YES TRS: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} DP: Strict: { active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> first#(X1, active(X2)), active#(first(X1, X2)) -> first#(active(X1), X2), active#(first(s(X), cons(Y, Z))) -> first#(X, Z), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z)), active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2), active#(s(X)) -> active#(X), active#(s(X)) -> s#(active(X)), active#(from(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X))), active#(from(X)) -> s#(X), active#(from(X)) -> from#(active(X)), active#(from(X)) -> from#(s(X)), first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2), s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X), from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2)), proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2)), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> s#(proper(X)), proper#(s(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X)), proper#(from(X)) -> proper#(X), top#(mark(X)) -> proper#(X), top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X), top#(ok(X)) -> top#(active(X))} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: { (active#(cons(X1, X2)) -> cons#(active(X1), X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (active#(cons(X1, X2)) -> cons#(active(X1), X2), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> from#(s(X))) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> from#(active(X))) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> s#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> cons#(X, from(s(X)))) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> s#(active(X))) (active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (active#(cons(X1, X2)) -> active#(X1), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> first#(active(X1), X2)) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> first#(X1, active(X2))) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> from#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(s(X)) -> s#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (active#(from(X)) -> from#(active(X)), from#(ok(X)) -> from#(X)) (active#(from(X)) -> from#(active(X)), from#(mark(X)) -> from#(X)) (proper#(s(X)) -> s#(proper(X)), s#(ok(X)) -> s#(X)) (proper#(s(X)) -> s#(proper(X)), s#(mark(X)) -> s#(X)) (top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))) (top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> active#(X)) (top#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> top#(proper(X))) (top#(mark(X)) -> top#(proper(X)), top#(mark(X)) -> proper#(X)) (first#(X1, mark(X2)) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)) (first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)) (first#(X1, mark(X2)) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2)) (first#(ok(X1), ok(X2)) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)) (first#(ok(X1), ok(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)) (first#(ok(X1), ok(X2)) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2)) (cons#(ok(X1), ok(X2)) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (cons#(ok(X1), ok(X2)) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2)) (proper#(first(X1, X2)) -> first#(proper(X1), proper(X2)), first#(ok(X1), ok(X2)) -> first#(X1, X2)) (proper#(first(X1, X2)) -> first#(proper(X1), proper(X2)), first#(mark(X1), X2) -> first#(X1, X2)) (proper#(first(X1, X2)) -> first#(proper(X1), proper(X2)), first#(X1, mark(X2)) -> first#(X1, X2)) (active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z)), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z)), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(from(X)) -> cons#(X, from(s(X))), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (active#(from(X)) -> cons#(X, from(s(X))), cons#(mark(X1), X2) -> cons#(X1, X2)) (active#(s(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (active#(s(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (active#(s(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(s(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(s(X)) -> s#(active(X))) (active#(s(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(s(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(s(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (active#(s(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (active#(s(X)) -> active#(X), active#(first(X1, X2)) -> first#(active(X1), X2)) (active#(s(X)) -> active#(X), active#(first(X1, X2)) -> first#(X1, active(X2))) (active#(s(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (active#(s(X)) -> active#(X), active#(first(X1, X2)) -> active#(X1)) (active#(from(X)) -> s#(X), s#(ok(X)) -> s#(X)) (active#(from(X)) -> s#(X), s#(mark(X)) -> s#(X)) (s#(ok(X)) -> s#(X), s#(ok(X)) -> s#(X)) (s#(ok(X)) -> s#(X), s#(mark(X)) -> s#(X)) (from#(ok(X)) -> from#(X), from#(ok(X)) -> from#(X)) (from#(ok(X)) -> from#(X), from#(mark(X)) -> from#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> from#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> s#(proper(X))) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(from(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (top#(ok(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (top#(ok(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (top#(ok(X)) -> active#(X), active#(from(X)) -> s#(X)) (top#(ok(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (top#(ok(X)) -> active#(X), active#(from(X)) -> active#(X)) (top#(ok(X)) -> active#(X), active#(s(X)) -> s#(active(X))) (top#(ok(X)) -> active#(X), active#(s(X)) -> active#(X)) (top#(ok(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (top#(ok(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (top#(ok(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (top#(ok(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (top#(ok(X)) -> active#(X), active#(first(X1, X2)) -> first#(active(X1), X2)) (top#(ok(X)) -> active#(X), active#(first(X1, X2)) -> first#(X1, active(X2))) (top#(ok(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (top#(ok(X)) -> active#(X), active#(first(X1, X2)) -> active#(X1)) (top#(mark(X)) -> proper#(X), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (top#(mark(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X1)) (top#(mark(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X2)) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (top#(mark(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (top#(mark(X)) -> proper#(X), proper#(s(X)) -> s#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (top#(mark(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (top#(mark(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (proper#(s(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X1)) (proper#(s(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X2)) (proper#(s(X)) -> proper#(X), proper#(cons(X1, X2)) -> cons#(proper(X1), 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#(s(X)) -> s#(proper(X))) (proper#(s(X)) -> proper#(X), proper#(s(X)) -> proper#(X)) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> from#(proper(X))) (proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(s(X)) -> s#(proper(X))) (proper#(first(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X)) (proper#(first(X1, X2)) -> proper#(X2), proper#(from(X)) -> from#(proper(X))) (proper#(first(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (from#(mark(X)) -> from#(X), from#(mark(X)) -> from#(X)) (from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)) (s#(mark(X)) -> s#(X), s#(mark(X)) -> s#(X)) (s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> first#(X1, active(X2))) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> first#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (active#(from(X)) -> active#(X), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(from(X)) -> active#(X), active#(s(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(s(X)) -> s#(active(X))) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> cons#(X, from(s(X)))) (active#(from(X)) -> active#(X), active#(from(X)) -> s#(X)) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(active(X))) (active#(from(X)) -> active#(X), active#(from(X)) -> from#(s(X))) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> first#(X1, active(X2))) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> first#(active(X1), X2)) (active#(first(X1, X2)) -> active#(X2), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (active#(first(X1, X2)) -> active#(X2), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(first(X1, X2)) -> active#(X2), active#(s(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X2), active#(s(X)) -> s#(active(X))) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> cons#(X, from(s(X)))) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> s#(X)) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> from#(active(X))) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> from#(s(X))) (active#(first(s(X), cons(Y, Z))) -> first#(X, Z), first#(X1, mark(X2)) -> first#(X1, X2)) (active#(first(s(X), cons(Y, Z))) -> first#(X, Z), first#(mark(X1), X2) -> first#(X1, X2)) (active#(first(s(X), cons(Y, Z))) -> first#(X, Z), first#(ok(X1), ok(X2)) -> first#(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#(first(X1, X2)) -> first#(X1, active(X2)), first#(X1, mark(X2)) -> first#(X1, X2)) (active#(first(X1, X2)) -> first#(X1, active(X2)), first#(mark(X1), X2) -> first#(X1, X2)) (active#(first(X1, X2)) -> first#(X1, active(X2)), first#(ok(X1), ok(X2)) -> first#(X1, X2)) (cons#(mark(X1), X2) -> cons#(X1, X2), cons#(mark(X1), X2) -> cons#(X1, X2)) (cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)) (first#(mark(X1), X2) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2)) (first#(mark(X1), X2) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)) (first#(mark(X1), X2) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)) (top#(ok(X)) -> top#(active(X)), top#(mark(X)) -> proper#(X)) (top#(ok(X)) -> top#(active(X)), top#(mark(X)) -> top#(proper(X))) (top#(ok(X)) -> top#(active(X)), top#(ok(X)) -> active#(X)) (top#(ok(X)) -> top#(active(X)), top#(ok(X)) -> top#(active(X))) (proper#(from(X)) -> from#(proper(X)), from#(mark(X)) -> from#(X)) (proper#(from(X)) -> from#(proper(X)), from#(ok(X)) -> from#(X)) (active#(from(X)) -> from#(s(X)), from#(mark(X)) -> from#(X)) (active#(from(X)) -> from#(s(X)), from#(ok(X)) -> from#(X)) (active#(s(X)) -> s#(active(X)), s#(mark(X)) -> s#(X)) (active#(s(X)) -> s#(active(X)), s#(ok(X)) -> s#(X)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> first#(proper(X1), proper(X2))) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> cons#(proper(X1), proper(X2))) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(s(X)) -> s#(proper(X))) (proper#(first(X1, X2)) -> proper#(X1), proper#(s(X)) -> proper#(X)) (proper#(first(X1, X2)) -> proper#(X1), proper#(from(X)) -> from#(proper(X))) (proper#(first(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> first#(X1, active(X2))) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> first#(active(X1), X2)) (active#(first(X1, X2)) -> active#(X1), active#(first(s(X), cons(Y, Z))) -> first#(X, Z)) (active#(first(X1, X2)) -> active#(X1), active#(first(s(X), cons(Y, Z))) -> cons#(Y, first(X, Z))) (active#(first(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> cons#(active(X1), X2)) (active#(first(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X1), active#(s(X)) -> s#(active(X))) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> cons#(X, from(s(X)))) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> s#(X)) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> from#(active(X))) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> from#(s(X))) (active#(first(X1, X2)) -> first#(active(X1), X2), first#(X1, mark(X2)) -> first#(X1, X2)) (active#(first(X1, X2)) -> first#(active(X1), X2), first#(mark(X1), X2) -> first#(X1, X2)) (active#(first(X1, X2)) -> first#(active(X1), X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)) } SCCS: Scc: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Scc: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)} Scc: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Scc: {s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)} Scc: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Scc: { first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)} Scc: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)} SCC: Strict: {top#(mark(X)) -> top#(proper(X)), top#(ok(X)) -> top#(active(X))} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(ok) = 0, pi(proper) = 0, pi(from) = [0], pi(s) = 0, pi(cons) = 0, pi(0) = [], pi(first) = [0,1], pi(active) = 0, pi(nil) = [], pi(mark) = [0] Usable Rules: {} Interpretation: [mark](x0) = x0 + 1 Strict: {top#(ok(X)) -> top#(active(X))} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} EDG: {(top#(ok(X)) -> top#(active(X)), top#(ok(X)) -> top#(active(X)))} SCCS: Scc: {top#(ok(X)) -> top#(active(X))} SCC: Strict: {top#(ok(X)) -> top#(active(X))} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} POLY: Argument Filtering: pi(top#) = 0, pi(top) = [], pi(ok) = [0], pi(proper) = [], pi(from) = 0, pi(s) = 0, pi(cons) = 1, pi(0) = [], pi(first) = [0,1], pi(active) = 0, pi(nil) = [], pi(mark) = 0 Usable Rules: {} Interpretation: [ok](x0) = x0 + 1 Strict: {} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} Qed SCC: Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(s(X)) -> proper#(X), proper#(from(X)) -> proper#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)} EDG: {(proper#(first(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(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#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(from(X)) -> proper#(X)) (proper#(from(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(first(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(from(X)) -> proper#(X), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(from(X)) -> proper#(X), proper#(from(X)) -> proper#(X))} SCCS: Scc: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)} SCC: Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2), proper#(from(X)) -> proper#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(first(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} EDG: {(proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)) (proper#(first(X1, X2)) -> proper#(X1), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(first(X1, X2)) -> proper#(X1)) (proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(first(X1, X2)) -> proper#(X1), proper#(cons(X1, X2)) -> proper#(X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {proper#(cons(X1, X2)) -> proper#(X2)} EDG: {(proper#(cons(X1, X2)) -> proper#(X2), proper#(cons(X1, X2)) -> proper#(X2))} SCCS: Scc: {proper#(cons(X1, X2)) -> proper#(X2)} SCC: Strict: {proper#(cons(X1, X2)) -> proper#(X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(proper#) = 0 Strict: {} Qed SCC: Strict: {from#(mark(X)) -> from#(X), from#(ok(X)) -> from#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), 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: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(from#) = 0 Strict: {} Qed SCC: Strict: {s#(mark(X)) -> s#(X), s#(ok(X)) -> s#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), 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: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(s#) = 0 Strict: {} Qed SCC: Strict: { cons#(mark(X1), X2) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} EDG: {(cons#(ok(X1), ok(X2)) -> cons#(X1, X2), cons#(ok(X1), ok(X2)) -> cons#(X1, X2))} SCCS: Scc: {cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} SCC: Strict: {cons#(ok(X1), ok(X2)) -> cons#(X1, X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(cons#) = 0 Strict: {} Qed SCC: Strict: { first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2), first#(ok(X1), ok(X2)) -> first#(X1, X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(first#) = 0 Strict: {first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)} EDG: {(first#(mark(X1), X2) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)) (first#(mark(X1), X2) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2)) (first#(X1, mark(X2)) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2)) (first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2))} SCCS: Scc: {first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)} SCC: Strict: {first#(X1, mark(X2)) -> first#(X1, X2), first#(mark(X1), X2) -> first#(X1, X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(first#) = 0 Strict: {first#(X1, mark(X2)) -> first#(X1, X2)} EDG: {(first#(X1, mark(X2)) -> first#(X1, X2), first#(X1, mark(X2)) -> first#(X1, X2))} SCCS: Scc: {first#(X1, mark(X2)) -> first#(X1, X2)} SCC: Strict: {first#(X1, mark(X2)) -> first#(X1, X2)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(first#) = 1 Strict: {} Qed SCC: Strict: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(s(X)) -> active#(X), active#(from(X)) -> active#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(cons(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(cons(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2)) (active#(cons(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X1), active#(cons(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X))} SCCS: Scc: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} SCC: Strict: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(cons(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} EDG: {(active#(first(X1, X2)) -> active#(X1), active#(from(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X1)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X1)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X))} SCCS: Scc: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} SCC: Strict: {active#(first(X1, X2)) -> active#(X1), active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} EDG: {(active#(from(X)) -> active#(X), active#(from(X)) -> active#(X)) (active#(from(X)) -> active#(X), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X2), active#(first(X1, X2)) -> active#(X2)) (active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X))} SCCS: Scc: {active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} SCC: Strict: {active#(first(X1, X2)) -> active#(X2), active#(from(X)) -> active#(X)} Weak: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), 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: { active(first(X1, X2)) -> first(X1, active(X2)), active(first(X1, X2)) -> first(active(X1), X2), active(first(0(), X)) -> mark(nil()), active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))), active(cons(X1, X2)) -> cons(active(X1), X2), active(s(X)) -> s(active(X)), active(from(X)) -> mark(cons(X, from(s(X)))), active(from(X)) -> from(active(X)), first(X1, mark(X2)) -> mark(first(X1, X2)), first(mark(X1), X2) -> mark(first(X1, X2)), first(ok(X1), ok(X2)) -> ok(first(X1, X2)), cons(mark(X1), X2) -> mark(cons(X1, X2)), cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)), s(mark(X)) -> mark(s(X)), s(ok(X)) -> ok(s(X)), from(mark(X)) -> mark(from(X)), from(ok(X)) -> ok(from(X)), proper(nil()) -> ok(nil()), proper(first(X1, X2)) -> first(proper(X1), proper(X2)), proper(0()) -> ok(0()), proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)), proper(s(X)) -> s(proper(X)), proper(from(X)) -> from(proper(X)), top(mark(X)) -> top(proper(X)), top(ok(X)) -> top(active(X))} SPSC: Simple Projection: pi(active#) = 0 Strict: {} Qed