MAYBE TRS: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} DP: Strict: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2), from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X), s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> cons#(X, from(s(X))), active#(from(X)) -> from#(s(X)), active#(from(X)) -> from#(active(X)), active#(from(X)) -> s#(X), active#(from(X)) -> active#(X), active#(s(X)) -> s#(active(X)), active#(s(X)) -> 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#(2nd(cons(X, XS))) -> head#(XS), active#(take(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2), active#(take(X1, X2)) -> take#(X1, active(X2)), active#(take(X1, X2)) -> take#(active(X1), X2), active#(take(s(N), cons(X, XS))) -> cons#(X, take(N, XS)), active#(take(s(N), cons(X, XS))) -> take#(N, XS), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> sel#(X1, active(X2)), active#(sel(X1, X2)) -> sel#(active(X1), X2), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS), head#(mark(X)) -> head#(X), head#(ok(X)) -> head#(X), 2nd#(mark(X)) -> 2nd#(X), 2nd#(ok(X)) -> 2nd#(X), take#(X1, mark(X2)) -> take#(X1, X2), take#(mark(X1), X2) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2), sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2), sel#(ok(X1), ok(X2)) -> sel#(X1, X2), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2)), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> from#(proper(X)), proper#(from(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X)), proper#(s(X)) -> proper#(X), proper#(head(X)) -> head#(proper(X)), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> 2nd#(proper(X)), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> take#(proper(X1), proper(X2)), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> sel#(proper(X1), proper(X2)), proper#(sel(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2), top#(mark(X)) -> proper#(X), top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X), top#(ok(X)) -> top#(active(X))} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: { (active#(sel(X1, X2)) -> sel#(X1, active(X2)), sel#(ok(X1), ok(X2)) -> sel#(X1, X2)) (active#(sel(X1, X2)) -> sel#(X1, active(X2)), sel#(mark(X1), X2) -> sel#(X1, X2)) (active#(sel(X1, X2)) -> sel#(X1, active(X2)), sel#(X1, mark(X2)) -> sel#(X1, X2)) (proper#(take(X1, X2)) -> take#(proper(X1), proper(X2)), take#(ok(X1), ok(X2)) -> take#(X1, 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)) (from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)) (from#(mark(X)) -> from#(X), from#(mark(X)) -> from#(X)) (s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)) (s#(mark(X)) -> s#(X), s#(mark(X)) -> s#(X)) (active#(from(X)) -> s#(X), s#(ok(X)) -> s#(X)) (active#(from(X)) -> s#(X), s#(mark(X)) -> s#(X)) (active#(s(X)) -> active#(X), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(X1, active(X2))) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (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#(take(X1, X2)) -> take#(active(X1), X2)) (active#(s(X)) -> active#(X), active#(take(X1, X2)) -> take#(X1, active(X2))) (active#(s(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(2nd(cons(X, XS))) -> head#(XS)) (active#(s(X)) -> active#(X), active#(2nd(X)) -> 2nd#(active(X))) (active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(head(X)) -> head#(active(X))) (active#(s(X)) -> active#(X), active#(head(X)) -> active#(X)) (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#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> from#(active(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#(cons(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(2nd(X)) -> active#(X), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(X1, active(X2))) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (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#(take(X1, X2)) -> take#(active(X1), X2)) (active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> take#(X1, active(X2))) (active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(2nd(cons(X, XS))) -> head#(XS)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> 2nd#(active(X))) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(head(X)) -> head#(active(X))) (active#(2nd(X)) -> active#(X), active#(head(X)) -> active#(X)) (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#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> from#(active(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#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (head#(ok(X)) -> head#(X), head#(ok(X)) -> head#(X)) (head#(ok(X)) -> head#(X), head#(mark(X)) -> head#(X)) (2nd#(ok(X)) -> 2nd#(X), 2nd#(ok(X)) -> 2nd#(X)) (2nd#(ok(X)) -> 2nd#(X), 2nd#(mark(X)) -> 2nd#(X)) (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)) -> 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#(2nd(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(2nd(X)) -> 2nd#(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#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (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#(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)) -> 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#(2nd(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(2nd(X)) -> 2nd#(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#(s(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (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))) (top#(ok(X)) -> active#(X), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (top#(ok(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (top#(ok(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(X1, active(X2))) (top#(ok(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (top#(ok(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (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#(take(X1, X2)) -> take#(active(X1), X2)) (top#(ok(X)) -> active#(X), active#(take(X1, X2)) -> take#(X1, active(X2))) (top#(ok(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (top#(ok(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1)) (top#(ok(X)) -> active#(X), active#(2nd(cons(X, XS))) -> head#(XS)) (top#(ok(X)) -> active#(X), active#(2nd(X)) -> 2nd#(active(X))) (top#(ok(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (top#(ok(X)) -> active#(X), active#(head(X)) -> head#(active(X))) (top#(ok(X)) -> active#(X), active#(head(X)) -> active#(X)) (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#(from(X)) -> active#(X)) (top#(ok(X)) -> active#(X), active#(from(X)) -> s#(X)) (top#(ok(X)) -> active#(X), active#(from(X)) -> from#(active(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#(cons(X1, X2)) -> active#(X1)) (top#(ok(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(sel(s(N), cons(X, XS))) -> sel#(N, XS), sel#(ok(X1), ok(X2)) -> sel#(X1, X2)) (active#(sel(s(N), cons(X, XS))) -> sel#(N, XS), sel#(mark(X1), X2) -> sel#(X1, X2)) (active#(sel(s(N), cons(X, XS))) -> sel#(N, XS), sel#(X1, mark(X2)) -> sel#(X1, X2)) (active#(sel(X1, X2)) -> active#(X2), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> sel#(X1, active(X2))) (active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)) (active#(sel(X1, 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active#(take(X1, X2)) -> active#(X1)) (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#(take(X1, X2)) -> take#(active(X1), X2)) (active#(head(X)) -> active#(X), active#(take(s(N), cons(X, XS))) -> cons#(X, take(N, XS))) (active#(head(X)) -> active#(X), active#(take(s(N), cons(X, XS))) -> take#(N, XS)) (active#(head(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (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#(head(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (active#(head(X)) -> active#(X), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (active#(from(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> s#(active(X))) (active#(from(X)) -> active#(X), active#(s(X)) -> 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#(2nd(cons(X, XS))) -> head#(XS)) (active#(from(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1)) (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#(take(X1, X2)) -> take#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(take(s(N), cons(X, XS))) -> cons#(X, take(N, XS))) (active#(from(X)) -> active#(X), active#(take(s(N), cons(X, XS))) -> take#(N, XS)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(X1, active(X2))) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> sel#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(sel(s(N), cons(X, XS))) -> sel#(N, XS)) (s#(ok(X)) -> s#(X), s#(mark(X)) -> s#(X)) (s#(ok(X)) -> s#(X), s#(ok(X)) -> s#(X)) (from#(ok(X)) -> from#(X), from#(mark(X)) -> from#(X)) (from#(ok(X)) -> from#(X), from#(ok(X)) -> from#(X)) (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#(mark(X1), X2) -> sel#(X1, X2)) (proper#(sel(X1, X2)) -> sel#(proper(X1), proper(X2)), sel#(ok(X1), ok(X2)) -> sel#(X1, 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)) (active#(take(X1, X2)) -> take#(X1, active(X2)), take#(X1, mark(X2)) -> take#(X1, X2)) (active#(take(X1, X2)) -> take#(X1, active(X2)), take#(mark(X1), X2) -> take#(X1, X2)) (active#(take(X1, X2)) -> take#(X1, active(X2)), take#(ok(X1), ok(X2)) -> take#(X1, X2)) } SCCS: Scc: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)} Scc: { sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2), sel#(ok(X1), ok(X2)) -> sel#(X1, X2)} Scc: { take#(X1, mark(X2)) -> take#(X1, X2), take#(mark(X1), X2) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)} Scc: {2nd#(mark(X)) -> 2nd#(X), 2nd#(ok(X)) -> 2nd#(X)} Scc: {head#(mark(X)) -> head#(X), head#(ok(X)) -> head#(X)} Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)} Scc: {s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)} Scc: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Scc: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} SCC: Strict: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} Fail SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} EDG: {(proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(from(X)) -> 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#(cons(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> 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#(from(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> 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#(head(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(from(X)) -> 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#(2nd(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(2nd(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X2)) (proper#(2nd(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(sel(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)) -> proper#(X2)) (proper#(take(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2)) (proper#(take(X1, X2)) -> proper#(X1), proper#(sel(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)) -> proper#(X2)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(2nd(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X1)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X2)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(sel(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)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(2nd(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} EDG: {(proper#(sel(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (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#(2nd(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X2)) (proper#(head(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(take(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X2)) (proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(head(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(2nd(X)) -> proper#(X)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(take(X1, X2)) -> proper#(X1)) (proper#(sel(X1, X2)) -> proper#(X2), proper#(sel(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1), proper#(sel(X1, X2)) -> proper#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(2nd(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(2nd(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(2nd(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(2nd(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(head(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(head(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(head(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(head(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X), proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)) (proper#(take(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(take(X1, X2)) -> proper#(X1)} EDG: {(proper#(take(X1, X2)) -> proper#(X1), proper#(take(X1, X2)) -> proper#(X1))} SCCS: Scc: {proper#(take(X1, X2)) -> proper#(X1)} SCC: Strict: {proper#(take(X1, X2)) -> proper#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {} Qed SCC: Strict: { sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2), sel#(ok(X1), ok(X2)) -> sel#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(sel#) = 0 Strict: {sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2)} EDG: {(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#(X1, mark(X2)) -> sel#(X1, X2), sel#(X1, mark(X2)) -> sel#(X1, X2)) (sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2))} SCCS: Scc: {sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2)} SCC: Strict: {sel#(X1, mark(X2)) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(sel#) = 1 Strict: {sel#(mark(X1), X2) -> sel#(X1, X2)} EDG: {(sel#(mark(X1), X2) -> sel#(X1, X2), sel#(mark(X1), X2) -> sel#(X1, X2))} SCCS: Scc: {sel#(mark(X1), X2) -> sel#(X1, X2)} SCC: Strict: {sel#(mark(X1), X2) -> sel#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(sel#) = 0 Strict: {} Qed SCC: Strict: { take#(X1, mark(X2)) -> take#(X1, X2), take#(mark(X1), X2) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(take#) = 0 Strict: { take#(X1, mark(X2)) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)} EDG: {(take#(ok(X1), ok(X2)) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)) (take#(ok(X1), ok(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#(X1, mark(X2)) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2))} SCCS: Scc: { take#(X1, mark(X2)) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)} SCC: Strict: { take#(X1, mark(X2)) -> take#(X1, X2), take#(ok(X1), ok(X2)) -> take#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(take#) = 0 Strict: {take#(X1, mark(X2)) -> take#(X1, X2)} EDG: {(take#(X1, mark(X2)) -> take#(X1, X2), take#(X1, mark(X2)) -> take#(X1, X2))} SCCS: Scc: {take#(X1, mark(X2)) -> take#(X1, X2)} SCC: Strict: {take#(X1, mark(X2)) -> take#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(take#) = 1 Strict: {} Qed SCC: Strict: {2nd#(mark(X)) -> 2nd#(X), 2nd#(ok(X)) -> 2nd#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(2nd#) = 0 Strict: {2nd#(ok(X)) -> 2nd#(X)} EDG: {(2nd#(ok(X)) -> 2nd#(X), 2nd#(ok(X)) -> 2nd#(X))} SCCS: Scc: {2nd#(ok(X)) -> 2nd#(X)} SCC: Strict: {2nd#(ok(X)) -> 2nd#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(2nd#) = 0 Strict: {} Qed SCC: Strict: {head#(mark(X)) -> head#(X), head#(ok(X)) -> head#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(head#) = 0 Strict: {head#(ok(X)) -> head#(X)} EDG: {(head#(ok(X)) -> head#(X), head#(ok(X)) -> head#(X))} SCCS: Scc: {head#(ok(X)) -> head#(X)} SCC: Strict: {head#(ok(X)) -> head#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(head#) = 0 Strict: {} Qed SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)} EDG: {(active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X2), active#(take(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X2), active#(2nd(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X2), active#(head(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X2), active#(s(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(head(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)) (active#(take(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(take(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(s(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(head(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(2nd(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(take(X1, X2)) -> active#(X2)) (active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)) (active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X2))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)} EDG: {(active#(cons(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(take(X1, X2)) -> active#(X2)) (active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(take(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(take(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(s(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(head(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(2nd(X)) -> active#(X)) (active#(take(X1, X2)) -> active#(X2), active#(take(X1, X2)) -> active#(X2)) (active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(take(X1, X2)) -> active#(X2), active#(sel(X1, X2)) -> active#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)} EDG: {(active#(s(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(sel(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(sel(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(sel(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X), active#(sel(X1, X2)) -> active#(X1)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)} EDG: {(active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(head(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(head(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(head(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(head(X)) -> active#(X), active#(2nd(X)) -> active#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)} EDG: {(active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(s(X)) -> active#(X), active#(2nd(X)) -> active#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(2nd(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(2nd(X)) -> active#(X), active#(2nd(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(2nd(X)) -> active#(X))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X), active#(2nd(X)) -> active#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} EDG: {(active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X))} SCCS: Scc: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} SCC: Strict: {active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(from(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(from(X)) -> active#(X))} SCCS: Scc: {active#(from(X)) -> active#(X)} SCC: Strict: {active#(from(X)) -> active#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {} Qed SCC: Strict: {s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(s#) = 0 Strict: {s#(ok(X)) -> s#(X)} EDG: {(s#(ok(X)) -> s#(X), s#(ok(X)) -> s#(X))} SCCS: Scc: {s#(ok(X)) -> s#(X)} SCC: Strict: {s#(ok(X)) -> s#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(s#) = 0 Strict: {} Qed SCC: Strict: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(from#) = 0 Strict: {from#(ok(X)) -> from#(X)} EDG: {(from#(ok(X)) -> from#(X), from#(ok(X)) -> from#(X))} SCCS: Scc: {from#(ok(X)) -> from#(X)} SCC: Strict: {from#(ok(X)) -> from#(X)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(from#) = 0 Strict: {} Qed SCC: Strict: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {cons#(mark(X1), X2) -> cons#(X1, X2)} EDG: {(cons#(mark(X1), X2) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2))} SCCS: Scc: {cons#(mark(X1), X2) -> cons#(X1, X2)} SCC: Strict: {cons#(mark(X1), X2) -> cons#(X1, X2)} Weak: { cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), active(cons(X1, X2)) -> cons(active(X1), X2), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), active(s(X)) -> s(active(X)), active(head(X)) -> head(active(X)), active(head(cons(X, XS))) -> mark(X), active(2nd(X)) -> 2nd(active(X)), active(2nd(cons(X, XS))) -> mark(head(XS)), active(take(X1, X2)) -> take(X1, active(X2)), active(take(X1, X2)) -> take(active(X1), X2), active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))), active(take(0(), XS)) -> mark(nil()), active(sel(X1, X2)) -> sel(X1, active(X2)), active(sel(X1, X2)) -> sel(active(X1), X2), active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)), active(sel(0(), cons(X, XS))) -> mark(X), head(mark(X)) -> mark(head(X)), head(ok(X)) -> ok(head(X)), 2nd(mark(X)) -> mark(2nd(X)), 2nd(ok(X)) -> ok(2nd(X)), take(X1, mark(X2)) -> mark(take(X1, X2)), take(mark(X1), X2) -> mark(take(X1, X2)), take(ok(X1), ok(X2)) -> ok(take(X1, X2)), sel(X1, mark(X2)) -> mark(sel(X1, X2)), sel(mark(X1), X2) -> mark(sel(X1, X2)), sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(from(X)) -> from(proper(X)), proper(s(X)) -> s(proper(X)), proper(head(X)) -> head(proper(X)), proper(2nd(X)) -> 2nd(proper(X)), proper(nil()) -> ok(nil()), proper(take(X1, X2)) -> take(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {} Qed