1),proper(X2)) proper(0()) -> ok(0()) proper(nil()) -> ok(nil()) proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) from(ok(X)) -> ok(from(X)) cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) s(ok(X)) -> ok(s(X)) head(ok(X)) -> ok(head(X)) 2nd(ok(X)) -> ok(2nd(X)) take(ok(X1),ok(X2)) -> ok(take(X1,X2)) sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Open