MAYBE 0.17/0.21 MAYBE 0.17/0.21 0.17/0.21 Problem: 0.17/0.21 active(from(X)) -> mark(cons(X,from(s(X)))) 0.17/0.21 active(head(cons(X,XS))) -> mark(X) 0.17/0.21 active(2nd(cons(X,XS))) -> mark(head(XS)) 0.17/0.21 active(take(0(),XS)) -> mark(nil()) 0.17/0.21 active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) 0.17/0.21 active(sel(0(),cons(X,XS))) -> mark(X) 0.17/0.21 active(sel(s(N),cons(X,XS))) -> mark(sel(N,XS)) 0.17/0.21 active(from(X)) -> from(active(X)) 0.17/0.21 active(cons(X1,X2)) -> cons(active(X1),X2) 0.17/0.21 active(s(X)) -> s(active(X)) 0.17/0.21 active(head(X)) -> head(active(X)) 0.17/0.21 active(2nd(X)) -> 2nd(active(X)) 0.17/0.21 active(take(X1,X2)) -> take(active(X1),X2) 0.17/0.21 active(take(X1,X2)) -> take(X1,active(X2)) 0.17/0.21 active(sel(X1,X2)) -> sel(active(X1),X2) 0.17/0.21 active(sel(X1,X2)) -> sel(X1,active(X2)) 0.17/0.21 from(mark(X)) -> mark(from(X)) 0.17/0.21 cons(mark(X1),X2) -> mark(cons(X1,X2)) 0.17/0.21 s(mark(X)) -> mark(s(X)) 0.17/0.21 head(mark(X)) -> mark(head(X)) 0.17/0.21 2nd(mark(X)) -> mark(2nd(X)) 0.17/0.21 take(mark(X1),X2) -> mark(take(X1,X2)) 0.17/0.21 take(X1,mark(X2)) -> mark(take(X1,X2)) 0.17/0.21 sel(mark(X1),X2) -> mark(sel(X1,X2)) 0.17/0.21 sel(X1,mark(X2)) -> mark(sel(X1,X2)) 0.17/0.21 proper(from(X)) -> from(proper(X)) 0.17/0.21 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 0.17/0.21 proper(s(X)) -> s(proper(X)) 0.17/0.21 proper(head(X)) -> head(proper(X)) 0.17/0.21 proper(2nd(X)) -> 2nd(proper(X)) 0.17/0.21 proper(take(X1,X2)) -> take(proper(X1),proper(X2)) 0.17/0.21 proper(0()) -> ok(0()) 0.17/0.21 proper(nil()) -> ok(nil()) 0.17/0.21 proper(sel(X1,X2)) -> sel(proper(X1),proper(X2)) 0.17/0.21 from(ok(X)) -> ok(from(X)) 0.17/0.21 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 0.17/0.21 s(ok(X)) -> ok(s(X)) 0.17/0.21 head(ok(X)) -> ok(head(X)) 0.17/0.21 2nd(ok(X)) -> ok(2nd(X)) 0.17/0.21 take(ok(X1),ok(X2)) -> ok(take(X1,X2)) 0.17/0.21 sel(ok(X1),ok(X2)) -> ok(sel(X1,X2)) 0.17/0.21 top(mark(X)) -> top(proper(X)) 0.17/0.21 top(ok(X)) -> top(active(X)) 0.17/0.21 0.17/0.21 Proof: 0.17/0.21 Open 0.17/0.22 EOF