(VAR L X X1 X2 Y ) (RULES active(eq(0, 0)) -> mark(true) active(eq(s(X), s(Y))) -> mark(eq(X, Y)) active(eq(X, Y)) -> mark(false) active(inf(X)) -> mark(cons(X, inf(s(X)))) active(take(0, X)) -> mark(nil) active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) active(length(nil)) -> mark(0) active(length(cons(X, L))) -> mark(s(length(L))) active(inf(X)) -> inf(active(X)) active(take(X1, X2)) -> take(active(X1), X2) active(take(X1, X2)) -> take(X1, active(X2)) active(length(X)) -> length(active(X)) inf(mark(X)) -> mark(inf(X)) take(mark(X1), X2) -> mark(take(X1, X2)) take(X1, mark(X2)) -> mark(take(X1, X2)) length(mark(X)) -> mark(length(X)) proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) proper(0) -> ok(0) proper(true) -> ok(true) proper(s(X)) -> s(proper(X)) proper(false) -> ok(false) proper(inf(X)) -> inf(proper(X)) proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) proper(take(X1, X2)) -> take(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(length(X)) -> length(proper(X)) eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) s(ok(X)) -> ok(s(X)) inf(ok(X)) -> ok(inf(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) take(ok(X1), ok(X2)) -> ok(take(X1, X2)) length(ok(X)) -> ok(length(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) any(X) -> s(X) any(proper(X)) -> any(any(any(X))) )